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$(6,6)$ |
3 |
20 |
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|
9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 4 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 2 & 4 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 0, -4}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{5, 6}, {4, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,4}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,1,0},{1,1,4},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,2,8},{1,1,8},{1,2,7},{1,1,7},{1,2,6},{1,1,6},{1,2,5},{1,2,4},{1,1,5},{1,1,4},{1,2,3},{1,1,3},{0,1,4},{1,2,2},{0,0,4},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,30,35,70,70,140,126,252,141,210,212,257,330,420,388,660,435,660,695,1060,1060,1625},{0,1,0,5,0,15,0,0,35,70,0,126,70,0,141,126,0,210,257,330,210,435,330,695,495,1060},{0,0,1,2,5,10,15,35,30,70,70,140,70,126,105,141,210,252,212,420,257,388,435,660,695,1060},{0,0,0,1,0,5,0,0,15,35,0,70,35,0,70,70,0,126,141,210,126,257,210,435,330,695},{0,0,0,0,1,2,5,15,10,30,35,70,30,70,45,70,126,140,105,252,141,212,257,388,435,660},{0,0,0,0,0,1,0,0,5,15,0,35,15,0,30,35,0,70,70,126,70,141,126,257,210,435},{0,0,0,0,0,0,1,5,2,10,15,30,10,35,15,30,70,70,45,140,70,105,141,212,257,388},{0,0,0,0,0,0,0,1,0,2,5,10,2,15,3,10,35,30,15,70,30,45,70,105,141,212},{0,0,0,0,0,0,0,0,1,5,0,15,5,0,10,15,0,35,30,70,35,70,70,141,126,257},{0,0,0,0,0,0,0,0,0,1,0,5,1,0,2,5,0,15,10,35,15,30,35,70,70,141},{T^4,2*T^4,0,0,0,0,0,0,0,0,1,2,T^4,5,2*T^4,2,15,10,3,30,10,15,30,45,70,105},{0,T^4,0,0,0,0,0,0,0,0,0,1,0,0,T^4,1,0,5,2,15,5,10,15,30,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,0,10,0,15,30,35,70,70,140},{5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,0,0,0,0,5*T^4,1,10*T^4,T^4,5,2,2*T^4,10,2,3,10,15,30,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,5,10,15,30,35,70},{15*T^4,30*T^4,5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,0,0,15*T^4,0,30*T^4,5*T^4,1,0,10*T^4,2,T^4,2*T^4,2,3,10,15},{0,5*T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,5*T^4,0,0,1,T^4,5,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,0,35},{0,15*T^4,0,5*T^4,0,T^4,0,0,0,0,0,0,0,0,15*T^4,0,0,0,5*T^4,1,0,T^4,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 4 & 0 & 4 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 12 & 11 & 10 & 9 & 8 & 8 & 7 & 8 & 7 & 6 & 7 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,4},{1,1,4}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,4},{1,0,0},{0,1,4},{0,1,0},{0,0,1}}
Theta-collection (29): {{1,2,12},{1,2,11},{1,2,10},{1,2,9},{1,2,8},{1,1,8},{1,2,7},{0,1,8},{1,1,7},{1,2,6},{0,1,7},{1,1,6},{1,2,5},{0,1,6},{1,1,5},{1,1,4},{0,1,5},{0,1,4},{1,1,3},{0,1,3},{0,0,4},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,35,70,71,126,72,131,210,136,225,330,240,365,565,400,635,841,967,637,1211,977,1695,1421,1451,2025,2095,2950},{0,1,5,15,35,35,70,35,71,126,72,131,210,136,225,365,240,400,565,635,400,841,637,1211,967,977,1421,1451,2095},{0,0,1,5,15,15,35,15,35,70,35,71,126,72,131,225,136,240,365,400,240,565,400,841,635,637,967,977,1451},{0,0,0,1,5,5,15,5,15,35,15,35,70,35,71,131,72,136,225,240,136,365,240,565,400,400,635,637,977},{0,0,0,0,1,1,5,1,5,15,5,15,35,15,35,71,35,72,131,136,72,225,136,365,240,240,400,400,637},{0,0,0,0,0,1,0,1,5,0,5,15,0,15,35,70,35,70,126,126,72,210,136,330,210,240,330,400,635},{T^4,0,0,0,0,T^4,1,2*T^4,1,5,1,5,15,5,15,35,15,35,71,72,35+2*T^4,131,72,225,136,136,240,240,400},{0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70,0,126,71,0,131,0,210,225,330,365,565},{0,0,0,0,0,0,0,0,1,0,1,5,0,5,15,35,15,35,70,70,35,126,72,210,126,136,210,240,400},{5*T^4,T^4,0,0,0,5*T^4,0,10*T^4,T^4,1,2*T^4,1,5,1,5,15,5,15,35,35,15+10*T^4,71,35+2*T^4,131,72,72,136,136,240},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35,0,70,35,0,71,0,126,131,210,225,365},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,15,5,15,35,35,15,70,35,126,70,72,126,136,240},{15*T^4,5*T^4,T^4,0,0,15*T^4,0,30*T^4,5*T^4,0,10*T^4,T^4,1,2*T^4,1,5,1,5,15,15,5+30*T^4,35,15+10*T^4,71,35,35+2*T^4,72,72,136},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15,0,35,15,0,35,0,70,71,126,131,225},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,1,5,15,15,5,35,15,70,35,35,70,72,136},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,5,1,15,5,35,15,15,35,35,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,15,5,0,15,0,35,35,70,71,131},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,15,35,35,71},{0,0,0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,1,1,2*T^4,5,1,15,5,5,15,15,35},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,T^4,0,1,0,5,5,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,0,0,5*T^4,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,0,0,0,10*T^4,1,2*T^4,5,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,0,0,15*T^4,0,15*T^4,5*T^4,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,30*T^4,0,10*T^4,1,0,2*T^4,1,1,5},{0,0,0,0,0,0,0,5*T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,5*T^4,0,T^4,0,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,15*T^4,0,0,5*T^4,0,0,T^4,0,0,0,0,0,0,15*T^4,0,5*T^4,0,0,T^4,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,11)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 4 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,4}},{{0,2,4},{2,3,4},{0,1,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,4},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,1,8},{0,1,8},{1,1,7},{0,1,7},{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,0,4},{1,1,3},{0,0,4},{0,1,3},{1,0,3},{0,0,3},{1,1,2},{0,1,2},{1,0,2},{0,0,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,6,11,21,36,56,91,126,196,127,252,198,378,258,389,462,672,483,708,792,1122,848,1213,1413,1978},{0,1,1,6,6,21,21,56,56,126,56,126,127,252,127,258,252,462,258,483,462,792,483,848,848,1413},{0,0,1,2,6,11,21,36,56,91,56,126,91,196,127,198,252,378,258,389,462,672,483,708,848,1213},{0,0,0,1,1,6,6,21,21,56,21,56,56,126,56,127,126,252,127,258,252,462,258,483,483,848},{0,0,0,0,1,2,6,11,21,36,21,56,36,91,56,91,126,196,127,198,252,378,258,389,483,708},{0,0,0,0,0,1,1,6,6,21,6,21,21,56,21,56,56,126,56,127,126,252,127,258,258,483},{0,0,0,0,0,0,1,2,6,11,6,21,11,36,21,36,56,91,56,91,126,196,127,198,258,389},{0,0,0,0,0,0,0,1,1,6,1,6,6,21,6,21,21,56,21,56,56,126,56,127,127,258},{0,0,0,0,0,0,0,0,1,2,1,6,2,11,6,11,21,36,21,36,56,91,56,91,127,198},{0,0,0,0,0,0,0,0,0,1,0,1,1,6,1,6,6,21,6,21,21,56,21,56,56,127},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,6,11,0,0,21,36,0,0,56,91,126,196},{0,T^4,0,0,0,0,0,0,0,0,0,1,T^4,2,1,2,6,11,6,11,21,36,21,36,56,91},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6,0,0,6,21,0,0,21,56,56,126},{T^5,0,0,0,0,0,0,0,0,0,T^5,0,0,1,0,1,1,6,1,6,6,21,6,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,6,11,0,0,21,36,56,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,6,0,0,6,21,21,56},{T^5,4*T^4,0,T^4,0,0,0,0,0,0,T^5,0,4*T^4,0,0,T^4,1,2,1,2,6,11,6,11,21,36},{6*T^5,T^5,T^5,0,0,0,0,0,0,0,6*T^5,0,T^5,0,T^5,0,0,1,0,1,1,6,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,6,11,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,6,6,21},{6*T^5,10*T^4+T^5,T^5,4*T^4,0,T^4,0,0,0,0,6*T^5,0,10*T^4+T^5,0,T^5,4*T^4,0,0,0,T^4,1,2,1,2,6,11},{21*T^5,6*T^5,6*T^5,T^5,T^5,0,0,0,0,0,21*T^5,0,6*T^5,0,6*T^5,T^5,0,0,T^5,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,15)$ |
3 |
23 |
|
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -3 & 0 & 4 & 0 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 4 & 7 & 3 & 6 & 2 & 5 & 1 & 4 & 4 & 0 & 7 & 3 & 3 & -1 & 6 & 2 & -2 & 2 & 5 & 1 & 1 & 4 & 4 & 0 & 3 & 3 & -1 & 2 & 2 & -2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (23): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-3},{0,0,1},{0,1,4},{-1,1,4}},{{0,3,4},{0,2,3},{0,1,2},{1,4,5},{3,4,5},{0,1,4}},{8,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,-1,-3},{1,0,0},{-1,1,4},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,0,4},{1,1,7},{2,0,3},{1,1,6},{2,0,2},{1,1,5},{2,0,1},{1,1,4},{1,0,4},{2,0,0},{0,1,7},{1,1,3},{1,0,3},{2,0,-1},{0,1,6},{1,1,2},{2,0,-2},{1,0,2},{0,1,5},{1,1,1},{1,0,1},{0,1,4},{0,0,4},{1,0,0},{0,1,3},{0,0,3},{1,0,-1},{0,1,2},{0,0,2},{1,0,-2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,15,35,35,37,70,37,70,80,126,80,126,210,156,156,210,280,280,283,470,470,485,747,747,792,1135,1135,1240,1871},{0,1,1,5,5,15,15,35,35,35,37,70,72,70,80,126,126,136,156,210,240,280,280,400,470,473,635,747,762,967,1135,1180,1766},{0,0,1,1,5,5,15,15,15,35,15,35,37,70,37,70,126,80,80,126,156,156,156,280,280,283,470,470,485,747,747,792,1240},{0,0,0,1,1,5,5,15,15,15,15,35,35,35,37,70,70,72,80,126,136,156,156,240,280,280,400,470,473,635,747,762,1180},{0,0,0,0,1,1,5,5,5,15,5,15,15,35,15,35,70,37,37,70,80,80,80,156,156,156,280,280,283,470,470,485,792},{0,0,0,0,0,1,1,5,5,5,5,15,15,15,15,35,35,35,37,70,72,80,80,136,156,156,240,280,280,400,470,473,762},{0,0,0,0,0,0,1,1,1,5,1,5,5,15,5,15,35,15,15,35,37,37,37,80,80,80,156,156,156,280,280,283,485},{0,0,0,0,0,0,0,1,1,1,1,5,5,5,5,15,15,15,15,35,35,37,37,72,80,80,136,156,156,240,280,280,473},{0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,0,15,15,0,35,35,37,70,70,80,126,126,156,210,210,280,470},{0,0,0,0,0,0,0,0,0,1,0,1,1,5,1,5,15,5,5,15,15,15,15,37,37,37,80,80,80,156,156,156,283},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,5,15,0,15,35,35,35,70,72,70,126,136,126,210,240,400},{T^4,0,0,0,0,0,0,0,2*T^4,0,0,1,1,1,1,5,5,5,5,15,15,15,15+3*T^4,35,37,37,72,80,80,136,156,156,280},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,5,0,15,15,15,35,35,37,70,70,80,126,126,156,280},{T^4,T^4,0,0,0,0,0,0,2*T^4,0,2*T^4,0,0,1,0,1,5,1,1,5,5,5,5+3*T^4,15,15,15,37,37,37,80,80,80,156},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,5,15,15,15,35,35,35,70,72,70,126,136,240},{5*T^4,T^4,T^4,0,0,0,0,0,10*T^4,0,2*T^4,0,2*T^4,0,0,1,1,1,1,5,5,5,5+15*T^4,15,15,15+3*T^4,35,37,37,72,80,80,156},{5*T^4,5*T^4,T^4,T^4,0,0,0,0,10*T^4,0,10*T^4,0,2*T^4,0,2*T^4,0,1,0,0,1,1,1,1+15*T^4,5,5,5+3*T^4,15,15,15,37,37,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,5,15,15,15,35,35,37,70,70,80,156},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,5,5,15,15,15,35,35,35,70,72,136},{15*T^4,5*T^4,5*T^4,T^4,T^4,0,0,0,30*T^4,0,10*T^4,0,10*T^4,0,2*T^4,0,0,2*T^4,0,1,1,1,1+45*T^4,5,5,5+15*T^4,15,15,15+3*T^4,35,37,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,35,35,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,35,35,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,37},{0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,1,1,1,5,5,5,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,1,1,1,5,5,5,15},{0,0,0,0,0,0,0,0,5*T^4,0,T^4,0,T^4,0,0,0,0,0,0,0,0,0,10*T^4,0,0,2*T^4,0,1,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,5*T^4,0,5*T^4,0,T^4,0,T^4,0,0,0,0,0,0,0,10*T^4,0,0,2*T^4,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,15*T^4,0,5*T^4,0,5*T^4,0,T^4,0,0,T^4,0,0,0,0,30*T^4,0,0,10*T^4,0,0,2*T^4,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,16)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & -1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 4 & 0 & 0 & 1\end{pmatrix}$
39: $\begin{pmatrix}-1 & -2 & 0 & -1 & 1 & 0 & -2 & 1 & -1 & 0 & -2 & 1 & -1 & -2 & 0 & -1 & 0 & 1 & -2 & 0 & 1 & -1 & 1 & 0 & -1 & -2 & -1 & 0 & 1 & 1 & -1 & 0 & 1 & -1 & 0 & 0 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 7 & 5 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, -1, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 3, 5}, {5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 4, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,4},{-1,1,4}},{{2,4,5},{1,3,5},{2,3,5},{0,2,4},{1,4,5},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{1,0,0},{-1,1,4},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (39): {{-1,1,8},{-2,1,8},{0,1,7},{-1,1,7},{1,1,6},{0,1,6},{-2,1,7},{1,1,5},{-1,1,6},{0,1,5},{-2,1,6},{1,1,4},{-1,1,5},{-2,1,5},{0,1,4},{-1,1,4},{0,0,4},{1,1,3},{-2,1,4},{0,1,3},{1,0,3},{-1,0,4},{1,1,2},{0,0,3},{-1,1,3},{-2,1,3},{-1,0,3},{0,1,2},{1,0,2},{1,1,1},{-1,1,2},{0,0,2},{1,0,1},{-1,0,2},{0,1,1},{0,0,1},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,7,3,12,12,17,27,42,42,57,77,112,112,182,113,147,252,252,149,184,322,259,378,504,390,504,334,630,714,531,672,756,924,1001,1366,1246,1766},{0,1,0,2,0,3,7,4,12,17,27,22+T^2,42,77,57,112,57,72+3*T^2,182,147,72,113,182+6*T^2,149,252,378,259,322,185,392+10*T^2,504,334,409,531,630,672,1001,813,1246},{0,0,1,2,2,7,3,12,12,27,17,42,42,57,77,112,77,112,147,182,113,112,252,184,252,322,255,378,259,504,504,390,531,521,714,756,981,1001,1366},{0,0,0,1,0,2,2,3,7,12,12,17,27,42,42,77,42,57,112,112,57,77,147,113,182,252,184,252,149,322,378,259,334,390,504,531,756,672,1001},{0,15*T^2,0,0,1,2,21*T^2,7,3,12,4+28*T^2,27,17,22+36*T^2,42,57,42,77,72+45*T^2,112,77,57,182,112,147,182+55*T^2,147,252,184,378,322,255,390,326,504,521,652,756,981},{0,0,0,0,0,1,0,2,2,7,3,12,12,17,27,42,27,42,57,77,42,42,112,77,112,147,112,182,113,252,252,184,259,255,378,390,521,531,756},{0,0,0,0,T^4,0,1,0,2,3,7,4,12,27,17,42,17,22+T^2,77,57,22,42,72+3*T^2,57,112,182,113,147,72,182+6*T^2,252,149,185,259,322,334,531,409,672},{0,10*T^2,0,0,0,0,15*T^2,1,0,2,21*T^2,7,3,4+28*T^2,12,17,12,27,22+36*T^2,42,27,17,77,42,57,72+45*T^2,57,112,77,182,147,112,184,147,252,255,326,390,521},{0,0,0,0,0,0,0,0,1,2,2,3,7,12,12,27,12,17,42,42,17,27,57,42,77,112,77,112,57,147,182,113,149,184,252,259,390,334,531},{0,0,0,0,0,0,0,0,0,1,0,2,2,3,7,12,7,12,17,27,12,12,42,27,42,57,42,77,42,112,112,77,113,112,182,184,255,259,390},{0,0,0,0,3*T^4,0,0,T^4,0,0,1,0,2,7,3,12,3,4,27,17,4,12,22+T^2,17,42,77,42,57,22,72+3*T^2,112,57,72,113,147,149,259,185,334},{0,6*T^2,0,0,0,0,10*T^2,0,0,0,15*T^2,1,0,21*T^2,2,3,2,7,4+28*T^2,12,7,3,27,12,17,22+36*T^2,17,42,27,77,57,42,77,57,112,112,147,184,255},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,7,2,3,12,12,3,7,17,12,27,42,27,42,17,57,77,42,57,77,112,113,184,149,259},{0,0,0,0,6*T^4,0,0,3*T^4,0,0,0,T^4,0,1,0,2,0,0,7,3,0,2,4,3,12,27,12,17,4,22+T^2,42,17,22,42,57,57,113,72,149},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,3,7,2,2,12,7,12,17,12,27,12,42,42,27,42,42,77,77,112,113,184},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,1,3,2,7,12,7,12,3,17,27,12,17,27,42,42,77,57,113},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,7,0,0,12,0,12,0,0,27,42,42,0,77,112,112,182},{T^4,3*T^2+2*T^4,0,0,0,0,6*T^2,0,0,0,10*T^2,0,0,15*T^2,0,0,T^4,1,21*T^2,2,1,2*T^4,7,2,3,4+28*T^2,3,12,7,27,17,12,27,17,42,42,57,77,112},{0,0,T^4,0,12*T^4,0,0,6*T^4,0,0,0,3*T^4,0,0,0,0,0,T^4,1,0,T^4,0,0,0,2,7,2,3,0,4,12,3,4,12,17,17,42,22,57},{0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^4,2,1,2,3,2,7,2,12,12,7,12,12,27,27,42,42,77},{0,3*T^2,0,0,0,0,6*T^2,0,0,0,10*T^2,0,0,15*T^2,0,0,0,0,21*T^2,0,1,0,0,2,0,28*T^2,3,0,7,0,0,12,27,17,0,42,57,77,112},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,1,6*T^2,2,0,0,7,0,3,10*T^2,0,12,17,27,0,42,77,57,112},{3*T^4,T^2+8*T^4,0,T^4,0,0,3*T^2+2*T^4,0,0,0,6*T^2,0,0,10*T^2,0,0,3*T^4,0,15*T^2,0,0,8*T^4,1,T^4,0,21*T^2,2*T^4,2,1,7,3,2,7,3,12,12,17,27,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,0,0,7,12,12,0,27,42,42,77},{T^5,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,1,2,1,2,0,3,7,2,3,7,12,12,27,17,42},{2*T^5,T^5,3*T^4,0,23*T^4,T^4,0,12*T^4,0,0,0,6*T^4,0,0,0,0,2*T^5,3*T^4,0,0,3*T^4,T^5,T^4,0,0,1,0,0,T^4,0,2,0,0,2,3,3,12,4,17},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,1,0,0,6*T^2,0,2,3,7,0,12,27,17,42},{2*T^5,3*T^4,T^5,0,0,0,T^4,0,0,0,0,0,0,0,0,0,2*T^5,0,0,0,T^5,3*T^4,0,0,0,0,T^4,1,0,2,2,1,2,2,7,7,12,12,27},{0,T^2,0,0,0,0,3*T^2,0,0,0,6*T^2,0,0,10*T^2,0,0,0,0,15*T^2,0,0,0,0,0,0,21*T^2,0,0,1,0,0,2,7,3,0,12,17,27,42},{6*T^4+3*T^5,18*T^4,2*T^5,3*T^4,T^5,0,T^2+8*T^4,0,T^4,0,3*T^2+2*T^4,0,0,6*T^2,0,0,6*T^4+3*T^5,0,10*T^2,0,2*T^5,18*T^4,0,3*T^4,0,15*T^2,8*T^4,0,0,1,0,T^4,1,2*T^4,2,2,3,7,12},{7*T^5,2*T^5,2*T^5,T^5,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,7*T^5,0,0,0,2*T^5,2*T^5,0,T^5,0,0,0,0,0,0,1,0,0,1,2,2,7,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,7,12,12,27},{0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,6*T^2,0,0,0,0,10*T^2,0,0,0,0,0,0,15*T^2,0,0,0,0,0,0,1,0,0,2,3,7,12},{0,0,0,0,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,1,0,2,7,3,12},{12*T^5,6*T^4+3*T^5,7*T^5,2*T^5,2*T^5,T^5,3*T^4,0,0,0,T^4,0,0,0,0,0,12*T^5,0,0,0,7*T^5,6*T^4+3*T^5,0,2*T^5,0,0,3*T^4,0,T^5,0,0,0,0,T^4,1,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,7},{0,0,0,0,6*T^4,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,0,0,0,10*T^2,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,17)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 4 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 5 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,4}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,4},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,1,8},{0,1,8},{1,1,7},{0,1,7},{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{1,1,3},{1,0,4},{0,1,4},{0,1,3},{0,0,4},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,30,35,70,70,126,71,140,252,142,131,210,420,262,225,330,450,365,660,730,565,1130},{0,1,0,5,0,15,0,35,0,0,0,70,126,71,0,0,210,131,0,0,225,0,330,365,0,565},{0,0,1,2,5,10,15,30,35,70,35,70,140,70,71,126,252,142,131,210,262,225,420,450,365,730},{0,0,0,1,0,5,0,15,0,0,0,35,70,35,0,0,126,71,0,0,131,0,210,225,0,365},{0,0,0,0,1,2,5,10,15,35,15,30,70,30,35,70,140,70,71,126,142,131,252,262,225,450},{0,0,0,0,0,1,0,5,0,0,0,15,35,15,0,0,70,35,0,0,71,0,126,131,0,225},{0,0,0,0,0,0,1,2,5,15,5,10,30,10,15,35,70,30,35,70,70,71,140,142,131,262},{0,0,0,0,0,0,0,1,0,0,0,5,15,5,0,0,35,15,0,0,35,0,70,71,0,131},{0,0,0,0,0,0,0,0,1,5,1,2,10,2,5,15,30,10,15,35,30,35,70,70,71,142},{T^4,2*T^4,0,0,0,0,0,0,0,1,T^4,0,2,2*T^4,1,5,10,2,5,15,10,15,30,30,35,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,0,10,15,0,30,35,0,70,70,140},{0,0,0,0,0,0,0,0,0,0,0,1,5,1,0,0,15,5,0,0,15,0,35,35,0,71},{0,T^4,0,0,0,0,0,0,0,0,0,0,1,T^4,0,0,5,1,0,0,5,0,15,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,10,15,0,30,35,70},{5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,0,0,5*T^4,0,0,10*T^4,T^4,1,2,2*T^4,1,5,2,5,10,10,15,30},{0,5*T^4,0,T^4,0,0,0,0,0,0,0,0,0,5*T^4,0,0,1,T^4,0,0,1,0,5,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,10,15,30},{15*T^4,30*T^4,5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,15*T^4,0,0,30*T^4,5*T^4,0,0,10*T^4,T^4,1,2*T^4,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,10},{0,15*T^4,0,5*T^4,0,T^4,0,0,0,0,0,0,0,15*T^4,0,0,0,5*T^4,0,0,T^4,0,1,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,18)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 4 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 8 & 5 & 7 & 4 & 6 & 3 & 4 & 5 & 2 & 3 & 4 & 2 & 1 & 3 & 4 & 1 & 3 & 2 & 0 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -4}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{4, 6}, {5, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,4},{-1,1,4}},{{0,2,3},{2,3,4},{0,1,3},{1,3,4}},{5,2,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,0},{-1,1,4},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,1,8},{1,1,7},{1,1,6},{0,1,8},{1,1,5},{0,1,7},{1,1,4},{0,1,6},{1,1,3},{1,0,4},{0,1,5},{1,1,2},{1,0,3},{0,1,4},{1,0,2},{1,1,1},{0,1,3},{0,0,4},{1,0,1},{0,0,3},{0,1,2},{1,0,0},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,2,35,10,70,30,126,72,70,210,136,140,240,330,252,143,400,267,420,635,465,660,765,1200},{0,1,5,0,15,2,35,10,70,35,30,126,72,70,136,210,140,70,240,143,252,400,267,420,465,765},{0,0,1,0,5,0,15,2,35,15,10,70,35,30,72,126,70,30,136,70,140,240,143,252,267,465},{0,0,0,1,0,5,0,15,0,1,35,0,5,70,15,0,126,72,35,136,210,70,240,330,400,635},{0,0,0,0,1,0,5,0,15,5,2,35,15,10,35,70,30,10,72,30,70,136,70,140,143,267},{0,0,0,0,0,1,0,5,0,0,15,0,1,35,5,0,70,35,15,72,126,35,136,210,240,400},{0,0,0,0,0,0,1,0,5,1,0,15,5,2,15,35,10,2,35,10,30,72,30,70,70,143},{0,0,0,0,0,0,0,1,0,0,5,0,0,15,1,0,35,15,5,35,70,15,72,126,136,240},{T^4,0,0,2*T^4,0,0,0,0,1,2*T^4,0,5,1,0,5,15,2,3*T^4,15,2,10,35,10,30,30,70},{0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,0,0,2,35,10,0,70,30,0,70,140},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,5,1,15,35,5,35,70,72,136},{5*T^4,T^4,0,10*T^4,0,2*T^4,0,0,0,10*T^4,0,1,2*T^4,0,1,5,0,15*T^4,5,3*T^4,2,15,2,10,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,0,15,2,0,35,10,0,30,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,5,15,1,15,35,35,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,2,0,10,30},{15*T^4,5*T^4,T^4,30*T^4,0,10*T^4,0,2*T^4,0,30*T^4,0,0,10*T^4,0,2*T^4,1,0,45*T^4,1,15*T^4,0,5,3*T^4,2,2,10},{0,0,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,1,2*T^4,0,1,5,0,5,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,5*T^4,0,T^4,0,0,0,5*T^4,0,0,T^4,0,0,0,0,10*T^4,0,2*T^4,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,15*T^4,0,5*T^4,0,T^4,0,15*T^4,0,0,5*T^4,0,T^4,0,0,30*T^4,0,10*T^4,0,0,2*T^4,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,25)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & -1 & 3 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 7 & 5 & 6 & 4 & 3 & 5 & 4 & 2 & 3 & 4 & 1 & 3 & 2 & 0 & 4 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, -1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{5, 6}, {4, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,4,0},{0,1,-1},{0,0,1},{1,1,3}},{{1,4,5},{1,2,5},{0,2,5},{1,2,3},{0,2,3},{0,4,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,1,-1},{1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,2,7},{1,2,6},{1,1,7},{1,2,5},{1,1,6},{1,2,4},{1,2,3},{1,1,5},{1,1,4},{1,2,2},{1,1,3},{0,1,4},{1,2,1},{0,1,3},{1,1,2},{1,2,0},{0,0,4},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,15,20,35,70,50,105,126,196,106,210,201,336,330,237,351,540,426,825,575,716,895,1140,1736},{0,1,1,5,6,15,35,20,50,70,105,50,126,106,196,210,121,201,336,237,540,351,426,575,716,1140},{0,0,1,0,5,0,0,15,35,0,70,35,0,70,126,0,106,126,210,201,330,210,351,330,575,895},{0,0,0,1,1,5,15,6,20,35,50,20,70,50,105,126,55,106,196,121,336,201,237,351,426,716},{0,0,0,0,1,0,0,5,15,0,35,15,0,35,70,0,50,70,126,106,210,126,201,210,351,575},{0,0,0,0,0,1,5,1,6,15,20,6,35,20,50,70,21,50,105,55,196,106,121,201,237,426},{0,0,0,0,0,0,1,0,1,5,6,1,15,6,20,35,6,20,50,21,105,50,55,106,121,237},{0,0,0,0,0,0,0,1,5,0,15,5,0,15,35,0,20,35,70,50,126,70,106,126,201,351},{0,0,0,0,0,0,0,0,1,0,5,1,0,5,15,0,6,15,35,20,70,35,50,70,106,201},{T^4,0,T^4,0,0,0,0,0,0,1,1,T^4,5,1,6,15,1+T^4,6,20,6,50,20,21,50,55,121},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,1,5,15,6,35,15,20,35,50,106},{0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,6,15,0,20,0,35,50,70,105,196},{5*T^4,T^4,6*T^4,0,T^4,0,0,0,0,0,0,5*T^4,1,T^4,1,5,6*T^4,1,6,1+T^4,20,6,6,20,21,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,0,15,20,35,50,105},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,0,T^4,1,5,1,15,5,6,15,20,50},{15*T^4,5*T^4,20*T^4,T^4,6*T^4,0,0,T^4,0,0,0,15*T^4,0,5*T^4,0,1,20*T^4,T^4,1,6*T^4,6,1,1+T^4,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,6,15,20,50},{0,0,5*T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,0,5*T^4,0,1,T^4,5,1,1,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,15*T^4,0,5*T^4,0,0,T^4,0,0,0,0,0,0,0,0,15*T^4,0,0,5*T^4,1,0,T^4,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,27)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 4 & 0 & 3 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 11 & 10 & 9 & 8 & 8 & 7 & 7 & 6 & 6 & 7 & 5 & 6 & 4 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{1,1,4},{3,4,12}},{{2,3,4},{3,4,5},{1,3,5},{0,2,4},{0,1,5},{0,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,4},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,11},{1,2,10},{1,2,9},{1,2,8},{1,1,8},{1,2,7},{1,1,7},{1,2,6},{1,1,6},{0,1,7},{1,2,5},{0,1,6},{1,2,4},{1,1,5},{1,1,4},{0,1,5},{0,1,4},{1,1,3},{0,1,3},{0,0,4},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,35,36,70,75,126,141,76,210,146,330,245,400,260,435,621,691,441,925,711,1331,1051,1101,1541,1646,2386},{0,1,5,15,15,35,36,70,75,36,126,76,210,141,245,146,260,400,435,261,621,441,925,691,711,1051,1101,1646},{0,0,1,5,5,15,15,35,36,15,70,36,126,75,141,76,146,245,260,146,400,261,621,435,441,691,711,1101},{0,0,0,1,1,5,5,15,15,5,35,15,70,36,75,36,76,141,146,76,245,146,400,260,261,435,441,711},{0,0,0,0,1,0,5,0,15,5,0,15,0,35,70,35,70,126,126,76,210,146,330,210,260,330,435,691},{0,0,0,0,0,1,1,5,5,1,15,5,35,15,36,15,36,75,76,36,141,76,245,146,146,260,261,441},{0,0,0,0,0,0,1,0,5,1,0,5,0,15,35,15,35,70,70,36,126,76,210,126,146,210,260,435},{T^4,0,0,0,T^4,0,0,1,1,T^4,5,1,15,5,15,5,15,36,36,15+T^4,75,36,141,76,76,146,146,261},{0,0,0,0,0,0,0,0,1,0,0,1,0,5,15,5,15,35,35,15,70,36,126,70,76,126,146,260},{0,0,0,0,0,0,0,0,0,1,0,5,0,0,0,15,35,0,70,36,0,75,0,126,141,210,245,400},{5*T^4,T^4,0,0,5*T^4,0,T^4,0,0,6*T^4,1,T^4,5,1,5,1,5,15,15,5+6*T^4,36,15+T^4,75,36,36,76,76,146},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,15,0,35,15,0,36,0,70,75,126,141,245},{15*T^4,5*T^4,T^4,0,15*T^4,0,5*T^4,0,T^4,20*T^4,0,6*T^4,1,0,1,T^4,1,5,5,1+20*T^4,15,5+6*T^4,36,15,15+T^4,36,36,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,1,5,15,15,5,35,15,70,35,36,70,76,146},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,5,1,15,5,35,15,15,35,36,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,15,5,0,15,0,35,36,70,75,141},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,15,35,36,75},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,1,1,T^4,5,1,15,5,5,15,15,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,15,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,0,5*T^4,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,6*T^4,1,T^4,5,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,0,15*T^4,0,5*T^4,0,T^4,5*T^4,0,T^4,0,0,0,0,0,0,0,20*T^4,0,6*T^4,1,0,T^4,1,1,5},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,5*T^4,0,T^4,0,0,0,0,0,0,0,5*T^4,0,T^4,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,32)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & -2 & 0 & 3 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 7 & 9 & 6 & 8 & 5 & 7 & 4 & 7 & 4 & 6 & 6 & 3 & 5 & 3 & 2 & 5 & 4 & 2 & 4 & 1 & 4 & 1 & 3 & 3 & 0 & 2 & 2 & -1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {5, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{1,0,1},{0,1,3},{-1,1,3}},{{3,4,5},{1,5,6},{0,1,5},{2,3,4},{3,5,6},{0,4,5},{0,2,4},{0,1,2}},{6,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,1,3},{1,-1,-2},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (31): {{1,1,7},{0,2,9},{1,1,6},{0,2,8},{1,1,5},{0,2,7},{1,1,4},{0,1,7},{1,0,4},{0,2,6},{0,1,6},{1,1,3},{0,2,5},{1,0,3},{1,1,2},{0,1,5},{0,2,4},{1,0,2},{0,1,4},{1,1,1},{0,0,4},{1,0,1},{0,1,3},{0,0,3},{1,0,0},{0,1,2},{0,0,2},{1,0,-1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,15,35,16,37,35,41,70,70,80,126,90,126,156,176,210,178,280,315,326,470,526,561,747,831,916,1430},{0,1,1,5,5,15,15,15,15,35,37,35,70,37,70,80,126,80,156,126,156,156,280,283,280,470,485,470,747,792,1240},{0,0,1,1,5,5,15,5,15,15,16,35,35,37,70,41,70,80,90,126,90,156,176,178,280,315,326,470,526,561,916},{0,0,0,1,1,5,5,5,5,15,15,15,35,15,35,37,70,37,80,70,80,80,156,156,156,280,283,280,470,485,792},{0,0,0,0,1,1,5,1,5,5,5,15,15,15,35,16,35,37,41,70,41,80,90,90,156,176,178,280,315,326,561},{0,0,0,0,0,1,1,1,1,5,5,5,15,5,15,15,35,15,37,35,37,37,80,80,80,156,156,156,280,283,485},{0,0,0,0,0,0,1,0,1,1,1,5,5,5,15,5,15,15,16,35,16,37,41,41,80,90,90,156,176,178,326},{0,0,0,0,0,0,0,1,1,0,5,0,0,5,0,15,0,15,35,0,37,35,70,80,70,126,156,126,210,280,470},{0,0,0,0,0,0,0,0,1,0,1,0,0,5,0,5,0,15,15,0,16,35,35,41,70,70,90,126,126,176,315},{0,0,0,0,0,0,0,0,0,1,1,1,5,1,5,5,15,5,15,15,15,15,37,37,37,80,80,80,156,156,283},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,0,5,15,0,15,15,35,37,35,70,80,70,126,156,280},{0,0,0,0,0,0,0,T^4,0,0,0,1,1,1,5,1,5,5,5,15,5+T^4,15,16,16,37,41,41,80,90,90,178},{T^4,0,0,0,0,0,0,2*T^4,2*T^4,0,0,0,1,0,1,1,5,1,5,5,5+3*T^4,5,15,15,15,37,37,37,80,80,156},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,0,5,15,15,16,35,35,41,70,70,90,176},{T^4,T^4,0,0,0,0,0,6*T^4,2*T^4,0,T^4,0,0,0,1,0,1,1,1,5,1+7*T^4,5,5,5+T^4,15,16,16,37,41,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,5,5,15,15,15,35,37,35,70,80,156},{5*T^4,T^4,T^4,0,0,0,0,10*T^4,10*T^4,0,2*T^4,0,0,2*T^4,0,0,1,0,1,1,1+15*T^4,1,5,5+3*T^4,5,15,15,15,37,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,5,5,5,15,15,16,35,35,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,5,15,15,15,35,37,80},{5*T^4,5*T^4,T^4,T^4,0,0,0,20*T^4,10*T^4,0,6*T^4,0,0,2*T^4,0,T^4,0,0,0,1,25*T^4,1,1,1+7*T^4,5,5,5+T^4,15,16,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,1,1,5,5,5,16},{0,0,0,0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,1,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,0,0,0,6*T^4,0,0,T^4,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,5*T^4,5*T^4,0,T^4,0,0,T^4,0,0,0,0,0,0,10*T^4,0,0,2*T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,37)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -2 & -1 & 3 & 0 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 5 & 2 & 4 & 1 & 4 & 3 & 6 & 3 & 0 & 2 & 5 & 2 & -1 & 1 & 4 & 4 & 1 & -2 & 3 & 0 & 3 & 0 & 2 & 2 & -1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (23): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{2,1,0},{1,-1,-2},{1,0,-1},{0,0,1},{0,1,2},{0,1,3},{-1,1,3}},{{0,5,7},{0,2,4},{1,3,4},{6,7,8},{0,2,6,7},{1,2,6},{0,3,5},{1,6,8},{1,2,4},{0,3,4},{5,7,8}},{6,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,-1,-2},{1,0,-1},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (29): {{2,0,3},{1,1,5},{2,0,2},{1,1,4},{2,0,1},{1,0,4},{1,1,3},{0,1,6},{1,0,3},{2,0,0},{1,1,2},{0,1,5},{1,0,2},{2,0,-1},{1,1,1},{0,1,4},{0,0,4},{1,0,1},{2,0,-2},{0,1,3},{1,1,0},{0,0,3},{1,0,0},{0,1,2},{0,0,2},{1,0,-1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,6,15,6,21,35,35,21,55,70,70,55,61,120,126,120,126,141,231,231,286,406,406,526,897},{0,1,1,5,5,5,15,6,16,15,35,21,41,35,70,55,56,90,70,120,126,126,176,231,252,315,406,461,786},{0,0,1,1,5,1,5,1,6,15,15,6,21,35,35,21,22,55,70,55,70,61,120,120,141,231,231,286,526},{0,0,0,1,1,1,5,1,5,5,15,6,16,15,35,21,21,41,35,55,70,56,90,120,126,176,231,252,461},{0,0,0,0,1,0,1,0,1,5,5,1,6,15,15,6,6,21,35,21,35,22,55,55,61,120,120,141,286},{0,0,0,0,0,1,0,1,5,0,0,5,15,0,0,15,21,35,0,35,0,55,70,70,120,126,126,231,406},{0,0,0,0,0,0,1,0,1,1,5,1,5,5,15,6,6,16,15,21,35,21,41,55,56,90,120,126,252},{0,0,0,0,0,0,0,1,1,0,0,5,5,0,0,15,16,15,0,35,0,41,35,70,90,70,126,176,315},{0,0,0,0,0,0,0,0,1,0,0,1,5,0,0,5,6,15,0,15,0,21,35,35,55,70,70,120,231},{0,0,0,0,0,0,0,0,0,1,1,0,1,5,5,1,1,6,15,6,15,6,21,21,22,55,55,61,141},{0,0,0,0,0,T^4,0,0,0,0,1,0,1,1,5,1,1+T^4,5,5,6,15,6,16,21,21,41,55,56,126},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,5,5,5,0,15,0,16,15,35,41,35,70,90,176},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,5,0,5,0,6,15,15,21,35,35,55,120},{0,0,0,0,0,T^4,0,T^4,0,0,0,0,0,1,1,0,T^4,1,5,1,5,1,6,6,6,21,21,22,61},{T^4,0,0,0,0,6*T^4,0,T^4,T^4,0,0,0,0,0,1,0,6*T^4,1,1,1,5,1+T^4,5,6,6,16,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,5,0,5,5,15,16,15,35,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,6,15,15,21,55},{T^4,T^4,0,0,0,6*T^4,0,6*T^4,T^4,0,0,T^4,0,0,0,0,6*T^4,0,1,0,1,T^4,1,1,1,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,5,15,16,41},{5*T^4,T^4,T^4,0,0,20*T^4,0,6*T^4,6*T^4,0,0,T^4,T^4,0,0,0,21*T^4,0,0,0,1,6*T^4,1,1,1+T^4,5,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,6,21},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,1,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,5*T^4,0,T^4,T^4,0,0,0,0,0,0,0,6*T^4,0,0,0,0,T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,40)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & -1 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 3 & 0 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}-2 & -1 & 0 & -2 & -1 & 0 & -2 & -2 & -1 & -1 & 0 & -2 & -1 & 0 & -2 & -2 & -1 & 0 & -2 & 0 & -1 & 0 & -1 & -2 & 0 & -1 & -1 & 0 & -2 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 9 & 8 & 7 & 8 & 7 & 6 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 5 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, -1, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{0,1,3},{-1,1,3}},{{2,5,6},{4,5,6},{1,3,6},{1,4,6},{2,3,6},{0,1,4},{0,2,5},{0,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{0,1,2},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (38): {{-2,2,9},{-1,2,8},{0,2,7},{-2,2,8},{-1,2,7},{0,2,6},{-2,2,7},{-2,1,7},{-1,2,6},{-1,1,6},{0,2,5},{-2,2,6},{-1,2,5},{0,1,5},{-2,1,6},{-2,2,5},{-1,1,5},{0,2,4},{-2,1,5},{0,1,4},{-1,2,4},{0,2,3},{-1,1,4},{-2,1,4},{0,1,3},{-1,0,4},{-1,1,3},{0,0,3},{-2,1,3},{-1,0,3},{0,1,2},{0,0,2},{-1,1,2},{0,1,1},{-1,0,2},{0,0,1},{-1,0,1},{0,0,0}}
Ext matrix: {{1,2,3,5,9,13,15,16,25,28,35,35,55,40,41,70,69,75,90,97,105,140,145,176,200,148,272,206,315,287,368,395,469,623,514,698,863,1155},{0,1,2,1,5,9,5,5,15,16,25,15,35,28,16,35,41,55,41,69,70,105,90,90,145,91,176,148,176,182,272,287,315,469,336,514,581,863},{0,0,1,0,1,5,1,1,5,5,15,5,15,16,5,15,16,35,16,41,35,70,41,41,90,41,90,91,90,91,176,182,176,315,182,336,336,581},{0,0,0,1,2,3,5,5,9,9,13,15,25,13,16,35,28,35,41,40,55,75,69,90,97,69,145,97,176,148,200,206,272,368,287,395,514,698},{0,0,0,0,1,2,1,1,5,5,9,5,15,9,5,15,16,25,16,28,35,55,41,41,69,41,90,69,90,91,145,148,176,272,182,287,336,514},{0,0,0,0,0,1,0,0,1,1,5,1,5,5,1,5,5,15,5,16,15,35,16,16,41,16,41,41,41,41,90,91,90,176,91,182,182,336},{0,0,0,0,0,0,1,1,2,2,3,5,9,3,5,15,9,13,16,13,25,35,28,41,40,28,69,40,90,69,97,97,145,200,148,206,287,395},{0,0,0,0,0,T^2,0,1,0,2,3*T^2,0,0,3,5,0,9,6*T^2,15,13,0,10*T^2,25,35,35,28,55,40,70,69,75,97,105,140,145,200,272,368},{0,0,0,0,0,0,0,0,1,1,2,1,5,2,1,5,5,9,5,9,15,25,16,16,28,16,41,28,41,41,69,69,90,145,91,148,182,287},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,5,0,5,9,0,0,15,15,25,16,35,28,35,41,55,69,70,105,90,145,176,272},{0,0,0,0,0,0,0,T^4,0,0,1,0,1,1,0,1,1,5,1,5,5,15,5,5,16,5+T^4,16,16,16,16,41,41,41,90,41,91,91,182},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,5,2,3,5,3,9,13,9,16,13,9,28,13,41,28,40,40,69,97,69,97,148,206},{0,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,1,1,2,1,2,5,9,5,5,9,5+T^4,16,9,16,16,28,28,41,69,41,69,91,148},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,5,0,0,5,5,15,5,15,16,15,16,35,41,35,70,41,90,90,176},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,1,0,2,3*T^2,5,3,0,6*T^2,9,15,13,9,25,13,35,28,35,40,55,75,69,97,145,200},{0,T^3,2*T^3,0,0,0,0,T^4,0,T^3,0,0,0,3*T^3,0,1,0,0,1,0,2,3,2,5,3,2+T^3+T^4,9,3+3*T^3,16,9,13,13,28,40,28,40,69,97},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,0,0,5,5,9,5,15,9,15,16,25,28,35,55,41,69,90,145},{T^4,0,0,0,0,0,0,6*T^4,0,T^4,0,0,0,0,T^4,0,0,1,0,1,1,5,1,1,5,1+6*T^4,5,5+T^4,5,5+T^4,16,16,16,41,16,41,41,91},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,0,3*T^2,2,5,3,2,9,3,15,9,13,13,25,35,28,40,69,97},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,5,1,5,5,5,5,15,16,15,35,16,41,41,90},{T^4,0,T^3,0,0,0,0,6*T^4,0,T^4,0,0,0,T^3,T^4,0,0,0,0,0,1,2,1,1,2,1+6*T^4,5,2+T^3+T^4,5,5+T^4,9,9,16,28,16,28,41,69},{5*T^4,T^4,0,T^4,0,0,0,20*T^4,0,6*T^4,0,0,0,T^4,6*T^4,0,T^4,0,T^4,0,0,1,0,0,1,21*T^4,1,1+6*T^4,1,1+6*T^4,5,5+T^4,5,16,5+T^4,16,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,5,2,5,5,9,9,15,25,16,28,41,69},{0,0,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,2,0,5,2,3,3,9,13,9,13,28,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,5,5,5,15,5,16,16,41},{0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,10*T^2,0,0,0,1,0,2,0,5,0,9,0,0,15,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,2,2,5,9,5,9,16,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,5,15,15,35},{0,0,6*T^4,0,0,3*T^4,0,0,0,T^3,T^4,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,3*T^3,1,0,0,0,2,3,2,3,9,13},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,0,0,0,1,0,2,0,0,5,9,15,25},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,1,1,1,5,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,5,15},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^4,0,T^3,0,0,0,0,1,2,1,2,5,9},{0,0,0,0,0,0,0,5*T^4,0,T^4,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,6*T^4,0,T^4,0,T^4,0,0,0,1,0,1,1,5},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,41)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 3 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 5 & 5 & 4 & 5 & 3 & 4 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,3},{3,1,3}},{{2,3,4},{0,1,5},{3,4,5},{0,3,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,1},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (25): {{1,1,8},{1,1,7},{0,1,7},{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{1,0,5},{1,1,3},{1,0,4},{0,1,4},{0,0,4},{0,1,3},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,15,20,35,50,70,36,126,75,105,111,196,141,210,336,216,245,330,386,400,540,645,1021},{0,1,1,5,6,15,20,35,15,70,36,50,51,105,75,126,196,111,141,210,216,245,336,386,645},{0,0,1,0,5,0,15,0,0,0,0,35,36,70,0,0,126,75,0,0,141,0,210,245,400},{0,0,0,1,1,5,6,15,5,35,15,20,20,50,36,70,105,51,75,126,111,141,196,216,386},{0,0,0,0,1,0,5,0,0,0,0,15,15,35,0,0,70,36,0,0,75,0,126,141,245},{0,0,0,0,0,1,1,5,1,15,5,6,6,20,15,35,50,20,36,70,51,75,105,111,216},{0,0,0,0,0,0,1,0,0,0,0,5,5,15,0,0,35,15,0,0,36,0,70,75,141},{0,0,0,0,0,0,0,1,0,5,1,1,1,6,5,15,20,6,15,35,20,36,50,51,111},{0,0,0,0,0,0,0,0,1,0,5,0,6,0,15,0,0,20,35,0,50,70,0,105,196},{T^4,0,T^4,0,0,0,0,0,T^4,1,0,0,T^4,1,1,5,6,1,5,15,6,15,20,20,51},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,6,15,0,20,35,0,50,105},{0,0,0,0,0,0,0,0,0,0,0,1,1,5,0,0,15,5,0,0,15,0,35,36,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,0,5,0,15,15,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,15,0,20,50},{5*T^4,T^4,6*T^4,0,T^4,0,0,0,5*T^4,0,T^4,0,6*T^4,0,0,1,1,T^4,1,5,1,5,6,6,20},{0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,0,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,6,20},{15*T^4,5*T^4,20*T^4,T^4,6*T^4,0,T^4,0,15*T^4,0,5*T^4,0,20*T^4,0,T^4,0,0,6*T^4,0,1,T^4,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,5*T^4,0,T^4,0,0,0,0,0,0,0,5*T^4,0,0,0,0,T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,43)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & -2 & 0 & 3 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 5 & 5 & 4 & 7 & 4 & 3 & 6 & 2 & 3 & 1 & 2 & 5 & 4 & 1 & 3 & 4 & 0 & 3 & -1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{1,0,1},{0,1,3}},{{3,4,5},{0,4,5},{2,3,4},{0,1,5},{0,1,2},{0,2,4}},{4,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,-1,-2},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,1,7},{1,1,6},{1,1,5},{1,0,5},{1,1,4},{0,1,7},{1,0,4},{1,1,3},{0,1,6},{1,1,2},{1,0,3},{1,1,1},{1,0,2},{0,1,5},{0,1,4},{1,0,1},{0,1,3},{0,0,4},{1,0,0},{0,0,3},{1,0,-1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,15,35,16,36,70,41,126,75,210,141,90,176,245,315,177,400,321,621,526,546,831,881,1360},{0,1,5,5,15,5,15,35,16,70,36,126,75,41,90,141,176,90,245,177,400,315,321,526,546,881},{0,0,1,1,5,1,5,15,5,35,15,70,36,16,41,75,90,41,141,90,245,176,177,315,321,546},{0,0,0,1,0,1,5,0,5,0,15,0,35,15,35,70,70,41,126,90,210,126,176,210,315,526},{0,0,0,0,1,0,1,5,1,15,5,35,15,5,16,36,41,16,75,41,141,90,90,176,177,321},{0,0,0,0,0,1,0,0,5,0,0,0,0,15,35,0,70,36,0,75,0,126,141,210,245,400},{0,0,0,0,0,0,1,0,1,0,5,0,15,5,15,35,35,16,70,41,126,70,90,126,176,315},{0,0,0,T^4,0,T^4,0,1,0,5,1,15,5,1,5,15,16,5+T^4,36,16,75,41,41,90,90,177},{0,0,0,0,0,0,0,0,1,0,0,0,0,5,15,0,35,15,0,36,0,70,75,126,141,245},{T^4,0,0,5*T^4,0,6*T^4,T^4,0,T^4,1,0,5,1,0,1,5,5,1+6*T^4,15,5+T^4,36,16,16,41,41,90},{0,0,0,0,0,0,0,0,0,0,1,0,5,1,5,15,15,5,35,16,70,35,41,70,90,176},{5*T^4,T^4,0,15*T^4,0,20*T^4,5*T^4,0,6*T^4,0,T^4,1,0,T^4,0,1,1,20*T^4,5,1+6*T^4,15,5,5+T^4,16,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,5,1,15,5,35,15,16,35,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,15,5,0,15,0,35,36,70,75,141},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,15,35,36,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,1,15,5,5,15,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,15,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,1,0,5,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,5*T^4,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,0,0,6*T^4,0,T^4,1,0,0,1,1,5},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,5*T^4,0,0,T^4,0,0,0,0,0,0,0,0,5*T^4,0,T^4,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,44)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & -1 & 3 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 7 & 4 & 6 & 4 & 3 & 5 & 2 & 3 & 4 & 1 & 2 & 3 & 4 & 0 & 1 & 3 & 2 & 0 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{4, 6}, {5, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{2,1,0},{1,0,-1},{0,0,1},{0,1,2},{0,1,3},{-1,1,3}},{{0,4,6},{1,2,3},{0,2,5,6},{0,2,3},{5,6,7},{1,5,7},{4,6,7},{1,2,5}},{5,2,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,-1},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,1,6},{1,1,5},{0,1,7},{1,1,4},{0,1,6},{1,0,4},{1,1,3},{0,1,5},{1,1,2},{1,0,3},{0,1,4},{1,1,1},{1,0,2},{0,1,3},{0,0,4},{1,1,0},{1,0,1},{0,0,3},{0,1,2},{1,0,0},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,1,15,6,16,35,20,70,41,50,126,90,105,56,210,176,126,196,315,251,336,456,771},{0,1,0,5,1,5,15,6,35,16,20,70,41,50,21,126,90,56,105,176,126,196,251,456},{0,0,1,0,5,1,0,15,0,5,35,0,15,70,41,0,35,90,126,70,176,210,315,526},{0,0,0,1,0,1,5,1,15,5,6,35,16,20,6,70,41,21,50,90,56,105,126,251},{0,0,0,0,1,0,0,5,0,1,15,0,5,35,16,0,15,41,70,35,90,126,176,315},{0,0,0,0,0,1,0,0,0,5,0,0,15,0,6,0,35,20,0,70,50,0,105,196},{0,0,0,0,0,0,1,0,5,1,1,15,5,6,1,35,16,6,20,41,21,50,56,126},{0,0,0,0,0,0,0,1,0,0,5,0,1,15,5,0,5,16,35,15,41,70,90,176},{0,0,T^4,0,0,T^4,0,0,1,0,0,5,1,1,T^4,15,5,1,6,16,6,20,21,56},{0,0,0,0,0,0,0,0,0,1,0,0,5,0,1,0,15,6,0,35,20,0,50,105},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,1,5,15,5,16,35,41,90},{T^4,0,6*T^4,0,T^4,6*T^4,0,0,0,T^4,0,1,0,0,6*T^4,5,1,T^4,1,5,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,1,0,15,6,0,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,5,1,5,15,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{5*T^4,T^4,20*T^4,0,6*T^4,20*T^4,0,T^4,0,6*T^4,0,0,T^4,0,21*T^4,1,0,6*T^4,0,1,T^4,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,5*T^4,0,T^4,5*T^4,0,0,0,T^4,0,0,0,0,6*T^4,0,0,T^4,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,45)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 3 & 0 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}-1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 9 & 8 & 8 & 7 & 7 & 6 & 7 & 6 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -3}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 5}, {4, 5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{0,1,3},{-1,1,3}},{{2,5,6},{1,3,6},{0,4,5},{2,3,6},{1,4,6},{0,2,5},{4,5,6},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,0,1},{0,1,2},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (29): {{-1,2,9},{0,2,8},{-1,2,8},{0,2,7},{-1,2,7},{0,2,6},{-1,1,7},{0,1,6},{-1,2,6},{-1,1,6},{0,2,5},{0,1,5},{-1,2,5},{-1,1,5},{0,2,4},{0,1,4},{-1,2,4},{0,2,3},{-1,1,4},{0,0,4},{0,1,3},{0,0,3},{-1,1,3},{0,1,2},{-1,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,15,16,17,35,41,35,45,70,90,70,100,126,126,176,102,196,207,315,350,526,385,582,667,1090},{0,1,1,5,5,15,5,16,15,16,35,41,35,41,70,90,70,126,90,91,176,182,176,315,315,336,526,581,951},{0,0,1,1,5,5,5,5,15,16,15,17,35,41,35,45,70,70,90,45,100,102,176,196,315,207,350,385,667},{0,0,0,1,1,5,1,5,5,5,15,16,15,16,35,41,35,70,41,41,90,91,90,176,176,182,315,336,581},{0,0,0,0,1,1,1,1,5,5,5,5,15,16,15,17,35,35,41,17,45,45,90,100,176,102,196,207,385},{0,0,0,0,0,1,0,1,1,1,5,5,5,5,15,16,15,35,16,16,41,41,41,90,90,91,176,182,336},{0,0,0,0,0,0,1,1,0,5,0,5,0,15,0,15,0,0,35,17,35,45,70,70,126,100,126,196,350},{0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,15,0,0,15,16,35,41,35,70,70,90,126,176,315},{0,0,0,0,0,0,0,0,1,1,1,1,5,5,5,5,15,15,16,5,17,17,41,45,90,45,100,102,207},{0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,0,15,5,15,17,35,35,70,45,70,100,196},{0,0,0,0,0,0,T^4,0,0,0,1,1,1,1,5,5,5,15,5,5+T^4,16,16,16,41,41,41,90,91,182},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,5,5,15,16,15,35,35,41,70,90,176},{0,0,0,0,0,0,T^4,0,0,0,0,0,1,1,1,1,5,5,5,1+T^4,5,5,16,17,41,17,45,45,102},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,1,5,5,15,15,35,17,35,45,100},{T^4,0,0,0,0,0,6*T^4,T^4,0,T^4,0,0,0,0,1,1,1,5,1,1+6*T^4,5,5+T^4,5,16,16,16,41,41,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,5,5,5,15,15,16,35,41,90},{T^4,T^4,0,0,0,0,6*T^4,2*T^4,0,T^4,0,0,0,0,0,0,1,1,1,7*T^4,1,1+T^4,5,5,16,5,17,17,45},{5*T^4,T^4,T^4,0,0,0,20*T^4,6*T^4,0,6*T^4,0,T^4,0,T^4,0,0,0,1,0,21*T^4,1,1+6*T^4,1,5,5,5+T^4,16,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,15,5,15,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,1,5,5,17},{0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,1,1,5,5,16},{0,0,0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,1,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,0,0,0,6*T^4,0,T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,51)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & -2 & 2 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 4 & 6 & 3 & 2 & 5 & 4 & 1 & 3 & 4 & 0 & 3 & -1 & 2 & 2 & 1 & 1 & 4 & 0 & 3 & -1 & 0 & 2 & -1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, -2, -2}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{5, 6}, {4, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-2},{0,0,1},{1,1,2}},{{1,4,5},{0,4,5},{1,2,3},{1,2,5},{0,2,5},{0,2,3}},{1,3,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,1,-2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,2,6},{1,2,5},{1,2,4},{1,1,6},{1,2,3},{1,2,2},{1,1,5},{1,1,4},{1,2,1},{1,1,3},{0,1,4},{1,2,0},{0,1,3},{1,2,-1},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,4},{1,1,0},{0,0,3},{1,1,-1},{0,1,0},{0,0,2},{0,1,-1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,16,35,70,40,85,126,161,86,210,166,330,280,295,456,491,311,705,531,1045,775,860,1171,1332,1986},{0,1,5,5,15,35,16,40,70,85,40,126,86,210,161,166,280,295,171,456,311,705,491,531,775,860,1332},{0,0,1,1,5,15,5,16,35,40,16,70,40,126,85,86,161,166,87,280,171,456,295,311,491,531,860},{0,0,0,1,0,0,5,15,0,35,15,0,35,0,70,70,126,126,86,210,166,330,210,295,330,491,775},{0,0,0,0,1,5,1,5,15,16,5,35,16,70,40,40,85,86,40,161,87,280,166,171,295,311,531},{0,0,0,0,0,1,0,1,5,5,1,15,5,35,16,16,40,40,16,85,40,161,86,87,166,171,311},{0,0,0,0,0,0,1,5,0,15,5,0,15,0,35,35,70,70,40,126,86,210,126,166,210,295,491},{0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,15,35,35,16,70,40,126,70,86,126,166,295},{T^4,0,0,T^4,0,0,0,0,1,1,T^4,5,1,15,5,5,16,16,5+T^4,40,16,85,40,40,86,87,171},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,15,5,35,16,70,35,40,70,86,166},{0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,16,0,40,0,70,85,126,161,280},{5*T^4,T^4,0,5*T^4,0,0,T^4,0,0,0,5*T^4,1,T^4,5,1,1,5,5,1+5*T^4,16,5+T^4,40,16,16,40,40,87},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,5,0,16,0,35,40,70,85,161},{15*T^4,5*T^4,T^4,16*T^4,0,0,5*T^4,T^4,0,0,16*T^4,0,5*T^4,1,0,T^4,1,1,17*T^4,5,1+5*T^4,16,5,5+T^4,16,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,5,1,15,5,35,15,16,35,40,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,16,35,40,85},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,1,1,T^4,5,1,15,5,5,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,5*T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,5*T^4,1,T^4,5,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,15*T^4,0,0,5*T^4,T^4,0,0,T^4,0,0,0,0,0,0,0,16*T^4,0,5*T^4,1,0,T^4,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,58)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -2, -2}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {5, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 4, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1},{1,0,2},{0,1,2}},{{3,6,7},{0,6,7},{3,5,7},{4,5,7},{1,3,6},{2,4,5},{0,2,4},{0,1,6},{0,4,7}},{2,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,1,1},{1,-1,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,1,6},{0,2,6},{0,1,6},{1,1,5},{1,0,5},{0,2,5},{0,1,5},{1,1,4},{0,2,4},{1,0,4},{0,1,4},{1,1,3},{0,0,4},{0,2,3},{1,0,3},{1,1,2},{0,1,3},{0,0,3},{1,0,2},{0,2,2},{1,1,1},{0,1,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,2,5,6,5,10,15,15,21,31,35,37,35,55,70,75,95,120,70,126,155,206,231,287,397,406,701},{0,1,1,1,1,5,6,5,15,6,21,15,22,35,21,35,55,61,55,70,70,120,141,120,231,286,231,526},{0,0,1,0,1,0,5,0,0,5,15,0,21,0,15,0,35,55,35,0,0,70,120,70,126,231,126,406},{0,0,0,1,1,1,2,5,5,6,10,15,11,15,21,35,31,37,55,35,70,75,95,120,155,206,231,397},{0,0,0,0,1,0,1,0,0,5,5,0,10,0,15,0,15,31,35,0,0,35,75,70,70,155,126,287},{0,0,0,0,0,1,1,1,5,1,6,5,6,15,6,15,21,22,21,35,35,55,61,55,120,141,120,286},{0,0,0,0,0,0,1,0,0,1,5,0,6,0,5,0,15,21,15,0,0,35,55,35,70,120,70,231},{0,0,0,0,0,0,0,1,1,1,2,5,2,5,6,15,10,11,21,15,35,31,37,55,75,95,120,206},{0,0,0,0,0,0,0,0,1,0,1,1,1,5,1,5,6,6,6,15,15,21,22,21,55,61,55,141},{0,0,0,0,0,0,0,0,0,1,1,0,2,0,5,0,5,10,15,0,0,15,31,35,35,75,70,155},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,5,6,5,0,0,15,21,15,35,55,35,120},{0,0,T^4,0,0,0,0,0,0,0,0,1,T^4,1,1,5,2,2,6,5,15,10,11,21,31,37,55,95},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,0,15,0,0,35,0,70},{0,0,T^4,0,T^4,0,0,0,0,0,0,0,T^4,1,0,1,1,1,1,5,5,6,6,6,21,22,21,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,5,0,0,5,10,15,15,31,35,75},{0,0,5*T^4,0,T^4,0,T^4,0,0,0,0,0,5*T^4,0,0,1,0,T^4,1,1,5,2,2,6,10,11,21,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,5,6,5,15,21,15,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,5,5,10,15,31},{T^4,0,6*T^4,0,6*T^4,0,T^4,0,0,T^4,0,0,6*T^4,0,0,0,0,T^4,0,1,1,1,1,1,6,6,6,22},{T^4,T^4,17*T^4,0,6*T^4,0,5*T^4,0,0,T^4,T^4,0,17*T^4,0,0,0,0,5*T^4,0,0,1,0,T^4,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,6,5,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,1,1,2,5,10},{0,0,T^4,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,5*T^4,0,T^4,0,T^4,0,0,0,0,0,5*T^4,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,64)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & -1 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}-2 & -1 & -2 & -2 & 0 & -1 & 0 & -1 & -2 & -1 & -2 & 0 & -1 & -1 & -2 & 0 & 0 & -1 & -2 & 0 & -2 & -1 & -1 & 0 & 0 & 0 & -1 & -1 & 0 & -1 & 0 & -1 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 2 & 0 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 6 & 5 & 6 & 5 & 4 & 5 & 4 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, -1, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -2, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2}},{{2,4,5},{0,2,4},{2,3,5},{1,4,5},{1,3,5},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{0,1,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{-2,2,6},{-1,2,5},{-2,1,6},{-2,2,5},{0,2,4},{-1,1,5},{0,1,4},{-1,2,4},{-2,1,5},{-1,1,4},{-2,2,4},{0,2,3},{-1,0,4},{-1,2,3},{-2,1,4},{0,1,3},{0,2,2},{-1,1,3},{-2,2,3},{0,0,3},{-2,1,3},{-1,0,3},{-1,2,2},{0,1,2},{0,2,1},{0,0,2},{-1,1,2},{-1,0,2},{0,1,1},{-1,1,1},{0,0,1},{-1,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,5,3,4,6,9,10,19,15,13,29,25,31,28,35,55,35,43,75,85,55,79,75,124,125,196,175,245,280,390,335,545},{0,1,0,1,2,2,4,5,2,10,5,9,15,15,10,19,25,31,15,29,31,47,35,55,55,85,75,115,125,155,196,241,245,390},{0,0,1,0,T^2,2,3,0,5,9,0,3*T^2,19,0,15,13,6*T^2,25,0,28,35,55,0,35,10*T^2,79,55,125,75,105,175,245,140,335},{0,0,0,1,0,0,0,2,2,4,5,3,6,9,10,6,13,19,15,9,31,29,25,28,35,43,55,85,79,125,124,196,175,280},{0,0,0,0,1,0,2,1,0,2,1,5,3,5,2,10,15,10,5,15,10,15,15,31,35,47,31,47,75,75,115,115,155,241},{0,0,0,0,0,1,2,0,1,5,0,0,10,0,5,9,0,15,0,19,15,31,0,25,0,55,35,75,55,70,125,155,105,245},{0,0,0,0,0,0,1,0,0,1,0,0,2,0,1,5,0,5,0,10,5,10,0,15,0,31,15,31,35,35,75,75,70,155},{0,0,0,0,0,0,0,1,0,2,1,2,3,5,2,4,9,10,5,6,10,15,15,19,25,29,31,47,55,75,85,115,125,196},{0,0,0,0,0,0,0,0,1,2,0,T^2,4,0,5,3,3*T^2,9,0,6,15,19,0,13,6*T^2,28,25,55,35,55,79,125,75,175},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,1,2,0,5,0,4,5,10,0,9,0,19,15,31,25,35,55,75,55,125},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,3,4,5,0,10,6,9,6,13,9,19,29,28,55,43,85,79,124},{0,0,T^4,0,0,0,0,0,0,0,0,1,T^4,1,0,2,5,2,1,3,2,3,5,10,15,15,10,15,31,31,47,47,75,115},{0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,1,0,0,0,6*T^2,0,0,2,0,5,0,0,10*T^2,9,0,15,0,0,25,35,0,55},{0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,1,0,0,2,2,1,0,2,3,5,4,9,6,10,15,19,31,29,47,55,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^2,2,0,0,5,4,0,3,3*T^2,6,9,19,13,25,28,55,35,79},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,1,2,0,5,0,10,5,10,15,15,31,31,35,75},{0,0,5*T^4,0,0,T^4,0,0,T^4,0,0,0,5*T^4,0,0,0,1,0,0,T^4,0,T^4,1,2,5,3,2,3,10,10,15,15,31,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,0,2,0,4,5,10,9,15,19,31,25,55},{0,0,T^4,0,0,0,T^3,0,0,0,0,0,T^4,0,0,0,0,0,1,0,2,0,2,0,3,0,4,6,6,19,9,29,28,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,5,0,5,0,0,15,15,0,35},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,T^2,0,2,4,3,9,6,19,13,28},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,1,0,0,6*T^2,2,0,5,0,0,9,15,0,25},{0,0,5*T^4,0,0,T^4,0,0,T^4,0,0,0,5*T^4,0,0,0,0,0,0,T^4,0,T^4,1,0,2,0,2,3,4,10,6,15,19,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,5,5,10,10,15,31},{T^4,0,17*T^4,0,0,5*T^4,T^4,0,5*T^4,T^4,0,0,17*T^4,0,T^4,0,0,0,0,5*T^4,0,5*T^4,0,0,1,T^4,0,T^4,2,2,3,3,10,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,5,4,10,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,1,0,0,2,5,0,9},{0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,5,10},{0,0,T^4,0,0,0,T^3,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,2},{0,0,5*T^4,0,0,T^4,0,0,T^4,0,0,0,5*T^4,0,0,0,0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,65)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 6 & 6 & 5 & 4 & 5 & 5 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -2, -2}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,2},{0,1,2},{1,1,2}},{{2,3,4},{0,3,5},{3,4,5},{0,1,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (25): {{1,1,8},{1,1,7},{1,1,6},{1,0,6},{0,1,6},{1,1,5},{1,1,4},{1,0,5},{0,1,5},{0,1,4},{1,1,3},{1,0,4},{0,0,4},{0,1,3},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,16,16,35,70,40,40,85,126,85,101,161,161,210,280,201,280,330,365,456,456,617,985},{0,1,5,5,5,15,35,16,16,40,70,40,45,85,85,126,161,101,161,210,201,280,280,365,617},{0,0,1,1,1,5,15,5,5,16,35,16,17,40,40,70,85,45,85,126,101,161,161,201,365},{0,0,0,1,0,0,0,5,0,0,0,15,16,0,35,0,0,40,70,0,85,126,0,161,280},{0,0,0,0,1,0,0,0,5,15,0,0,16,35,0,0,70,40,0,0,85,0,126,161,280},{0,0,0,0,0,1,5,1,1,5,15,5,5,16,16,35,40,17,40,70,45,85,85,101,201},{0,0,0,0,0,0,1,0,0,1,5,1,1,5,5,15,16,5,16,35,17,40,40,45,101},{0,0,0,0,0,0,0,1,0,0,0,5,5,0,15,0,0,16,35,0,40,70,0,85,161},{0,0,0,0,0,0,0,0,1,5,0,0,5,15,0,0,35,16,0,0,40,0,70,85,161},{0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,0,15,5,0,0,16,0,35,40,85},{T^4,0,0,T^4,T^4,0,0,0,0,0,1,0,T^4,1,1,5,5,1,5,15,5,16,16,17,45},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,0,0,5,15,0,16,35,0,40,85},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,0,5,0,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,5,15,0,16,40},{5*T^4,T^4,0,5*T^4,5*T^4,0,0,T^4,T^4,0,0,0,5*T^4,0,0,1,1,T^4,1,5,1,5,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,5,16},{15*T^4,5*T^4,T^4,16*T^4,16*T^4,0,0,5*T^4,5*T^4,T^4,0,T^4,17*T^4,0,0,0,0,5*T^4,0,1,T^4,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,67)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 4 & 5 & 3 & 4 & 2 & 3 & 4 & 3 & 2 & 1 & 3 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -2, -2}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,2},{0,1,2}},{{3,4,5},{0,4,5},{0,2,5},{1,3,4},{0,1,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,-1,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,1,6},{1,0,6},{1,1,5},{0,1,6},{1,0,5},{1,1,4},{1,0,4},{0,1,5},{1,1,3},{0,1,4},{1,1,2},{1,0,3},{0,0,4},{0,1,3},{1,0,2},{1,1,1},{0,0,3},{1,0,1},{0,1,2},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,2,5,15,16,10,35,31,70,40,32,75,85,126,80,161,155,171,280,287,327,575},{0,1,0,1,5,0,15,5,0,15,0,35,31,35,70,0,75,126,70,155,210,126,287,490},{0,0,1,0,1,5,5,2,15,10,35,16,10,31,40,70,32,85,75,80,161,155,171,327},{0,0,0,1,0,0,0,5,0,15,0,0,16,35,0,0,40,0,70,85,0,126,161,280},{0,0,0,0,1,0,5,1,0,5,0,15,10,15,35,0,31,70,35,75,126,70,155,287},{0,0,0,0,0,1,1,0,5,2,15,5,2,10,16,35,10,40,31,32,85,75,80,171},{0,0,0,0,0,0,1,0,0,1,0,5,2,5,15,0,10,35,15,31,70,35,75,155},{0,0,0,0,0,0,0,1,0,5,0,0,5,15,0,0,16,0,35,40,0,70,85,161},{0,T^4,0,T^4,0,0,0,0,1,0,5,1,T^4,2,5,15,2,16,10,10,40,31,32,80},{0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,0,5,0,15,16,0,35,40,85},{0,5*T^4,0,5*T^4,T^4,0,0,T^4,0,0,1,0,5*T^4,0,1,5,T^4,5,2,2,16,10,10,32},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,2,15,5,10,35,15,31,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,0,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,2,15,5,10,31},{T^4,16*T^4,0,17*T^4,5*T^4,0,T^4,5*T^4,0,T^4,0,0,17*T^4,0,0,1,5*T^4,1,0,T^4,5,2,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,T^4,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,5,1,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,5*T^4,0,5*T^4,T^4,0,0,T^4,0,0,0,0,5*T^4,0,0,0,T^4,0,0,0,1,0,0,2},{0,0,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,68)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}-1 & 0 & -1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 1 & 0 \\ 6 & 5 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -2, -2}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 5}, {4, 5, 7}, {4, 6, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2}},{{2,4,5},{1,4,5},{2,3,5},{0,2,4},{0,1,4},{1,3,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,0,1},{0,1,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{-1,2,6},{0,2,5},{-1,1,6},{0,1,5},{-1,2,5},{-1,1,5},{0,2,4},{0,1,4},{-1,2,4},{0,0,4},{0,2,3},{-1,1,4},{-1,2,3},{0,1,3},{0,2,2},{-1,1,3},{0,0,3},{-1,2,2},{0,1,2},{-1,1,2},{0,0,2},{0,2,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,1,2,2,5,10,5,11,15,17,15,31,35,35,35,75,55,70,85,155,136,70,175,285,322,533},{0,1,0,2,1,2,5,10,5,15,15,10,15,31,35,31,47,35,75,75,115,70,155,241,287,453},{0,0,1,1,0,5,0,5,0,11,0,15,0,15,0,35,35,0,35,70,85,0,70,175,126,322},{0,0,0,1,0,1,0,5,0,10,0,5,0,15,0,15,31,0,35,35,75,0,70,155,126,287},{0,0,0,0,1,2,1,2,5,3,5,10,15,11,15,31,17,35,35,75,55,35,85,136,175,285},{0,0,0,0,0,1,0,1,0,2,0,5,0,5,0,15,11,0,15,35,35,0,35,85,70,175},{0,0,0,0,0,0,1,2,1,3,5,2,5,10,15,10,15,15,31,31,47,35,75,115,155,241},{0,0,0,0,0,0,0,1,0,2,0,1,0,5,0,5,10,0,15,15,31,0,35,75,70,155},{0,0,0,0,0,0,0,0,1,0,1,2,5,2,5,10,3,15,11,31,17,15,35,55,85,136},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,5,0,0,0,15,0,0,35,0,70},{0,0,T^4,0,0,0,0,0,0,T^4,1,0,1,2,5,2,3,5,10,10,15,15,31,47,75,115},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,2,0,5,15,11,0,15,35,35,85},{0,0,T^4,0,0,0,0,0,0,T^4,0,0,1,0,1,2,0,5,2,10,3,5,11,17,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,0,5,5,10,0,15,31,35,75},{0,0,5*T^4,T^4,0,T^4,0,0,0,5*T^4,0,0,0,0,1,0,T^4,1,2,2,3,5,10,15,31,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,2,0,5,11,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,35},{0,0,5*T^4,T^4,0,T^4,0,0,0,5*T^4,0,0,0,0,0,0,T^4,1,0,2,0,1,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,5,10,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{T^4,0,17*T^4,5*T^4,0,5*T^4,0,T^4,0,17*T^4,0,T^4,0,0,0,0,5*T^4,0,0,0,T^4,1,2,3,10,15},{0,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,5*T^4,T^4,0,T^4,0,0,0,5*T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,72)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 2 & 4 & 3 & 1 & 2 & 3 & 4 & 1 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 5 & 3 & 4 & 5 & 4 & 3 & 2 & 4 & 2 & 3 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -2}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,2,3}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,2,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,4,6},{1,3,6},{1,4,5},{1,2,6},{1,3,5},{1,4,4},{1,2,5},{1,4,3},{1,3,4},{1,1,5},{1,2,4},{1,3,3},{1,4,2},{1,1,4},{1,3,2},{1,2,3},{0,2,3},{1,1,3},{1,3,1},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,24,20,30,40,60,60,35,100,105,120,121,200,168,210,203,214,336,350,306,362,560,346,549,524,590,900,900,1380},{0,1,0,3,4,0,12,0,10,24,30,20,0,60,35,60,60,120,56,105,121,105,168,210,203,214,336,168,362,252,346,590,524,900},{0,0,1,0,3,4,6,10,12,10,24,30,20,40,60,60,60,100,105,120,100,121,210,200,150,203,350,214,306,346,362,549,590,900},{0,0,0,1,0,0,4,0,0,12,10,0,0,30,0,20,20,60,0,35,60,35,56,105,121,105,168,56,214,84,168,346,252,524},{0,0,0,0,1,0,3,0,4,6,12,10,0,24,20,30,30,60,35,60,60,60,105,120,100,121,210,105,203,168,214,362,346,590},{0,0,0,0,0,1,0,4,3,0,6,12,10,10,30,24,24,40,60,60,40,60,120,100,60,100,200,121,150,214,203,306,362,549},{0,0,0,0,0,0,1,0,0,3,4,0,0,12,0,10,10,30,0,20,30,20,35,60,60,60,105,35,121,56,105,214,168,346},{0,0,0,0,0,0,0,1,0,0,0,3,4,0,12,6,6,10,30,24,10,24,60,40,15,40,100,60,60,121,100,150,203,306},{0,0,0,0,0,0,0,0,1,0,3,4,0,6,10,12,12,24,20,30,24,30,60,60,40,60,120,60,100,105,121,203,214,362},{0,0,T^2,0,0,4*T^2,0,10*T^2,0,1,0,0,20*T^2,4,0,0,0,10,0,0,10,T^2,0,20,30,20,35,4*T^2,60,10*T^2,35,105,56,168},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,4,12,0,10,12,10,20,30,24,30,60,20,60,35,60,121,105,214},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,3,3,6,10,12,6,12,30,24,10,24,60,30,40,60,60,100,121,203},{T^3,3*T^3,0,6*T^3,0,0,0,0,0,0,0,0,1,0,3,0,T^3,0,12,6,3*T^3,6,24,10,6*T^3,10,40,24,15,60,40,60,100,150},{0,0,0,0,0,T^2,0,4*T^2,0,0,0,0,10*T^2,1,0,0,0,4,0,0,4,0,0,10,12,10,20,T^2,30,4*T^2,20,60,35,105},{0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,3,T^3,3,12,6,3*T^3,6,24,12,10,30,24,40,60,100},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,3,4,10,12,6,12,30,10,24,20,30,60,60,121},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,6,12,0,10,24,20,30,60,60,120},{0,0,0,0,0,0,0,T^2,0,0,0,0,4*T^2,0,0,0,0,1,0,0,1,0,0,4,3,4,10,0,12,T^2,10,30,20,60},{0,4*T^3,0,12*T^3,T^3,0,3*T^3,0,0,6*T^3,0,0,0,0,0,0,0,0,1,0,4*T^3,0,3,0,12*T^3,T^3,6,3,3*T^3,12,6,10,24,40},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,3,T^3,3,12,4,6,10,12,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,12,24,30,60},{0,0,0,4*T^3,0,0,T^3,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4*T^3,0,3,1,T^3,4,3,6,12,24},{T^5,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^5,0,0,0,0,0,0,1,0,1,4,0,3,0,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,12,10,30},{4*T^5,0,T^5,0,0,0,0,0,0,T^3,0,0,0,0,0,0,4*T^5,0,0,0,0,T^5,0,0,0,0,1,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,114)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 3 & 3 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 9 & 9 & 8 & 8 & 7 & 6 & 7 & 6 & 5 & 6 & 4 & 5 & 6 & 4 & 5 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {3, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,3}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{1,1,3},{1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,3,9},{2,2,9},{2,3,8},{2,2,8},{2,3,7},{2,3,6},{2,2,7},{2,2,6},{2,3,5},{1,2,6},{2,3,4},{2,2,5},{1,1,6},{2,2,4},{1,2,5},{1,1,5},{1,2,4},{1,2,3},{1,1,4},{1,1,3},{1,2,2},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,20,20,40,35,42,56,70,64,112,78,121,132,208,208,332,310,335,442,500,462,719,512,714,749,1056,1056,1504},{0,1,0,4,0,0,10,20,0,20,0,35,42,56,35,78,56,84,132,208,120,208,165,310,335,442,310,512,442,749,608,1056},{0,0,1,2,4,10,8,20,20,20,35,40,30,70,42,64,78,132,121,208,208,208,310,332,284,500,335,462,512,714,749,1056},{0,0,0,1,0,0,4,10,0,10,0,20,20,35,20,42,35,56,78,132,84,132,120,208,208,310,208,335,310,512,442,749},{0,0,0,0,1,4,2,8,10,8,20,20,12,40,20,30,42,78,64,121,132,121,208,208,164,332,208,284,335,462,512,714},{0,0,0,0,0,1,0,2,4,2,10,8,3,20,8,12,20,42,30,64,78,64,132,121,86,208,121,164,208,284,335,462},{0,0,0,0,0,0,1,4,0,4,0,10,8,20,10,20,20,35,42,78,56,78,84,132,121,208,132,208,208,335,310,512},{0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,8,10,20,20,42,35,42,56,78,64,132,78,121,132,208,208,335},{T^3,2*T^3,0,0,0,0,0,0,1,2*T^3,4,2,4*T^3,8,2,3,8,20,12,30,42,30+3*T^3,78,64,40+6*T^3,121,64,86,121,164,208,284},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40,35,42,56,70,64,112,78,121,132,208,208,332},{4*T^3,8*T^3,T^3,2*T^3,0,0,0,0,0,8*T^3,1,0,16*T^3,2,2*T^3,4*T^3,2,8,3,12,20,12+12*T^3,42,30,16+24*T^3,64,30+3*T^3,40+6*T^3,64,86,121,164},{0,T^3,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,2,4,10,8,20,20,20,35,42,30+3*T^3,78,42,64,78,121,132,208},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,20,0,35,42,56,35,78,56,132,84,208},{0,4*T^3,0,T^3,0,0,0,0,0,0,0,0,8*T^3,1,0,2*T^3,1,4,2,8,10,8,20,20,12+12*T^3,42,20,30+3*T^3,42,64,78,121},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,10,8,20,20,20,35,40,30,70,42,64,78,121,132,208},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,10,0,20,20,35,20,42,35,78,56,132},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8,10,8,20,20,12,40,20,30,42,64,78,121},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,2,10,8,3,20,8,12,20,30,42,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,8,20,10,20,20,42,35,78},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,8,10,20,20,42},{0,0,0,0,0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,1,2*T^3,4,2,4*T^3,8,2,3,8,12,20,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{0,0,0,0,0,0,0,0,0,4*T^3,0,0,8*T^3,0,T^3,2*T^3,0,0,0,0,0,8*T^3,1,0,16*T^3,2,2*T^3,4*T^3,2,3,8,12},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,0,0,8*T^3,1,0,2*T^3,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,141)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 3 & 0 & 3 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 9 & 8 & 9 & 7 & 6 & 8 & 7 & 6 & 5 & 6 & 5 & 4 & 6 & 4 & 5 & 4 & 3 & 5 & 2 & 4 & 3 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 5}, {4, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{-1,1,3}},{{0,2,3},{1,3,4},{2,3,4},{0,1,3}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{-1,1,3},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,2,9},{1,2,8},{0,2,9},{1,2,7},{1,2,6},{0,2,8},{0,2,7},{1,1,6},{1,2,5},{0,2,6},{1,1,5},{1,2,4},{0,1,6},{1,1,4},{0,2,5},{0,2,4},{1,1,3},{0,1,5},{1,1,2},{0,1,4},{1,0,3},{0,1,3},{1,0,2},{1,1,1},{0,1,2},{0,0,3},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,2,10,20,8,20,23,35,40,47,56,45,86,70,112,144,90,225,162,150,268,249,333,415,277,393,451,592,610,700,1040},{0,1,0,4,10,2,8,10,20,20,23,35,20,47,40,70,86,45,144,90,86,162,150,225,268,162,249,277,393,415,451,700},{0,0,1,0,0,4,10,1,0,20,4,0,23,10,35,56,20,47,35,86,23,144,47,56,225,150,86,249,144,333,393,592},{0,0,0,1,4,0,2,4,10,8,10,20,8,23,20,40,47,20,86,45,47,90,86,144,162,90,150,162,249,268,277,451},{0,0,0,0,1,0,0,1,4,2,4,10,2,10,8,20,23,8,47,20,23,45,47,86,90,45,86,90,150,162,162,277},{0,0,0,0,0,1,4,0,0,10,1,0,10,4,20,35,10,23,20,47,10,86,23,35,144,86,47,150,86,225,249,393},{0,0,0,0,0,0,1,0,0,4,0,0,4,1,10,20,4,10,10,23,4,47,10,20,86,47,23,86,47,144,150,249},{0,0,0,0,0,0,0,1,0,0,4,0,2,10,0,0,20,8,35,20,23,40,47,56,70,45,86,90,144,112,162,268},{T^3,0,2*T^3,0,0,0,0,3*T^3,1,0,1,4,5*T^3,4,2,8,10,2,23,8,10+6*T^3,20,23,47,45,20+9*T^3,47,45,86,90,90,162},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,10,1,4,4,10,1,23,4,10,47,23,10,47,23,86,86,150},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,2,20,8,10,20,23,35,40,20,47,45,86,70,90,162},{4*T^3,T^3,8*T^3,0,0,2*T^3,0,12*T^3,0,0,3*T^3,1,20*T^3,1,0,2,4,5*T^3,10,2,4+24*T^3,8,10+6*T^3,23,20,8+36*T^3,23,20+9*T^3,47,45,45,90},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,10,1,20,4,0,35,23,10,47,20,56,86,144},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,2,4,8,10,20,20,8,23,20,47,40,45,90},{0,0,T^3,0,0,0,0,T^3,0,0,0,0,3*T^3,0,1,4,0,1,1,4,3*T^3,10,1,4,23,10+6*T^3,4,23,10,47,47,86},{0,0,4*T^3,0,0,T^3,0,4*T^3,0,0,T^3,0,12*T^3,0,0,1,0,3*T^3,0,1,12*T^3,4,3*T^3,1,10,4+24*T^3,1,10+6*T^3,4,23,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,2,4,10,8,2,10,8,23,20,20,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10,1,0,20,10,4,23,10,35,47,86},{0,0,0,0,0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,0,1,0,3*T^3,0,1,4,2,5*T^3,4,2,10,8,8,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,4,1,10,4,20,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,2,10,8,20,0,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,4,1,10,10,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,10,0,8,20},{0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,8*T^3,0,0,0,0,2*T^3,0,0,12*T^3,0,3*T^3,1,0,20*T^3,1,5*T^3,4,2,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,1,3*T^3,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,0,0,T^3,0,0,4*T^3,0,T^3,0,0,12*T^3,0,3*T^3,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,142)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 6 & 0 & 3 & 0 & 1\end{pmatrix}$
40: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 15 & 14 & 13 & 12 & 12 & 11 & 11 & 10 & 10 & 9 & 9 & 8 & 9 & 7 & 8 & 8 & 7 & 6 & 7 & 6 & 6 & 5 & 6 & 4 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{1,2,6}},{{2,3,4},{0,1,4},{1,3,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,3},{1,2,6},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (40): {{1,4,15},{1,4,14},{1,4,13},{1,4,12},{1,3,12},{1,4,11},{1,3,11},{1,4,10},{1,3,10},{1,3,9},{1,2,9},{1,3,8},{0,2,9},{1,3,7},{1,2,8},{0,2,8},{1,2,7},{1,2,6},{0,2,7},{0,2,6},{1,1,6},{1,2,5},{0,1,6},{1,2,4},{0,2,5},{1,1,5},{0,1,5},{0,2,4},{1,1,4},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,20,22,35,43,56,76,124,127,190,128,277,202,206,307,448,317,468,452,631,474,862,666,647,690,918,902,978,1227,1351,1632,1359,2127,1822,1854,2404,2484,3270},{0,1,4,10,10,20,22,35,43,76,76,124,76,190,127,128,202,307,206,317,307,448,317,631,468,452,474,666,647,690,902,978,1227,978,1632,1351,1359,1822,1854,2484},{0,0,1,4,4,10,10,20,22,43,43,76,43,124,76,76,127,202,128,206,202,307,206,448,317,307,317,468,452,474,647,690,902,690,1227,978,978,1351,1359,1854},{0,0,0,1,1,4,4,10,10,22,22,43,22,76,43,43,76,127,76,128,127,202,128,307,206,202,206,317,307,317,452,474,647,474,902,690,690,978,978,1359},{0,0,0,0,1,0,4,0,10,20,22,35,22,56,43,43,76,124,76,124,127,190,128,277,190,202,206,277,307,317,448,468,631,474,862,666,690,918,978,1351},{T^3,0,0,0,2*T^3,1,1,4,4,10,10+3*T^3,22,10+4*T^3,43,22,22,43,76,43,76,76+4*T^3,127,76+6*T^3,202,128,127,128,206,202,206,307,317,452,317+8*T^3,647,474,474,690,690,978},{0,0,0,0,0,0,1,0,4,10,10,20,10,35,22,22,43,76,43,76,76,124,76,190,124,127,128,190,202,206,307,317,448,317,631,468,474,666,690,978},{4*T^3,T^3,0,0,8*T^3,0,2*T^3,1,1,4,4+12*T^3,10,4+16*T^3,22,10+3*T^3,10+4*T^3,22,43,22,43,43+16*T^3,76,43+24*T^3,127,76,76+4*T^3,76+6*T^3,128,127,128,202,206,307,206+32*T^3,452,317,317+8*T^3,474,474,690},{0,0,0,0,0,0,0,0,1,4,4,10,4,20,10,10,22,43,22,43,43,76,43,124,76,76,76,124,127,128,202,206,307,206,448,317,317,468,474,690},{0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,22,10,22,22,43,22,76,43,43,43,76,76,76,127,128,202,128,307,206,206,317,317,474},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,20,10,20,22,35,22,56,35,43,43,56,76,76,124,124,190,128,277,190,206,277,317,468},{0,0,0,0,T^3,0,0,0,0,0,2*T^3,1,2*T^3,4,1,1,4,10,4,10,10+3*T^3,22,10+4*T^3,43,22,22,22,43,43,43,76,76,127,76+6*T^3,202,128,128,206,206,317},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,0,22,0,35,0,43,56,0,76,0,124,0,127,0,190,202,277,307,448},{0,0,0,0,4*T^3,0,T^3,0,0,0,8*T^3,0,8*T^3,1,2*T^3,2*T^3,1,4,1,4,4+12*T^3,10,4+16*T^3,22,10,10+3*T^3,10+4*T^3,22,22,22,43,43,76,43+24*T^3,127,76,76+6*T^3,128,128,206},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,10,4,10,10,20,10,35,20,22,22,35,43,43,76,76,124,76,190,124,128,190,206,317},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,0,10,0,20,0,22,35,0,43,0,76,0,76,0,124,127,190,202,307},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,4,10,4,20,10,10,10,20,22,22,43,43,76,43,124,76,76,124,128,206},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,10,4,4,4,10,10,10,22,22,43,22,76,43,43,76,76,128},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,4,0,10,0,10,20,0,22,0,43,0,43,0,76,76,124,127,202},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,4,10,0,10,0,22,0,22,0,43,43,76,76,127},{0,0,0,T^2,0,4*T^2,0,10*T^2,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,1,0,4*T^2,4,4,10*T^2,10,10,20,20,35,22,56,35,43,56,76,124},{0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,2*T^3,1,2*T^3,4,1,1,1,4,4,4,10,10,22,10+4*T^3,43,22,22,43,43,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20,0,22,0,35,43,56,76,124},{0,0,0,0,0,0,0,0,0,0,4*T^3,0,4*T^3,0,T^3,T^3,0,0,0,0,8*T^3,0,8*T^3,1,0,2*T^3,2*T^3,1,1,1,4,4,10,4+16*T^3,22,10,10+4*T^3,22,22,43},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,1,0,1,4,0,4,0,10,0,10+3*T^3,0,22,22,43,43,76},{T^5,0,0,0,0,T^2,0,4*T^2,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,T^2,1,1,4*T^2,4,4,10,10,20,10,35,20,22,35,43,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,10,0,20,22,35,43,76},{0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,8*T^3,0,0,0,2*T^3,1,0,1,0,4,0,4+12*T^3,0,10,10+3*T^3,22,22,43},{4*T^5,T^5,0,0,0,0,0,T^2,0,0,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,T^2,1,1,4,4,10,4,20,10,10,20,22,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,10,20,22,43},{10*T^5,4*T^5,T^5,0,0,0,0,0,0,0,0,0,10*T^5,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,10,22},{20*T^5,10*T^5,4*T^5,T^5,0,0,0,0,0,0,0,0,20*T^5,0,0,10*T^5,0,0,4*T^5,T^5,T^3,0,T^3,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{35*T^5,20*T^5,10*T^5,4*T^5,0,T^5,0,0,0,0,0,0,35*T^5,0,0,20*T^5,0,0,10*T^5,4*T^5,4*T^3,0,4*T^3,0,T^5,T^3,T^3,0,0,0,0,0,0,8*T^3,1,0,2*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,0,T^3,0,0,0,0,0,0,8*T^3,0,0,2*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,157)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 3 & 0 & 3 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 12 & 11 & 10 & 9 & 9 & 8 & 9 & 7 & 8 & 8 & 7 & 6 & 7 & 6 & 5 & 6 & 4 & 5 & 6 & 4 & 5 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{1,1,3}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,1,3},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (34): {{2,3,12},{2,3,11},{2,3,10},{2,3,9},{2,2,9},{2,3,8},{1,2,9},{2,3,7},{2,2,8},{1,2,8},{2,2,7},{2,2,6},{1,2,7},{1,2,6},{2,2,5},{1,1,6},{2,2,4},{1,2,5},{0,1,6},{1,2,4},{1,1,5},{0,1,5},{1,1,4},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,20,21,35,23,56,39,47,66,104,86,144,155,147,221,225,150,333,237,249,363,532,393,592,751,598,1027,856,880,1195,1255,1739},{0,1,4,10,10,20,10,35,21,23,39,66,47,86,104,86,155,144,86,225,147,150,237,363,249,393,532,393,751,592,598,856,880,1255},{0,0,1,4,4,10,4,20,10,10,21,39,23,47,66,47,104,86,47,144,86,86,147,237,150,249,363,249,532,393,393,592,598,880},{0,0,0,1,1,4,1,10,4,4,10,21,10,23,39,23,66,47,23,86,47,47,86,147,86,150,237,150,363,249,249,393,393,598},{0,0,0,0,1,0,1,0,4,4,10,20,10,20,35,23,56,35,23,56,47,47,86,144,86,144,225,150,333,225,249,333,393,592},{T^3,0,0,0,T^3,1,3*T^3,4,1,1,4,10,4,10,21,10+3*T^3,39,23,10+6*T^3,47,23,23,47,86,47,86,147,86+6*T^3,237,150,150,249,249,393},{0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,21,0,35,23,56,39,47,66,104,86,144,155,147,221,225,237,333,363,532},{4*T^3,T^3,0,0,4*T^3,0,12*T^3,1,T^3,3*T^3,1,4,1,4,10,4+12*T^3,21,10,4+24*T^3,23,10+3*T^3,10+6*T^3,23,47,23,47,86,47+24*T^3,147,86,86+6*T^3,150,150,249},{0,0,0,0,0,0,0,0,1,1,4,10,4,10,20,10,35,20,10,35,23,23,47,86,47,86,144,86,225,144,150,225,249,393},{0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,10,0,20,10,35,21,23,39,66,47,86,104,86,155,144,147,225,237,363},{0,0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,4,20,10,10,23,47,23,47,86,47,144,86,86,144,150,249},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,1,10,4,4,10,23,10,23,47,23,86,47,47,86,86,150},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,4,20,10,10,21,39,23,47,66,47,104,86,86,144,147,237},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,1,10,4,4,10,21,10,23,39,23,66,47,47,86,86,147},{0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,1,3*T^3,4,1,3*T^3,4,1,1,4,10,4,10,23,10+6*T^3,47,23,23,47,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,10,20,10,20,35,23,56,35,47,56,86,144},{0,0,0,0,4*T^3,0,4*T^3,0,T^3,T^3,0,0,0,0,0,12*T^3,1,0,12*T^3,1,3*T^3,3*T^3,1,4,1,4,10,4+24*T^3,23,10,10+6*T^3,23,23,47},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,1,3*T^3,4,1,1,4,10,4,10,21,10+3*T^3,39,23,23,47,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,21,0,35,39,56,66,104},{0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,4*T^3,0,0,12*T^3,1,T^3,3*T^3,1,4,1,4,10,4+12*T^3,21,10,10+3*T^3,23,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,10,4,10,20,10,35,20,23,35,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,10,0,20,21,35,39,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,10,20,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,10,10,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,10,20,21,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,10,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,T^3,0,0,0,0,0,0,0,1,3*T^3,4,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,4*T^3,0,T^3,T^3,0,0,0,0,0,12*T^3,1,0,3*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,4*T^3,0,0,T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,160)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 1 & 3 & 2 & 0 & 1 & 3 & 0 & 2 & 1 & 3 & 0 & 2 & 2 & 3 & 1 & 0 & 2 & 1 & 0 & 2 & 1 & 3 & 2 & 0 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 0 \\ 6 & 6 & 6 & 5 & 5 & 6 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, -1, 1, 1, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,3},{1,0,4}},{{1,2,4},{0,1,4},{2,3,5},{0,4,5},{0,3,5},{2,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{0,-1,1},{0,1,0},{0,1,0},{1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{1,3,6},{1,2,6},{1,1,6},{1,3,5},{1,2,5},{1,0,6},{1,1,5},{1,3,4},{1,0,5},{1,2,4},{1,1,4},{1,3,3},{1,0,4},{1,2,3},{0,2,3},{1,3,2},{1,1,3},{1,0,3},{1,2,2},{0,1,3},{0,0,3},{0,2,2},{1,1,2},{1,3,1},{1,2,1},{1,0,2},{0,1,2},{0,0,2},{1,1,1},{0,2,1},{1,0,1},{0,1,1},{0,0,1},{0,2,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,6,6,15,10,28,21,45,46,81,56,126,111,112,126,186,281,231,189,287,237,371,252,434,546,386,574,672,455,966,718,1047,812,1245,1782},{0,1,3,1,6,6,15,6,28,21,46,21,81,56,56,56,111,186,126,112,189,127,231,126,252,371,237,386,434,258,672,455,718,483,812,1245},{0,0,1,0,1,3,6,1,15,6,21,6,46,21,21,21,56,111,56,56,112,56,126,56,126,231,127,237,252,127,434,258,455,258,483,812},{0,0,0,1,3,0,6,6,10,15,28,21,45,46,46,56,81,126,111,81,126,112,186,126,231,281,189,287,371,237,546,386,574,455,718,1047},{0,0,0,0,1,0,3,1,6,6,15,6,28,21,21,21,46,81,56,46,81,56,111,56,126,186,112,189,231,127,371,237,386,258,455,718},{T^2,0,0,3*T^2,0,1,1,6*T^2,6,1,6,1+10*T^2,21,6,6+T^2,6+15*T^2,21,56,21,21,56,21+3*T^2,56,21+21*T^2,56,126,56,127,126,56+6*T^2,252,127,258,127+10*T^2,258,483},{0,0,0,0,0,0,1,0,3,1,6,1,15,6,6,6,21,46,21,21,46,21,56,21,56,111,56,112,126,56,231,127,237,127,258,455},{0,0,0,0,0,0,0,1,0,3,6,6,10,15,15,21,28,45,46,28,45,46,81,56,111,126,81,126,186,112,281,189,287,237,386,574},{0,0,0,T^2,0,0,0,3*T^2,1,0,1,6*T^2,6,1,1,1+10*T^2,6,21,6,6,21,6+T^2,21,6+15*T^2,21,56,21,56,56,21+3*T^2,126,56,127,56+6*T^2,127,258},{0,0,0,0,0,0,0,0,0,1,3,1,6,6,6,6,15,28,21,15,28,21,46,21,56,81,46,81,111,56,186,112,189,127,237,386},{0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,1,6,15,6,6,15,6,21,6,21,46,21,46,56,21,111,56,112,56,127,237},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,6,10,15,6,10,15,28,21,46,45,28,45,81,46,126,81,126,112,189,287},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,1,0,0,6*T^2,1,6,1,1,6,1,6,1+10*T^2,6,21,6,21,21,6+T^2,56,21,56,21+3*T^2,56,127},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,6,6,3,6,6,15,6,21,28,15,28,46,21,81,46,81,56,112,189},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6,6,0,0,0,0,15,28,0,21,0,46,81,56,111,186},{0,T^3,3*T^3,0,0,6*T^3,0,0,0,0,0,0,0,0,0,1,0,0,3,T^3,3*T^3,3,6,6,15,10,6,10,28,15,45,28,45,46,81,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,1,3,1,6,1,6,15,6,15,21,6,46,21,46,21,56,112},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,0,1,0,1,6*T^2,1,6,1,6,6,1,21,6,21,6+T^2,21,56},{0,0,T^3,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^3,1,3,1,6,6,3,6,15,6,28,15,28,21,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,0,0,6,15,0,6,0,21,46,21,56,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,6,0,1,0,6,21,6,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6,0,6,0,15,28,21,46,81},{T^5,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,1,0,1,3,1,3,6,1,15,6,15,6,21,46},{0,3*T^3,10*T^3,0,T^3,21*T^3,3*T^3,0,6*T^3,0,0,0,0,0,0,0,0,0,0,3*T^3,10*T^3,0,0,1,3,0,T^3,3*T^3,6,3,10,6,10,15,28,45},{T^5,0,3*T^3,0,0,10*T^3,T^3,0,3*T^3,0,0,0,0,0,T^5,0,0,0,0,0,3*T^3,0,0,0,1,0,0,T^3,3,1,6,3,6,6,15,28},{3*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,0,3*T^5,T^2,0,0,0,T^5,0,0,0,3*T^2,0,1,0,1,1,0,6,1,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,0,6,15,6,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,6,1,6,21},{6*T^5,T^5,0,T^5,0,3*T^3,0,0,T^3,0,0,0,0,0,6*T^5,0,0,0,0,T^5,0,T^5,0,0,0,0,0,0,1,0,3,1,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6,6,15,28},{15*T^5,6*T^5,T^5,3*T^5,T^5,0,0,0,0,0,0,0,0,0,15*T^5,0,0,0,0,6*T^5,T^5,3*T^5,0,T^2,0,0,T^5,0,0,0,1,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,179)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 3 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 9 & 9 & 8 & 8 & 7 & 7 & 6 & 6 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, -1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3}},{{0,2,4},{2,3,4},{0,1,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,3},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,2,9},{0,2,9},{1,2,8},{0,2,8},{1,2,7},{0,2,7},{1,2,6},{0,2,6},{1,1,6},{0,1,6},{1,2,5},{1,1,5},{0,2,5},{0,1,5},{1,2,4},{1,1,4},{0,2,4},{0,1,4},{1,1,3},{0,1,3},{1,0,3},{1,1,2},{0,0,3},{0,1,2},{1,0,2},{0,0,2},{1,1,1},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,9,15,25,35,55,37,59,70,80,105,123,126,156,182,232,280,404,283,470,410,660,485,687,747,792,1024,1099,1240,1688},{0,1,1,5,5,15,15,35,15,37,35,37,70,80,70,80,126,156,156,280,156,280,283,470,283,485,470,485,747,792,792,1240},{0,0,1,2,5,9,15,25,15,25,35,37,55,59,70,80,105,123,156,232,156,280,232,404,283,410,470,485,660,687,792,1099},{0,0,0,1,1,5,5,15,5,15,15,15,35,37,35,37,70,80,80,156,80,156,156,280,156,283,280,283,470,485,485,792},{0,0,0,0,1,2,5,9,5,9,15,15,25,25,35,37,55,59,80,123,80,156,123,232,156,232,280,283,404,410,485,687},{0,0,0,0,0,1,1,5,1,5,5,5,15,15,15,15,35,37,37,80,37,80,80,156,80,156,156,156,280,283,283,485},{0,0,0,0,0,0,1,2,1,2,5,5,9,9,15,15,25,25,37,59,37,80,59,123,80,123,156,156,232,232,283,410},{0,0,0,0,0,0,0,1,0,1,1,1,5,5,5,5,15,15,15,37,15,37,37,80,37,80,80,80,156,156,156,283},{0,0,0,0,0,0,0,0,1,2,0,5,0,9,0,15,0,25,35,55,37,70,59,105,80,123,126,156,182,232,280,404},{0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,15,15,35,15,35,37,70,37,80,70,80,126,156,156,280},{0,T^3,0,0,0,0,0,0,0,2*T^3,1,1,2,2,5,5,9,9,15,25,15,37,25+3*T^3,59,37,59,80,80,123,123,156,232},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,5,0,9,15,25,15,35,25,55,37,59,70,80,105,123,156,232},{T^4,0,0,0,0,0,0,0,2*T^4,0,0,0,1,1,1,1,5,5,5,15,5+3*T^4,15,15,37,15,37,37,37,80,80,80,156},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15,5,15,15,35,15,37,35,37,70,80,80,156},{T^4,3*T^3,0,T^3,0,0,0,0,2*T^4,6*T^3,0,0,0,2*T^3,1,1,2,2,5,9,5+3*T^4,15,9+9*T^3,25,15,25+3*T^3,37,37,59,59,80,123},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9,5,15,9,25,15,25,35,37,55,59,80,123},{5*T^4,T^4,T^4,0,0,0,0,0,10*T^4,2*T^4,0,2*T^4,0,0,0,0,1,1,1,5,1+15*T^4,5,5+3*T^4,15,5+3*T^4,15,15,15,37,37,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,1,5,5,15,5,15,15,15,35,37,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,5,2,9,5,9,15,15,25,25,37,59},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,1,5,5,5,15,15,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,5,9,0,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,2*T^3,2,1,2,5,5,9,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,1,0,1,1,1,5,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,T^4,3*T^3,0,0,0,T^3,0,0,0,0,0,0,2*T^4,0,6*T^3,0,0,2*T^3,1,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,5*T^4,T^4,0,T^4,0,0,0,0,0,0,0,0,10*T^4,0,2*T^4,0,2*T^4,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,209)$ |
3 |
25 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -2 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}3 & 2 & 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 5 & 2 & 4 & 1 & 3 & 3 & 0 & 5 & 2 & -1 & 2 & 4 & 1 & 1 & 3 & 3 & 0 & 5 & 2 & -1 & 2 & 4 & 1 & 1 & 3 & 3 & 0 & 2 & 2 & -1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (25): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 1, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{0,1,3},{-1,1,3}},{{0,3,4},{0,1,2},{1,4,5},{3,4,5},{0,1,4},{0,2,3}},{6,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-2},{1,0,0},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{3,0,3},{2,1,5},{3,0,2},{2,1,4},{3,0,1},{2,1,3},{2,0,3},{3,0,0},{1,1,5},{2,1,2},{3,0,-1},{2,0,2},{1,1,4},{2,1,1},{2,0,1},{1,1,3},{1,0,3},{2,0,0},{0,1,5},{1,1,2},{2,0,-1},{1,0,2},{0,1,4},{1,1,1},{1,0,1},{0,1,3},{0,0,3},{1,0,0},{0,1,2},{0,0,2},{1,0,-1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,4,10,10,13,20,13,20,35,32,32,35,65,65,71,116,71,116,189,140,140,189,249,249,259,408,408,448,627,627,727,1116},{0,1,1,4,4,10,10,10,13,20,20,23,32,35,47,65,65,86,71,116,144,122,140,189,213,249,249,348,408,418,537,627,667,1016},{0,0,1,1,4,4,4,10,4,10,20,13,13,20,32,32,32,65,32,65,116,71,71,116,140,140,140,249,249,259,408,408,448,727},{0,0,0,1,1,4,4,4,4,10,10,10,13,20,23,32,32,47,32,65,86,65,71,116,122,140,140,213,249,249,348,408,418,667},{0,0,0,0,1,1,1,4,1,4,10,4,4,10,13,13,13,32,13,32,65,32,32,65,71,71,71,140,140,140,249,249,259,448},{0,0,0,0,0,1,1,1,1,4,4,4,4,10,10,13,13,23,13,32,47,32,32,65,65,71,71,122,140,140,213,249,249,418},{0,0,0,0,0,0,1,0,1,0,0,4,4,0,10,10,13,20,13,20,35,32,32,35,65,65,71,116,116,140,189,189,249,408},{0,0,0,0,0,0,0,1,0,1,4,1,1,4,4,4,4,13,4,13,32,13,13,32,32,32,32,71,71,71,140,140,140,259},{0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10,10,10,13,20,20,23,32,35,47,65,65,86,116,122,144,189,213,348},{T^3,0,0,0,0,0,3*T^3,0,0,1,1,1,1,4,4,4,4+6*T^3,10,4,13,23,13,13,32,32,32,32+10*T^3,65,71,71,122,140,140,249},{T^3,T^3,0,0,0,0,3*T^3,0,3*T^3,0,1,0,0,1,1,1,1+6*T^3,4,1+6*T^3,4,13,4,4,13,13,13,13+10*T^3,32,32,32,71,71,71,140},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,4,4,10,4,10,20,13,13,20,32,32,32,65,65,71,116,116,140,249},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,4,4,10,10,10,13,20,23,32,32,47,65,65,86,116,122,213},{4*T^3,T^3,T^3,0,0,0,12*T^3,0,3*T^3,0,0,3*T^3,0,1,1,1,1+24*T^3,4,1+6*T^3,4,10,4+6*T^3,4,13,13,13,13+40*T^3,32,32,32+10*T^3,65,71,71,140},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,1,4,10,4,4,10,13,13,13,32,32,32,65,65,71,140},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,4,4,4,4,10,10,13,13,23,32,32,47,65,65,122},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,4,0,10,10,13,20,20,32,35,35,65,116},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,1,4,4,4,4,13,13,13,32,32,32,71},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10,10,10,20,23,20,35,47,86},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,3*T^3,0,0,1,1,1,1,4,4,4,4+6*T^3,10,13,13,23,32,32,65},{0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,3*T^3,0,3*T^3,0,1,0,0,1,1,1,1+6*T^3,4,4,4,13,13,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,4,4,10,10,13,20,20,32,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,4,10,10,10,20,23,47},{0,0,0,0,0,0,4*T^3,0,T^3,0,0,T^3,0,0,0,0,12*T^3,0,3*T^3,0,0,3*T^3,0,1,1,1,1+24*T^3,4,4,4+6*T^3,10,13,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,10,10,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,10,10,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,3*T^3,0,1,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,1,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,T^3,0,0,T^3,0,0,0,0,12*T^3,0,0,3*T^3,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,210)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -2 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
39: $\begin{pmatrix}2 & 1 & 0 & -1 & 2 & 1 & 0 & 2 & -1 & 1 & 0 & 2 & -1 & 2 & 1 & 0 & 1 & 0 & -1 & 2 & 1 & -1 & 2 & 1 & 0 & 0 & -1 & 2 & -1 & 2 & 1 & 1 & 0 & -1 & 0 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 6 & 6 & 5 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -2, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,3}},{{0,2,4},{1,3,4},{0,1,4},{2,3,4}},{1,1,3})
Cox degrees: {{0,0,1},{0,0,1},{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (39): {{2,1,6},{1,1,6},{0,1,6},{-1,1,6},{2,1,5},{1,1,5},{0,1,5},{2,1,4},{-1,1,5},{1,1,4},{0,1,4},{2,1,3},{-1,1,4},{2,0,3},{1,1,3},{0,1,3},{1,0,3},{0,0,3},{-1,1,3},{2,1,2},{1,1,2},{-1,0,3},{2,0,2},{1,0,2},{0,1,2},{0,0,2},{-1,1,2},{2,1,1},{-1,0,2},{2,0,1},{1,1,1},{1,0,1},{0,1,1},{-1,1,1},{0,0,1},{-1,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,10,9,19,33,39,51,69,109,119,159,120,189,279,192,285,389,294,434,399,303,453,609,642,819,630,870,669,882,951,1190,1554,1299,1713,1337,1827,2421},{0,1,3,6,3,9,19,19,33,39,69,69,109,69,119,189,120,192,279,189,294,285,192,303,434,453,609,434,642,453,630,669,882,1190,951,1299,951,1337,1827},{0,0,1,3,1,3,9,9,19,19,39,39,69,39,69,119,69,120,189,119,189,192,120,192,294,303,434,294,453,303,434,453,630,882,669,951,669,951,1337},{T^2,0,0,1,3*T^2,1,3,3+6*T^2,9,9,19,19+10*T^2,39,19+11*T^2,39,69,39,69,119,69+15*T^2,119,120,69+18*T^2,120,189,192,294,189+21*T^2,303,192+27*T^2,294,303,434,630,453,669,453+38*T^2,669,951},{0,0,0,0,1,3,6,9,10,19,33,39,51,39,69,109,69,109,159,119,189,159,120,192,279,285,389,294,399,303,434,453,609,819,642,870,669,951,1299},{0,0,0,0,0,1,3,3,6,9,19,19,33,19,39,69,39,69,109,69,119,109,69,120,189,192,279,189,285,192,294,303,434,609,453,642,453,669,951},{0,0,0,0,0,0,1,1,3,3,9,9,19,9,19,39,19,39,69,39,69,69,39,69,119,120,189,119,192,120,189,192,294,434,303,453,303,453,669},{0,0,0,0,0,0,0,1,0,3,6,9,10,9,19,33,19,33,51,39,69,51,39,69,109,109,159,119,159,120,189,192,279,389,285,399,303,453,642},{0,0,0,0,T^2,0,0,3*T^2,1,1,3,3+6*T^2,9,3+6*T^2,9,19,9,19,39,19+10*T^2,39,39,19+11*T^2,39,69,69,119,69+15*T^2,120,69+18*T^2,119,120,189,294,192,303,192+27*T^2,303,453},{0,0,0,0,0,0,0,0,0,1,3,3,6,3,9,19,9,19,33,19,39,33,19,39,69,69,109,69,109,69,119,120,189,279,192,285,192,303,453},{0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,9,3,9,19,9,19,19,9,19,39,39,69,39,69,39,69,69,119,189,120,192,120,192,303},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,3,6,10,9,19,10,9,19,33,33,51,39,51,39,69,69,109,159,109,159,120,192,285},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,1,3*T^2,1,3,1,3,9,3+6*T^2,9,9,3+6*T^2,9,19,19,39,19+10*T^2,39,19+11*T^2,39,39,69,119,69,120,69+18*T^2,120,192},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6,0,0,0,10,9,19,0,33,0,0,51,39,0,69,0,0,109,159,119,189,279},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,6,3,9,6,3,9,19,19,33,19,33,19,39,39,69,109,69,109,69,120,192},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,3,1,3,9,9,19,9,19,9,19,19,39,69,39,69,39,69,120},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,0,6,3,9,0,19,0,0,33,19,0,39,0,0,69,109,69,119,189},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,3,0,9,0,0,19,9,0,19,0,0,39,69,39,69,119},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,0,1,3*T^2,1,1,3*T^2,1,3,3,9,3+6*T^2,9,3+6*T^2,9,9,19,39,19,39,19+11*T^2,39,69},{0,0,T^3,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,3,3*T^3,1,3,6,6,10,9,10,9,19,19,33,51,33,51,39,69,109},{T^5,0,0,T^3,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,1,T^3,0,1,3,3,6,3,6,3,9,9,19,33,19,33,19,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,3*T^2,1,0,3,0,0,9,3+6*T^2,0,9,0,0,19,39,19+10*T^2,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,0,10,9,0,19,0,0,33,51,39,69,109},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,3,0,9,0,0,19,33,19,39,69},{3*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,3*T^5,0,0,T^5,0,0,0,0,0,0,0,1,1,3,1,3,1,3,3,9,19,9,19,9,19,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,0,0,9,19,9,19,39},{6*T^5,3*T^5,T^5,0,0,0,0,0,0,0,0,0,0,6*T^5,0,0,3*T^5,T^5,0,T^2,0,0,T^2,0,0,0,1,3*T^2,1,3*T^2,1,1,3,9,3,9,3+6*T^2,9,19},{3*T^5,T^5,3*T^3,9*T^3,0,0,T^3,0,3*T^3,0,0,0,0,3*T^5,0,0,T^5,3*T^3,0,0,0,9*T^3,0,0,0,T^3,0,1,3*T^3,1,3,3,6,10,6,10,9,19,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,3*T^2,0,1,0,0,3,9,3+6*T^2,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,10,9,19,33},{9*T^5,3*T^5,T^5,3*T^3,T^5,0,0,0,T^3,0,0,0,0,9*T^5,0,0,3*T^5,T^5,0,0,0,3*T^3,T^5,0,0,0,0,0,T^3,0,1,1,3,6,3,6,3,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6,3,9,19},{19*T^5,9*T^5,3*T^5,T^5,3*T^5,T^5,0,0,0,0,0,0,0,19*T^5,0,0,9*T^5,3*T^5,0,0,0,T^5,3*T^5,T^5,0,0,0,0,0,0,0,0,1,3,1,3,1,3,9},{33*T^5,19*T^5,9*T^5,3*T^5,6*T^5,3*T^5,T^5,0,0,0,0,0,0,33*T^5,0,0,19*T^5,9*T^5,0,0,0,3*T^5,6*T^5,3*T^5,0,T^5,0,T^2,0,T^2,0,0,0,1,0,1,3*T^2,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,3*T^2,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,211)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}1 & 0 & 2 & 1 & -1 & 2 & 0 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 2 & 1 & 2 & 1 & 0 & -1 & 0 & -1 & 1 & 2 & 1 & -1 & 2 & 0 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 6 & 4 & 5 & 4 & 5 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 3 & 2 & 3 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3}},{{0,2,4},{1,3,4},{0,1,4},{2,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (36): {{1,1,6},{0,1,6},{2,1,5},{1,1,5},{-1,1,6},{2,1,4},{0,1,5},{1,1,4},{-1,1,5},{2,1,3},{0,1,4},{-1,1,4},{1,1,3},{0,1,3},{2,1,2},{1,0,3},{2,0,2},{1,1,2},{0,0,3},{-1,1,3},{0,1,2},{-1,0,3},{1,0,2},{2,1,1},{1,1,1},{-1,1,2},{2,0,1},{0,0,2},{1,0,1},{0,1,1},{-1,0,2},{0,0,1},{2,0,0},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,2,8,6,13,18,33,32,48,63,103,98,168,133,99,135,238,171,258,378,264,246,308,504,553,321,396,537,756,585,819,678,1167,1064,1554},{0,1,0,2,3,3,8,13,18,18,33,63,48,98,63,48,63,133,99,168,238,171,135,168,308,378,171,246,321,504,396,537,396,819,678,1064},{0,0,1,3,0,8,6,18,10,33,32,50,63,103,98,63,99,168,103,153,258,153,171,238,378,368,246,264,396,553,378,585,537,813,819,1167},{0,0,0,1,0,2,3,8,6,13,18,32,33,63,48,33,48,98,63,103,168,103,99,133,238,258,135,171,246,378,264,396,321,585,537,819},{0,0,2*T^2,0,1,3*T^2,2,3,8,4+4*T^2,13,33,18,48,23+5*T^2,18,23+7*T^2,63,48,98,133,99,63,78+6*T^2,168,238,78+9*T^2,135,171,308,246,321,207+11*T^2,537,396,678},{0,0,0,0,0,1,0,3,0,8,6,10,18,32,33,18,33,63,32,50,103,50,63,98,168,153,99,103,171,258,153,264,246,378,396,585},{0,0,0,0,0,0,1,2,3,3,8,18,13,33,18,13,18,48,33,63,98,63,48,63,133,168,63,99,135,238,171,246,171,396,321,537},{0,0,0,0,0,0,0,1,0,2,3,6,8,18,13,8,13,33,18,32,63,32,33,48,98,103,48,63,99,168,103,171,135,264,246,396},{0,0,T^2,0,0,2*T^2,0,0,1,3*T^2,2,8,3,13,4+4*T^2,3,4+5*T^2,18,13,33,48,33,18,23+5*T^2,63,98,23+7*T^2,48,63,133,99,135,78+9*T^2,246,171,321},{0,0,0,0,0,0,0,0,0,1,0,0,3,6,8,3,8,18,6,10,32,10,18,33,63,50,33,32,63,103,50,103,99,153,171,264},{0,0,0,0,0,0,0,0,0,0,1,3,2,8,3,2,3,13,8,18,33,18,13,18,48,63,18,33,48,98,63,99,63,171,135,246},{0,0,0,0,0,T^2,0,0,0,2*T^2,0,1,0,2,3*T^2,0,3*T^2,3,2,8,13,8,3,4+4*T^2,18,33,4+5*T^2,13,18,48,33,48,23+7*T^2,99,63,135},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,1,2,8,3,6,18,6,8,13,33,32,13,18,33,63,32,63,48,103,99,171},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,3,8,3,2,3,13,18,3,8,13,33,18,33,18,63,48,99},{0,T^3,0,0,3*T^3,0,0,0,0,0,0,0,0,0,1,0,1,3,T^3,0,6,3*T^3,3,8,18,10,8,6,18,32,10,32,33,50,63,103},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,3,0,0,6,8,0,0,0,13,18,33,0,32,63,48,103,98,168},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,0,8,6,18,0,10,32,33,50,63,103},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,T^3,1,2,8,6,2,3,8,18,6,18,13,32,33,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,0,0,0,3,8,13,0,18,33,18,63,48,98},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,2*T^2,0,0,1,2,1,0,3*T^2,3,8,3*T^2,2,3,13,8,13,4+5*T^2,33,18,48},{T^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,1,0,0,0,2,3,0,1,2,8,3,8,3,18,13,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,0,0,0,0,3*T^2,2,3,0,8,13,4+4*T^2,33,18,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,8,0,6,18,13,32,33,63},{0,2*T^3,0,0,8*T^3,0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,8*T^3,0,1,3,0,1,T^3,3,6,3*T^3,6,8,10,18,32},{2*T^5,0,T^5,0,2*T^3,0,0,0,T^3,0,0,0,0,0,0,2*T^5,T^5,0,0,0,0,2*T^3,0,0,1,0,0,0,1,3,T^3,3,2,6,8,18},{3*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,0,T^2,3*T^5,T^2,0,T^5,0,0,0,0,2*T^2,0,1,2*T^2,0,0,2,1,2,3*T^2,8,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,8,10,18,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,3,8,3,18,13,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,6,8,18},{8*T^5,2*T^5,3*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,8*T^5,3*T^5,0,2*T^5,0,0,0,T^5,0,0,0,0,0,0,1,0,1,0,3,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,1,2,3*T^2,8,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,215)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & -2 & -2 & 3 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
46: $\begin{pmatrix}2 & 1 & 3 & 2 & 0 & 1 & 3 & 0 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0 & 3 & 2 & 2 & -1 & 0 & 1 & 2 & 0 & 1 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & -1 & 1 & 2 & 0 & 1 & -1 & 0 & -1 & 1 & 0 & 0 & -1 & 1 & 0 \\ 0 & 1 & -1 & 0 & 2 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 2 & 0 & 1 & 1 & -1 & -1 & 0 & 2 & 2 & 0 & -1 & 1 & 1 & 0 & 2 & 1 & -1 & 0 & 2 & 0 & 1 & -1 & -1 & 1 & 0 & 2 & 0 & 1 & -1 & 1 & 0 & 1 & -1 & 0 \\ 3 & 5 & 0 & 2 & 7 & 4 & -1 & 6 & 1 & -2 & 3 & 0 & 5 & 3 & 2 & 5 & -3 & 0 & -1 & 7 & 4 & 2 & -1 & 4 & 1 & 1 & 6 & 3 & -2 & 3 & 5 & 0 & 5 & 0 & -3 & 2 & -1 & 4 & 2 & 4 & -1 & 1 & 1 & 3 & -2 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, -1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 6, 8}}
Primitive collections: {{1, 2, 4, 6}, {3, 5, 7}, {4, 6, 7}, {0, 1, 2, 8}, {0, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{0,1,3},{-1,1,3}},{{0,3,4},{1,4,5},{3,4,5},{0,2,3},{0,1,2},{0,1,4}},{6,1,2})
Cox degrees: {{0,0,1},{1,-1,-2},{1,-1,-2},{-1,1,3},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (46): {{2,0,3},{1,1,5},{3,-1,0},{2,0,2},{0,2,7},{1,1,4},{3,-1,-1},{0,2,6},{2,0,1},{3,-1,-2},{1,1,3},{2,0,0},{0,2,5},{1,0,3},{1,1,2},{0,1,5},{3,-1,-3},{2,-1,0},{2,0,-1},{-1,2,7},{0,2,4},{1,0,2},{2,-1,-1},{0,1,4},{1,1,1},{1,0,1},{-1,2,6},{0,1,3},{2,-1,-2},{0,0,3},{-1,2,5},{1,0,0},{-1,1,5},{1,-1,0},{2,-1,-3},{0,1,2},{1,0,-1},{-1,2,4},{0,0,2},{-1,1,4},{1,-1,-1},{0,1,1},{0,0,1},{-1,1,3},{1,-1,-2},{0,0,0}}
Ext matrix: {{1,2,2,6,3,10,10,14,20,30,30,50,40,32,70,44,70,54,105,56,90,82,125,110,140,180,138,235,256,238,290,352,296,358,476,448,630,544,466,574,660,784,844,1028,1142,1434},{0,1,0,2,2,6,3,10,10,14,20,30,30,20,50,32,40,30,70,44,70,54,76,82,105,125,110,180,168,180,235,256,238,256,332,352,476,448,358,466,485,630,660,844,862,1142},{0,0,1,2,0,3,6,4+2*T^2,10,20,14,30,18+4*T^2,14,40,18,50,32,70,22,50+6*T^2,44,82,56,90,110,68+3*T^2,138,180,138,166+6*T^2,235,166,238,352,290,448,345+9*T^2,296,354,466,544,574,682,844,1028},{0,0,0,1,0,2,2,3,6,10,10,20,14,10,30,14,30,20,50,18,40,32,54,44,70,82,56,110,125,110,138,180,138,180,256,235,352,290,238,296,358,448,466,574,660,844},{0,0,0,0,1,2,0,6,3,4,10,14,20,10,30,20,18,14,40,32,50,30,40,54,70,76,82,125,98,125,180,168,180,168,211,256,332,352,256,358,332,476,485,660,612,862},{0,0,0,0,0,1,0,2,2,3,6,10,10,6,20,10,14,10,30,14,30,20,30,32,50,54,44,82,76,82,110,125,110,125,168,180,256,235,180,238,256,352,358,466,485,660},{0,0,0,0,2*T^3,0,1,0,2,6,3,10,4+2*T^2,3,14,4,20,10,30,5+3*T^3,18+4*T^2,14,32,18,40,44,22,56,82,56,68+3*T^2,110,68,110,180,138,235,166+6*T^2,138,166,238,290,296,354,466,574},{0,0,0,0,0,0,0,1,0,0,2,3,6,2,10,6,4,3,14,10,20,10,14,20,30,30,32,54,40,54,82,76,82,76,98,125,168,180,125,180,168,256,256,358,332,485},{0,0,0,0,0,0,0,0,1,2,2,6,3,2,10,3,10,6,20,4,14,10,20,14,30,32,18,44,54,44,56,82,56,82,125,110,180,138,110,138,180,235,238,296,358,466},{0,0,0,0,4*T^3,0,0,2*T^3,0,1,0,2,0,0,3,0,6,2,10,6*T^3,4+2*T^2,3,10,4,14,14,5+3*T^3,18,32,18,22,44,22,44,82,56,110,68+3*T^2,56,68,110,138,138,166,238,296},{0,0,0,0,0,0,0,0,0,0,1,2,2,1,6,2,3,2,10,3,10,6,10,10,20,20,14,32,30,32,44,54,44,54,76,82,125,110,82,110,125,180,180,238,256,358},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,1,6,0,3,2,6,3,10,10,4,14,20,14,18,32,18,32,54,44,82,56,44,56,82,110,110,138,180,238},{T^3,0,2*T^3,0,0,0,0,0,0,0,0,0,1,2*T^3,2,1,0,4*T^3,3,2,6,2,3,6,10,10,10,20,14,20+3*T^3,32,30,32,30+6*T^3,40,54,76,82,54,82,76,125,125,180,168,256},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,0,3,0,6,10,10,0,20,14,30,30,32,40,50,44,54,70,70,105,90,82,110,125,140,180,235,256,352},{0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2*T^3,2,0,2,1,2,2,6,6,3,10,10,10,14,20,14,20+3*T^3,30,32,54,44,32,44,54,82,82,110,125,180},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,3,6,0,10,10,20,14,20,30,30,32,30,40,50,70,70,54,82,76,105,125,180,168,256},{0,T^3,0,0,8*T^3,0,0,4*T^3,0,0,0,0,2*T^3,0,0,2*T^3,1,0,2,13*T^3,0,0,2,0,3,3,6*T^3,4,10,4,5+3*T^3,14,5+3*T^3,14,32,18,44,22,18,22,44,56,56,68,110,138},{0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,1,0,0,3*T^2,2,6,3,0,10,4+2*T^2,14,20,14,18+4*T^2,30,18,32,50,40,70,50+6*T^2,44,56,82,90,110,138,180,235},{T^4,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,1,2*T^3,0,0,1,0,2,2,0,3,6,3+3*T^4,4,10,4,10,20,14,32,18,14,18,32,44,44,56,82,110},{0,0,4*T^3,0,0,0,5*T^3,0,0,6*T^3,0,0,0,0,0,0,7*T^3,0,0,1,0,0,0,2,0,3,6,10,4,10,20,14,20,14,18,30,40,50,30,54,40,70,76,125,98,168},{2*T^3,0,6*T^3,T^3,0,0,2*T^3,0,0,0,0,0,0,4*T^3,0,0,0,12*T^3,0,0,1,2*T^3,4*T^3,1,2,2,2,6,3,6+6*T^3,10,10,10,10+18*T^3,14,20,30,32,20+3*T^3,32,30+6*T^3,54,54,82,76,125},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,6,3,10,10,10,14,20,14,20,30,30,50,40,32,44,54,70,82,110,125,180},{0,0,0,0,T^3,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^3,2*T^2,0,1,0,0,2,0,3,6,3,4+2*T^2,10,4,10,20,14,30,18+4*T^2,14,18,32,40,44,56,82,110},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,6,3,6,10,10,10,10,14,20,30,30,20,32,30,50,54,82,76,125},{2*T^4,T^4,2*T^3,0,0,0,T^3,0,0,0,0,0,0,4*T^4,0,2*T^4,0,4*T^3,0,0,0,0,2*T^3,0,1,1,0,2,2,2+6*T^4,3,6,3+3*T^4,6+6*T^3,10,10,20,14,10,14,20+3*T^3,32,32,44,54,82},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,2,3,6,3,6,10,10,20,14,10,14,20,30,32,44,54,82},{0,0,3*T^3,0,0,0,4*T^3,0,0,5*T^3,0,0,0,0,0,0,6*T^3,0,0,0,0,0,0,0,0,0,1,2,0,2,6,3,6,3,4,10,14,20,10,20,14,30,30,54,40,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,2,3,6,10,10,6,10,10,20,20,32,30,54},{0,0,0,0,2*T^3,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,4*T^3,T^2,0,0,0,0,0,2*T^3,0,1,0,0,2,0,2,6,3,10,4+2*T^2,3,4,10,14,14,18,32,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,0,0,6,10,10,0,20,30,30,50},{0,0,2*T^3,0,0,0,3*T^3,0,0,4*T^3,0,0,0,T^3,0,0,5*T^3,2*T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,1,0,1,4*T^3,0,2,3,6,2,6,3,10,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,6,3,2,3,6,10,10,14,20,32},{0,0,2*T^3,0,0,0,3*T^3,0,0,4*T^3,0,0,0,0,0,0,5*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,6,3,0,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,1,0,0,0,3*T^2,2,3,6,0,10,14,20,30},{0,0,0,0,3*T^3,0,0,2*T^3,0,0,0,0,T^3,0,0,T^3,0,0,0,8*T^3,0,0,0,0,0,0,4*T^3,0,0,0,2*T^3,0,2*T^3,0,1,0,2,0,0,0,2,3,3,4,10,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,1,2,2,1,2,2,6,6,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,0,0,0,1,2,2,3,6,10},{0,0,T^3,0,0,0,2*T^3,0,0,3*T^3,0,0,0,2*T^3,0,0,4*T^3,6*T^3,0,0,0,T^3,2*T^3,0,0,0,0,0,0,4*T^3,0,0,0,12*T^3,0,0,0,1,2*T^3,1,4*T^3,2,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,6,10,10,20},{0,0,T^3,0,0,0,2*T^3,0,0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,1,0,2,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,T^4,0,2*T^3,0,0,0,0,T^3,0,0,0,0,0,0,4*T^4,0,0,2*T^4,4*T^3,0,0,0,0,0,0,2*T^3,1,1,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,216)$ |
3 |
25 |
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9: $\begin{pmatrix}-1 & -1 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}-1 & 0 & -2 & 1 & -1 & -3 & 2 & 0 & -2 & 1 & -3 & -1 & 2 & 0 & -2 & -1 & -3 & 1 & 0 & -1 & 1 & 2 & -2 & 0 & 1 & 0 & -2 & 2 & -1 & 1 & 0 & -1 & 2 & -2 & 0 & 1 & -1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 6 & 3 & 4 & 5 & 3 & 5 & 4 & 2 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {-1, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{0, 1, 2, 5}, {5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {3, 4, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3},{-1,1,3}},{{2,4,5},{0,2,4},{1,4,5},{1,3,5},{2,3,5},{0,1,4}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{-1,0,1},{1,0,0},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (38): {{-1,1,6},{0,1,5},{-2,1,6},{1,1,4},{-1,1,5},{-3,1,6},{2,1,3},{0,1,4},{-2,1,5},{1,1,3},{-3,1,5},{-1,1,4},{2,1,2},{0,1,3},{-2,1,4},{-1,1,3},{-3,1,4},{1,1,2},{0,0,3},{-1,0,3},{1,0,2},{2,1,1},{-2,1,3},{0,1,2},{1,1,1},{0,0,2},{-2,0,3},{2,0,1},{-1,1,2},{1,0,1},{0,1,1},{-1,0,2},{2,0,0},{-2,0,2},{0,0,1},{1,0,0},{-1,0,1},{0,0,0}}
Ext matrix: {{1,3,3,6,10,6,10,21,21,36,36,46,55,81,81,146,126,126,82,149,129,181,231,231,336,241,237,187,371,357,546,392,497,582,592,837,893,1280},{0,1,0,3,3,0,6,10,6,21,10,21,36,46,36,81,55,81,46,81,82,126,126,146,231,149,126,129,231,241,371,237,357,346,392,592,582,893},{0,0,1,0,3,3,T^3,6,10,10,21,21,15+T^3,36,46,81,81,55,36,82,55,78+T^3,146,126,181,129,149,78,231,187,336,241,256,392,357,497,592,837},{0,0,0,1,0,T^3,3,3,0,10,T^3,6,21,21,10,36,15+T^3,46,21,36,46,81,55,81,146,81,55,82,126,149,231,126,241,181,237,392,346,582},{0,0,0,0,1,0,0,3,3,6,6,10,10,21,21,46,36,36,21,46,36,55,81,81,126,82,81,55,146,129,231,149,187,237,241,357,392,592},{0,0,0,T^3,0,1,7*T^3,0,3,T^3,10,6,7*T^3,10,21,36,46,15+T^3,10,36,15,21+7*T^3,81,55,78+T^3,55,82,21+T^3,126,78,181,129,105+T^3,241,187,256,357,497},{0,0,T^3,0,0,7*T^3,1,0,T^3,3,7*T^3,0,10,6,T^3,10,7*T^3,21,6,10,21,46,15+T^3,36,81,36,15+T^3,46,55,81,126,55,149,78+T^3,126,237,181,346},{0,0,0,0,0,0,0,1,0,3,0,3,6,10,6,21,10,21,10,21,21,36,36,46,81,46,36,36,81,82,146,81,129,126,149,241,237,392},{0,0,0,0,0,0,T^3,0,1,0,3,3,T^3,6,10,21,21,10,6,21,10,15+T^3,46,36,55,36,46,15,81,55,126,82,78,149,129,187,241,357},{0,0,0,0,0,T^3,0,0,0,1,T^3,0,3,3,0,6,T^3,10,3,6,10,21,10,21,46,21,10,21,36,46,81,36,82,55,81,149,126,237},{0,0,0,T^3,0,0,7*T^3,0,0,T^3,1,0,7*T^3,0,3,6,10,T^3,0,6,0,7*T^3,21,10,15+T^3,10,21,T^3,36,15,55,36,21+T^3,82,55,78,129,187},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,10,6,6,3,10,6,10,21,21,36,21,21,10,46,36,81,46,55,81,82,129,149,241},{T^3,0,4*T^3,0,0,13*T^3,0,0,T^3,0,7*T^3,0,1,0,T^3,0,7*T^3,3,T^3,3*T^3,3,10,T^3,6,21,6,7*T^3,10,10,21,36,10,46,15+T^3,36,81,55,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,1,3,3,6,6,10,21,10,6,6,21,21,46,21,36,36,46,82,81,149},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,1,3,3,0,0,3,0,T^3,10,6,10,6,10,0,21,10,36,21,15,46,36,55,82,129},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,3,3,6,3,3,0,10,6,21,10,10,21,21,36,46,82},{0,T^3,0,4*T^3,0,0,13*T^3,0,0,T^3,0,0,7*T^3,0,0,0,1,T^3,0,0,T^3,7*T^3,3,0,T^3,0,3,4*T^3,6,0,10,6,T^3,21,10,15,36,55},{0,0,T^3,0,0,4*T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,1,0,T^3,1,3,0,3,10,3,3*T^3,3,6,10,21,6,21,10,21,46,36,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,0,0,0,0,10,6,6,0,21,0,21,36,36,46,81,81,146},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,T^3,0,0,0,3,3,0,0,6,0,10,10,21,21,36,46,81},{0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,1,0,0,0,0,3,0,3,0,10,0,6,21,10,21,46,36,81},{T^3,0,7*T^3,0,T^3,22*T^3,0,0,4*T^3,0,13*T^3,0,0,0,T^3,0,7*T^3,0,T^3,6*T^3,0,1,T^3,0,3,T^3,16*T^3,1,0,3,6,3*T^3,10,7*T^3,6,21,10,36},{0,0,0,T^3,0,0,4*T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,1,0,0,0,1,T^3,3,0,6,3,0,10,6,10,21,36},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,T^3,0,3,3,10,3,6,6,10,21,21,46},{0,0,T^3,0,0,7*T^3,0,0,T^3,0,4*T^3,0,0,0,0,0,T^3,0,0,T^3,0,0,0,0,1,0,6*T^3,0,0,1,3,T^3,3,3*T^3,3,10,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,6,6,10,21,21,46},{0,0,0,T^3,0,0,7*T^3,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,0,0,7*T^3,0,0,T^3,0,1,T^3,0,0,0,3,T^3,10,6,10,21,36},{0,0,T^3,0,0,7*T^3,0,0,T^3,0,7*T^3,0,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,1,0,3,0,0,10,T^3,6,21,10,36},{T^5,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,1,0,3,1,0,3,3,6,10,21},{0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,10,6,21},{3*T^5,T^5,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,3*T^5,0,T^5,0,0,0,0,0,T^3,0,0,0,1,0,0,T^3,1,3,3,10},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,3,3,6,10,21},{0,0,T^3,0,0,7*T^3,0,0,T^3,0,7*T^3,0,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,1,T^3,0,3,0,6},{0,0,0,T^3,0,0,7*T^3,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,0,0,7*T^3,0,0,T^3,0,0,T^3,0,0,0,0,T^3,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,10},{0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,217)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 1 & 2 & 1 & 3 & 1 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 6 & 4 & 5 & 3 & 4 & 2 & 3 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,3}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,6},{1,2,6},{1,3,5},{1,2,5},{1,3,4},{1,1,6},{1,2,4},{1,1,5},{1,3,3},{1,1,4},{1,3,2},{1,2,3},{0,2,3},{1,1,3},{1,3,1},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,12,10,6,30,24,20,60,35,60,61,120,56,105,123,109,168,210,206,222,336,178,374,272,366,620,564,960},{0,1,0,4,0,3,10,12,0,30,0,20,20,60,0,35,61,35,56,105,123,109,168,56,222,84,178,366,272,564},{0,0,1,3,4,0,12,6,10,24,20,30,30,60,35,60,60,61,105,120,100,123,210,109,206,178,222,374,366,620},{0,0,0,1,0,0,4,3,0,12,0,10,10,30,0,20,30,20,35,60,60,61,105,35,123,56,109,222,178,366},{0,0,0,0,1,0,3,0,4,6,10,12,12,24,20,30,24,30,60,60,40,60,120,61,100,109,123,206,222,374},{0,0,0,0,0,1,0,4,0,10,0,0,0,20,0,0,20,0,0,35,61,35,56,0,109,0,56,178,84,272},{0,0,0,0,0,0,1,0,0,3,0,4,4,12,0,10,12,10,20,30,24,30,60,20,60,35,61,123,109,222},{0,0,0,0,0,0,0,1,0,4,0,0,0,10,0,0,10,0,0,20,30,20,35,0,61,0,35,109,56,178},{0,0,0,0,0,0,0,0,1,0,4,3,3,6,10,12,6,12,30,24,10,24,60,30,40,61,60,100,123,206},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,4,0,0,10,12,10,20,0,30,0,20,61,35,109},{T^3,3*T^3,0,0,0,6*T^3,0,0,0,0,1,0,T^3,0,4,3,3*T^3,3,12,6,6*T^3,6,24,12,10,30,24,40,60,100},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,3,4,10,12,6,12,30,10,24,20,30,60,61,123},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,6,12,0,10,24,20,30,60,60,120},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,3,4,10,0,12,0,10,30,20,61},{4*T^3,12*T^3,T^3,3*T^3,0,24*T^3,0,6*T^3,0,0,0,0,4*T^3,0,1,0,12*T^3,T^3,3,0,24*T^3,3*T^3,6,3,6*T^3,12,6,10,24,40},{0,T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,1,T^3,1,4,3,3*T^3,3,12,4,6,10,12,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,12,24,30,60},{0,4*T^3,0,T^3,0,12*T^3,0,3*T^3,0,0,0,0,0,0,0,0,4*T^3,0,1,0,12*T^3,T^3,3,1,3*T^3,4,3,6,12,24},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,T^3,1,4,0,3,0,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,12,10,30},{0,0,0,0,0,4*T^3,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,1,0,T^3,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,220)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 0 & 3 & 3 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 12 & 11 & 10 & 9 & 9 & 8 & 9 & 7 & 8 & 8 & 7 & 6 & 7 & 6 & 6 & 5 & 6 & 4 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{1,1,3}},{{2,3,4},{0,1,4},{1,3,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,0,0},{0,1,3},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,3,12},{1,3,11},{1,3,10},{1,3,9},{1,2,9},{1,3,8},{0,2,9},{1,3,7},{1,2,8},{0,2,8},{1,2,7},{1,2,6},{0,2,7},{0,2,6},{1,1,6},{1,2,5},{0,1,6},{1,2,4},{0,2,5},{1,1,5},{0,1,5},{0,2,4},{1,1,4},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,20,22,35,23,56,43,47,76,124,86,144,127,190,149,277,225,202,245,333,307,383,448,572,631,579,862,821,849,1139,1209,1675},{0,1,4,10,10,20,10,35,22,23,43,76,47,86,76,124,86,190,144,127,149,225,202,245,307,383,448,383,631,572,579,821,849,1209},{0,0,1,4,4,10,4,20,10,10,22,43,23,47,43,76,47,124,86,76,86,144,127,149,202,245,307,245,448,383,383,572,579,849},{0,0,0,1,1,4,1,10,4,4,10,22,10,23,22,43,23,76,47,43,47,86,76,86,127,149,202,149,307,245,245,383,383,579},{0,0,0,0,1,0,1,0,4,4,10,20,10,20,22,35,23,56,35,43,47,56,76,86,124,144,190,149,277,225,245,333,383,572},{T^3,0,0,0,2*T^3,1,3*T^3,4,1,1,4,10,4,10,10+3*T^3,22,10+5*T^3,43,23,22,23,47,43,47,76,86,127,86+7*T^3,202,149,149,245,245,383},{0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,0,22,0,35,0,43,56,0,76,0,124,0,127,0,190,202,277,307,448},{4*T^3,T^3,0,0,8*T^3,0,12*T^3,1,2*T^3,3*T^3,1,4,1,4,4+12*T^3,10,4+20*T^3,22,10,10+3*T^3,10+5*T^3,23,22,23,43,47,76,47+28*T^3,127,86,86+7*T^3,149,149,245},{0,0,0,0,0,0,0,0,1,1,4,10,4,10,10,20,10,35,20,22,23,35,43,47,76,86,124,86,190,144,149,225,245,383},{0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,0,10,0,20,0,22,35,0,43,0,76,0,76,0,124,127,190,202,307},{0,0,0,0,0,0,0,0,0,0,1,4,1,4,4,10,4,20,10,10,10,20,22,23,43,47,76,47,124,86,86,144,149,245},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,10,4,4,4,10,10,10,22,23,43,23,76,47,47,86,86,149},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,4,0,10,0,10,20,0,22,0,43,0,43,0,76,76,124,127,202},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,4,10,0,10,0,22,0,22,0,43,43,76,76,127},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,4,0,10,10,20,20,35,23,56,35,47,56,86,144},{0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,2*T^3,1,3*T^3,4,1,1,1,4,4,4,10,10,22,10+5*T^3,43,23,23,47,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20,0,22,0,35,43,56,76,124},{0,0,0,0,4*T^3,0,4*T^3,0,T^3,T^3,0,0,0,0,8*T^3,0,12*T^3,1,0,2*T^3,3*T^3,1,1,1,4,4,10,4+20*T^3,22,10,10+5*T^3,23,23,47},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,1,0,1,4,0,4,0,10,0,10+3*T^3,0,22,22,43,43,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,4,10,10,20,10,35,20,23,35,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,10,0,20,22,35,43,76},{0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,8*T^3,0,0,0,2*T^3,1,0,1,0,4,0,4+12*T^3,0,10,10+3*T^3,22,22,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,10,4,20,10,10,20,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,10,20,22,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,10,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,0,0,1,3*T^3,4,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,4*T^3,0,0,T^3,T^3,0,0,0,0,0,0,12*T^3,1,0,3*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,0,T^3,0,0,0,0,0,0,8*T^3,0,0,2*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,221)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 3 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 9 & 9 & 8 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 5 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,3},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,2,9},{0,2,9},{1,2,8},{0,2,8},{1,2,7},{0,2,7},{1,2,6},{1,1,6},{1,2,5},{0,2,6},{0,1,6},{0,2,5},{1,1,5},{1,2,4},{0,2,4},{1,1,4},{0,1,5},{0,1,4},{1,1,3},{1,0,3},{1,1,2},{0,1,3},{0,1,2},{1,0,2},{1,1,1},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,20,20,22,35,40,44,70,43,56,112,76,86,152,124,127,190,248,380,202,277,254,404,307,554,614,448,896},{0,1,0,4,0,10,0,0,0,20,22,35,0,0,56,0,43,76,0,0,0,124,190,0,0,127,202,0,277,307,0,448},{0,0,1,2,4,8,10,10,20,20,20,40,22,35,70,43,44,86,76,76,124,152,248,127,190,152,254,202,380,404,307,614},{0,0,0,1,0,4,0,0,0,10,10,20,0,0,35,0,22,43,0,0,0,76,124,0,0,76,127,0,190,202,0,307},{0,0,0,0,1,2,4,4,10,8,8,20,10,20,40,22,20,44,43,43,76,86,152,76,124,86,152,127,248,254,202,404},{0,0,0,0,0,1,0,0,0,4,4,10,0,0,20,0,10,22,0,0,0,43,76,0,0,43,76,0,124,127,0,202},{0,0,0,0,0,0,1,1,4,2,2,8,4,10,20,10,8,20,22,22,43,44,86,43,76,44,86,76,152,152,127,254},{0,0,0,0,0,0,0,1,0,0,2,0,4,0,0,10,8,20,20,22,35,40,70,43,56,44,86,76,112,152,124,248},{T^3,2*T^3,0,0,0,0,0,2*T^3,1,0,4*T^3,2,1,4,8,4,2,8,10,10+3*T^3,22,20,44,22,43,20+6*T^3,44,43,86,86,76,152},{0,0,0,0,0,0,0,0,0,1,1,4,0,0,10,0,4,10,0,0,0,22,43,0,0,22,43,0,76,76,0,127},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,10,0,0,0,20,35,0,0,22,43,0,56,76,0,124},{0,T^3,0,0,0,0,0,0,0,0,2*T^3,1,0,0,4,0,1,4,0,0,0,10,22,0,0,10+3*T^3,22,0,43,43,0,76},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,8,10,10,20,20,40,22,35,20,44,43,70,86,76,152},{4*T^3,8*T^3,T^3,2*T^3,0,0,0,8*T^3,0,0,16*T^3,0,2*T^3,1,2,1,4*T^3,2,4,4+12*T^3,10,8,20,10+3*T^3,22,8+24*T^3,20+6*T^3,22,44,44,43,86},{0,4*T^3,0,T^3,0,0,0,0,0,0,8*T^3,0,0,0,1,0,2*T^3,1,0,0,0,4,10,0,0,4+12*T^3,10+3*T^3,0,22,22,0,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,4,10,8,20,10,20,8,20,22,40,44,43,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,10,20,0,0,10,22,0,35,43,0,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,0,4,10,0,20,22,0,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,2,8,4,10,2,8,10,20,20,22,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,0,2*T^3,1,0,2,1,4,4*T^3,2,4,8,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,1,4,0,10,10,0,22},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2*T^3,1,0,4,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,0,0,4*T^3,0,0,8*T^3,0,T^3,0,0,0,2*T^3,0,0,8*T^3,0,0,0,2*T^3,1,16*T^3,4*T^3,1,2,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,8*T^3,2*T^3,0,1,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,222)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 0 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 6 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3}},{{0,2,4},{1,3,4},{2,3,4},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,6},{1,1,6},{0,1,6},{2,1,5},{1,1,5},{0,1,5},{2,1,4},{1,1,4},{2,1,3},{0,1,4},{1,1,3},{2,0,3},{1,0,3},{2,1,2},{0,1,3},{0,0,3},{2,0,2},{1,1,2},{2,1,1},{0,1,2},{1,0,2},{1,1,1},{0,0,2},{2,0,1},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,6,15,28,21,46,56,81,111,57,114,126,186,192,132,231,252,371,246,434,399,273,480,672,753,518,867,1320},{0,1,3,1,6,15,6,21,21,46,56,21,57,56,111,114,57,126,126,231,132,252,246,132,273,434,480,273,518,867},{0,0,1,0,1,6,1,6,6,21,21,6,21,21,56,57,21,56,56,126,57,126,132,57,132,252,273,132,273,518},{0,0,0,1,3,6,6,15,21,28,46,21,46,56,81,81,57,111,126,186,114,231,192,132,246,371,399,273,480,753},{0,0,0,0,1,3,1,6,6,15,21,6,21,21,46,46,21,56,56,111,57,126,114,57,132,231,246,132,273,480},{0,0,0,0,0,1,0,1,1,6,6,1,6,6,21,21,6,21,21,56,21,56,57,21,57,126,132,57,132,273},{0,0,0,0,0,0,1,3,6,6,15,6,15,21,28,28,21,46,56,81,46,111,81,57,114,186,192,132,246,399},{0,0,0,0,0,0,0,1,1,3,6,1,6,6,15,15,6,21,21,46,21,56,46,21,57,111,114,57,132,246},{0,0,0,0,0,0,0,0,1,0,3,1,3,6,6,6,6,15,21,28,15,46,28,21,46,81,81,57,114,192},{0,0,0,0,0,0,0,0,0,1,1,0,1,1,6,6,1,6,6,21,6,21,21,6,21,56,57,21,57,132},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,3,1,6,6,15,6,21,15,6,21,46,46,21,57,114},{0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,6,0,0,0,15,0,28,21,46,0,81,56,111,186},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,0,0,6,0,15,6,21,0,46,21,56,111},{0,T^3,3*T^3,0,0,0,0,0,0,0,0,0,T^3,1,0,3*T^3,1,3,6,6,3,15,6,6,15,28,28,21,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,6,1,6,6,1,6,21,21,6,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,6,1,6,0,21,6,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,6,15,0,28,21,46,81},{0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,1,3,1,6,3,1,6,15,15,6,21,46},{0,3*T^3,10*T^3,0,T^3,3*T^3,0,0,0,0,0,0,3*T^3,0,0,10*T^3,0,0,1,0,T^3,3,3*T^3,1,3,6,6,6,15,28},{T^5,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,1,0,1,1,0,1,6,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,6,0,15,6,21,46},{T^5,0,3*T^3,0,0,T^3,0,0,0,0,0,T^5,0,0,0,3*T^3,0,0,0,0,0,1,T^3,0,1,3,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,6,15},{6*T^5,T^5,0,T^5,0,0,0,0,0,0,0,6*T^5,T^5,0,0,0,T^5,0,0,0,0,0,0,0,0,1,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,223)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 0 & 0 & 1 & 2 & 0 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 4 & 3 & 5 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 3 & 2 & 1 & 1 & 3 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,6},{1,1,6},{2,1,5},{0,1,6},{1,1,5},{2,1,4},{1,1,4},{2,1,3},{0,1,5},{0,1,4},{1,1,3},{2,0,3},{2,1,2},{1,0,3},{2,1,1},{2,0,2},{1,1,2},{0,1,3},{0,1,2},{1,1,1},{2,0,1},{0,0,3},{1,0,2},{0,1,1},{0,0,2},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,30,20,24,60,60,21,35,63,56,39,105,120,210,168,66,126,117,336,234,104,198,396,312,624},{0,1,0,3,4,0,10,0,12,30,20,0,0,21,0,0,35,60,105,56,0,63,39,168,117,0,66,198,104,312},{0,0,1,0,3,4,12,10,6,24,30,10,20,30,35,21,60,60,120,105,39,60,63,210,126,66,117,234,198,396},{0,0,0,1,0,0,0,0,4,10,0,0,0,0,0,0,0,20,35,0,0,21,0,56,39,0,0,66,0,104},{0,0,0,0,1,0,4,0,3,12,10,0,0,10,0,0,20,30,60,35,0,30,21,105,63,0,39,117,66,198},{0,0,0,0,0,1,3,4,0,6,12,4,10,12,20,10,30,24,60,60,21,24,30,120,60,39,63,126,117,234},{0,0,0,0,0,0,1,0,0,3,4,0,0,4,0,0,10,12,30,20,0,12,10,60,30,0,21,63,39,117},{0,0,0,0,0,0,0,1,0,0,3,1,4,3,10,4,12,6,24,30,10,6,12,60,24,21,30,60,63,126},{0,0,0,0,0,0,0,0,1,4,0,0,0,0,0,0,0,10,20,0,0,10,0,35,21,0,0,39,0,66},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,10,0,0,4,0,20,10,0,0,21,0,39},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,3,12,10,0,3,4,30,12,0,10,30,21,63},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,0,0,0,0,10,6,12,0,24,20,30,60,60,120},{T^3,3*T^3,0,6*T^3,0,0,0,0,0,0,0,T^3,1,3*T^3,4,1,3,0,6,12,4,6*T^3,3,24,6,10,12,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,3,4,0,12,0,10,30,20,60},{4*T^3,12*T^3,T^3,24*T^3,3*T^3,0,0,0,6*T^3,0,0,4*T^3,0,12*T^3,1,T^3,0,0,0,3,1,24*T^3,3*T^3,6,6*T^3,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,3,0,6,10,12,24,30,60},{0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,1,0,3,4,0,3*T^3,1,12,3,0,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,1,0,10,4,0,0,10,0,21},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,T^3,0,4,1,0,0,4,0,10},{0,4*T^3,0,12*T^3,T^3,0,0,0,3*T^3,0,0,0,0,4*T^3,0,0,0,0,0,1,0,12*T^3,T^3,3,3*T^3,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,12,10,30},{0,0,0,4*T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,1,T^3,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,225)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 0 & 2 & 1 & -1 & 0 & 2 & 1 & -1 & 2 & 0 & -1 & 2 & 1 & 2 & 0 & 1 & 0 & -1 & 2 & 1 & 2 & 0 & 1 & -1 & 0 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 6 & 5 & 4 & 4 & 5 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3},{-1,1,3}},{{0,2,4},{0,1,4},{1,3,5},{1,4,5},{2,4,5},{2,3,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,1,6},{0,1,6},{2,1,5},{1,1,5},{-1,1,6},{0,1,5},{2,1,4},{1,1,4},{-1,1,5},{2,1,3},{0,1,4},{-1,1,4},{2,0,3},{1,1,3},{2,1,2},{0,1,3},{1,0,3},{0,0,3},{-1,1,3},{2,0,2},{1,1,2},{2,1,1},{0,1,2},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{1,0,1},{0,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,1,6,6,15,6,21,28,21,46,81,22,56,56,111,59,117,186,62,126,126,231,141,371,259,252,147,298,434,308,515,573,942},{0,1,0,1,3,6,1,6,15,6,21,46,6,21,21,56,22,59,111,22,56,56,126,62,231,141,126,62,147,252,147,298,308,573},{0,0,1,3,0,6,6,15,10,21,28,45,21,46,56,81,46,81,126,59,111,126,186,117,281,196,231,141,259,371,298,416,515,798},{0,0,0,1,0,3,1,6,6,6,15,28,6,21,21,46,21,46,81,22,56,56,111,59,186,117,126,62,141,231,147,259,298,515},{0,0,3*T^2,0,1,1,6*T^2,1,6,1+10*T^2,6,21,1+10*T^2,6,6+15*T^2,21,6,22,56,6+15*T^2,21,21+21*T^2,56,22,126,62,56,22+21*T^2,62,126,62+28*T^2,147,147,308},{0,0,0,0,0,1,0,1,3,1,6,15,1,6,6,21,6,21,46,6,21,21,56,22,111,59,56,22,62,126,62,141,147,298},{0,0,0,0,0,0,1,3,0,6,6,10,6,15,21,28,15,28,45,21,46,56,81,46,126,81,111,59,117,186,141,196,259,416},{0,0,0,0,0,0,0,1,0,1,3,6,1,6,6,15,6,15,28,6,21,21,46,21,81,46,56,22,59,111,62,117,141,259},{0,0,T^2,0,0,0,3*T^2,0,1,6*T^2,1,6,6*T^2,1,1+10*T^2,6,1,6,21,1+10*T^2,6,6+15*T^2,21,6,56,22,21,6+15*T^2,22,56,22+21*T^2,62,62,147},{0,0,0,0,0,0,0,0,0,1,0,0,1,3,6,6,3,6,10,6,15,21,28,15,45,28,46,21,46,81,59,81,117,196},{0,0,0,0,0,0,0,0,0,0,1,3,0,1,1,6,1,6,15,1,6,6,21,6,46,21,21,6,22,56,22,59,62,141},{0,0,0,0,0,0,T^2,0,0,3*T^2,0,1,3*T^2,0,6*T^2,1,0,1,6,6*T^2,1,1+10*T^2,6,1,21,6,6,1+10*T^2,6,21,6+15*T^2,22,22,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,0,6,0,0,0,15,0,28,0,21,46,0,56,81,111,186},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,6,1,6,6,15,6,28,15,21,6,21,46,22,46,59,117},{T^3,3*T^3,0,0,6*T^3,0,0,0,0,0,0,0,T^3,0,1,0,3*T^3,6*T^3,0,1,3,6,6,3,10,6,15,6,15,28,21,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,0,1,1,6,1,15,6,6,1,6,21,6,21,22,59},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,0,0,0,6,0,15,0,6,21,0,21,46,56,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,6,0,1,6,0,6,21,21,56},{0,0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,3*T^2,0,0,0,1,3*T^2,0,6*T^2,1,0,6,1,1,6*T^2,1,6,1+10*T^2,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,0,6,15,0,21,28,46,81},{0,T^3,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,3*T^3,0,0,1,1,3,1,6,3,6,1,6,15,6,15,21,46},{3*T^3,10*T^3,0,T^3,21*T^3,3*T^3,0,0,6*T^3,0,0,0,3*T^3,0,0,0,10*T^3,21*T^3,0,T^3,0,1,0,3*T^3,0,6*T^3,3,1,3,6,6,6,15,28},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,3,1,1,0,1,6,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,6,0,6,15,21,46},{T^5,0,0,0,0,0,0,0,0,0,0,0,T^5,0,T^2,0,0,0,0,T^2,0,3*T^2,0,0,1,0,0,3*T^2,0,1,6*T^2,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6,6,21},{0,3*T^3,0,0,10*T^3,T^3,0,0,3*T^3,0,0,0,0,0,0,0,3*T^3,10*T^3,0,0,0,0,0,T^3,0,3*T^3,1,0,1,3,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,15},{T^5,0,T^5,0,3*T^3,0,0,0,T^3,0,0,0,T^5,0,0,0,0,3*T^3,0,0,0,0,0,0,0,T^3,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,226)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 2 & 1 & 0 & 2 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 3 & 6 & 4 & 3 & 2 & 3 & 5 & 2 & 1 & 3 & 1 & 2 & 4 & 3 & 1 & 0 & 2 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{-1,1,3}},{{0,2,3},{1,3,4},{2,3,4},{0,1,3}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,6},{2,1,5},{1,1,6},{2,1,4},{1,1,5},{2,1,3},{0,1,6},{1,1,4},{2,0,3},{2,1,2},{1,1,3},{0,1,5},{2,0,2},{2,1,1},{1,0,3},{2,0,1},{1,1,2},{0,1,4},{0,1,3},{1,1,1},{2,0,0},{1,0,2},{0,1,2},{0,0,3},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,3,10,12,20,6,30,23,35,60,24,47,56,66,86,105,60,120,168,144,129,210,130,228,250,372,336,436,704},{0,1,0,4,3,10,0,12,10,20,30,6,23,35,30,47,60,24,60,105,86,66,120,60,129,130,228,210,250,436},{0,0,1,0,4,0,3,10,1,0,20,12,4,0,23,10,35,30,60,56,20,47,105,66,86,129,144,168,228,372},{0,0,0,1,0,4,0,3,4,10,12,0,10,20,12,23,30,6,24,60,47,30,60,24,66,60,129,120,130,250},{0,0,0,0,1,0,0,4,0,0,10,3,1,0,10,4,20,12,30,35,10,23,60,30,47,66,86,105,129,228},{0,0,0,0,0,1,0,0,1,4,3,0,4,10,3,10,12,0,6,30,23,12,24,6,30,24,66,60,60,130},{0,0,0,0,0,0,1,0,0,0,0,4,0,0,1,0,0,10,20,0,0,4,35,23,10,47,20,56,86,144},{0,0,0,0,0,0,0,1,0,0,4,0,0,0,4,1,10,3,12,20,4,10,30,12,23,30,47,60,66,129},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,10,0,0,0,0,20,12,0,6,30,24,60,0,60,120},{T^3,0,3*T^3,0,0,0,6*T^3,0,3*T^3,1,0,0,1,4,6*T^3,4,3,0,0,12,10,3,6,10*T^3,12,6,30,24,24,60},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,0,3,10,1,4,12,3,10,12,23,30,30,66},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,10,0,0,1,20,10,4,23,10,35,47,86},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,0,0,10,3,0,0,12,6,30,0,24,60},{4*T^3,T^3,12*T^3,0,3*T^3,0,24*T^3,0,12*T^3,0,0,6*T^3,3*T^3,1,24*T^3,1,0,0,0,3,4,6*T^3,0,40*T^3,3,10*T^3,12,6,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,3,10,12,20,0,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,3,0,12,0,6,24},{0,0,T^3,0,0,0,3*T^3,0,T^3,0,0,0,0,0,3*T^3,0,1,0,0,4,0,1,3,6*T^3,4,3,10,12,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,10,4,1,10,4,20,23,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,4,1,10,10,23},{0,0,4*T^3,0,T^3,0,12*T^3,0,4*T^3,0,0,3*T^3,T^3,0,12*T^3,0,0,0,0,1,0,3*T^3,0,24*T^3,1,6*T^3,4,3,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,3,10,0,12,30},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,3*T^3,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,4*T^3,0,0,0,0,T^3,0,0,4*T^3,0,0,0,0,0,0,T^3,0,12*T^3,0,3*T^3,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,227)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & -1 & -1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}-2 & -1 & -2 & -1 & 0 & -2 & -1 & 0 & -2 & 1 & -2 & -1 & 0 & 1 & -2 & -2 & -1 & -1 & 0 & 1 & -2 & -1 & -1 & 0 & 0 & -2 & 1 & -1 & 0 & 0 & 1 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 7 & 7 & 6 & 6 & 6 & 5 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 2}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{0,1,0},{0,0,1},{-1,0,1},{2,1,1},{0,1,3}},{{1,2,4},{0,3,4},{0,2,4},{1,3,4}},{-1,3,3})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{-1,0,1},{2,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{-2,1,7},{-1,1,7},{-2,1,6},{-1,1,6},{0,1,6},{-2,1,5},{-1,1,5},{0,1,5},{-2,0,5},{1,1,5},{-2,1,4},{-1,1,4},{0,1,4},{1,1,4},{-2,1,3},{-2,0,4},{-1,1,3},{-1,0,4},{0,1,3},{1,1,3},{-2,0,3},{-1,0,3},{-1,1,2},{0,0,3},{0,1,2},{-2,0,2},{1,1,2},{-1,0,2},{0,0,2},{0,1,1},{1,1,1},{-1,0,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,0,4,3,0,10,12,6,10,0,20,30,24,10,35,26,60,30,60,40,59,70,105,60,120,116,100,145,135,210,200,268,270,486},{0,1,0,4,3,0,10,12,3,6,0,20,30,24,0,12,35,26,60,60,30,59,56,70,105,60,120,116,145,168,210,204,268,452},{0,0,1,0,0,4,3,0,4,0,10,12,6,0,20,10,30,12,24,10,26,30,60,24,60,59,40,70,60,120,100,145,135,270},{0,0,0,1,0,0,4,3,0,0,0,10,12,6,0,3,20,10,30,24,12,26,35,30,60,30,60,59,70,105,120,116,145,268},{0,0,0,0,1,0,0,4,1,3,0,0,10,12,0,4,0,3,20,30,10,12,0,26,35,20,60,30,59,56,105,60,116,204},{0,0,0,0,0,1,0,0,1,0,4,3,0,0,10,4,12,3,6,0,10,12,30,6,24,26,10,30,24,60,40,70,60,135},{0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,0,10,4,12,6,3,10,20,12,30,12,24,26,30,60,60,59,70,145},{0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,1,0,0,10,12,4,3,0,10,20,10,30,12,26,35,60,30,59,116},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,3,0,0,10,12,0,6,0,20,0,30,24,0,0,60,60,120},{4*T^2,0,10*T^2,0,0,20*T^2,0,0,20*T^2,1,35*T^2,0,0,4,56*T^2,35*T^2,0,1,0,10,56*T^2,4,0,3,0,84*T^2,20,10,12,0,35,20,30,60},{0,3*T^3,0,0,6*T^3,0,0,0,6*T^3,10*T^3,1,0,0,0,4,1,3,10*T^3,0,0,4,3,12,15*T^3,6,10,0,12,6,24,10,30,24,60},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,1,3,0,0,4,10,3,12,3,6,10,12,30,24,26,30,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,3,1,0,0,4,10,4,12,3,10,20,30,12,26,59},{T^2,0,4*T^2,0,0,10*T^2,0,0,10*T^2,0,20*T^2,0,0,1,35*T^2,20*T^2,0,0,0,4,35*T^2,1,0,0,0,56*T^2,10,4,3,0,20,10,12,30},{T^3,12*T^3,0,3*T^3,24*T^3,0,0,6*T^3,24*T^3,40*T^3,0,0,0,10*T^3,1,6*T^3,0,40*T^3,0,0,1,10*T^3,3,60*T^3,0,4,0,3,15*T^3,6,0,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,0,10,0,12,6,0,0,30,24,60},{0,T^3,0,0,3*T^3,0,0,0,3*T^3,6*T^3,0,0,0,0,0,0,1,6*T^3,0,0,0,1,4,10*T^3,3,0,0,4,3,12,6,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,0,0,0,10,12,0,0,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,1,3,0,4,10,12,3,10,26},{0,0,T^2,0,0,4*T^2,0,0,4*T^2,0,10*T^2,0,0,0,20*T^2,10*T^2,0,0,0,1,20*T^2,0,0,0,0,35*T^2,4,1,0,0,10,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,3,0,0,0,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,3,0,0,10,12,30},{0,4*T^3,0,T^3,12*T^3,0,0,3*T^3,12*T^3,24*T^3,0,0,0,6*T^3,0,3*T^3,0,24*T^3,0,0,0,6*T^3,1,40*T^3,0,0,0,1,10*T^3,3,0,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,10,20},{0,0,0,0,T^3,0,0,0,T^3,3*T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,6*T^3,1,0,0,0,1,4,3,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,6},{0,0,0,0,0,T^2,0,0,T^2,0,4*T^2,0,0,0,10*T^2,4*T^2,0,0,0,0,10*T^2,0,0,0,0,20*T^2,1,0,0,0,4,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10},{0,0,0,0,4*T^3,0,0,T^3,4*T^3,12*T^3,0,0,0,3*T^3,0,T^3,0,12*T^3,0,0,0,3*T^3,0,24*T^3,0,0,0,0,6*T^3,1,0,0,1,4},{0,0,0,0,0,0,0,0,0,T^3,T^2,0,0,0,4*T^2,T^2,0,T^3,0,0,4*T^2,0,0,3*T^3,0,10*T^2,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,228)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -2 & 3 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
40: $\begin{pmatrix}1 & 0 & 2 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 2 & 0 & 1 & -1 & 1 & 0 & -1 & 0 & 1 & 2 & 0 & 1 & -1 & 1 & 0 & -1 & 1 & -1 & 0 & 0 & -1 & -1 & 1 & 0 & -1 & 0 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 6 & 8 & 3 & 5 & 2 & 7 & 4 & 6 & 1 & 6 & 3 & 0 & 5 & 3 & 8 & 2 & 5 & 7 & 4 & 2 & -1 & 4 & 1 & 6 & 1 & 3 & 6 & 0 & 5 & 3 & 2 & 5 & 4 & -1 & 2 & 4 & 1 & 1 & 3 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -3}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 4, 6}, {3, 5, 7}, {4, 6, 7}, {0, 1, 2, 8}, {0, 1, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{0,1,3},{-1,1,3}},{{0,3,4},{0,1,2},{0,1,4},{1,4,5},{3,4,5},{0,2,3}},{6,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-2},{-1,1,3},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (40): {{1,1,6},{0,2,8},{2,0,3},{1,1,5},{2,0,2},{0,2,7},{1,1,4},{0,2,6},{2,0,1},{0,1,6},{1,1,3},{2,0,0},{0,2,5},{1,0,3},{-1,2,8},{1,1,2},{0,1,5},{-1,2,7},{0,2,4},{1,0,2},{2,0,-1},{0,1,4},{1,1,1},{-1,2,6},{1,0,1},{0,1,3},{-1,1,6},{1,0,0},{-1,2,5},{0,0,3},{0,1,2},{-1,1,5},{-1,2,4},{1,0,-1},{0,0,2},{-1,1,4},{0,1,1},{0,0,1},{-1,1,3},{0,0,0}}
Ext matrix: {{1,1,2,5,9,5,15,15,25,17,35,55,35,39,17,70,45,45,70,88,105,100,126,100,176,196,103,320,196,202,350,211,350,540,377,395,582,657,687,1080},{0,1,0,2,3,5,9,15,13,15,25,35,35,25,17,55,39,45,70,61,75,88,105,100,131,176,100,252,196,176,320,202,350,444,329,377,540,579,657,964},{0,0,1,1,5,1,5,5,15,5,15,35,15,17,5,35,17,17,35,45,70,45,70,45,100,100,45,196,100,103,196,103,196,350,211,211,350,395,395,687},{0,0,0,1,2,1,5,5,9,5,15,25,15,15,5,35,17,17,35,39,55,45,70,45,88,100,45,176,100,100,196,103,196,320,202,211,350,377,395,657},{0,0,0,0,1,0,1,1,5,1,5,15,5,5,1,15,5,5,15,17,35,17,35,17,45,45,17,100,45,45,100,45,100,196,103,103,196,211,211,395},{0,0,0,0,0,1,2,5,3,5,9,13,15,9,5,25,15,17,35,25,35,39,55,45,61,88,45,131,100,88,176,100,196,252,176,202,320,329,377,579},{0,0,0,0,0,0,1,1,2,1,5,9,5,5,1,15,5,5,15,15,25,17,35,17,39,45,17,88,45,45,100,45,100,176,100,103,196,202,211,377},{0,0,0,0,0,0,0,1,0,1,2,3,5,2,1,9,5,5,15,9,13,15,25,17,25,39,17,61,45,39,88,45,100,131,88,100,176,176,202,329},{0,0,0,0,0,0,0,0,1,0,1,5,1,1,0,5,1,1,5,5,15,5,15,5,17,17,5,45,17,17,45,17,45,100,45,45,100,103,103,211},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,5,5,0,9,0,15,0,15,25,35,17,55,35,39,70,45,70,105,88,100,126,176,196,320},{0,0,0,0,0,0,0,0,0,0,1,2,1,1,0,5,1,1,5,5,9,5,15,5,15,17,5,39,17,17,45,17,45,88,45,45,100,100,103,202},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,1,5,1,5,1,5,5,1,17,5,5,17,5,17,45,17,17,45,45,45,103},{T^3,0,2*T^3,0,0,0,0,0,0,2*T^3,0,0,1,4*T^3,0,2,1,1,5,2,3,5,9,5,9,15,5+3*T^3,25,17,15+6*T^3,39,17,45,61,39,45,88,88,100,176},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,5,0,5,0,5,15,15,5,35,15,17,35,17,35,70,45,45,70,100,100,196},{0,0,10*T^2,0,15*T^2,0,0,0,21*T^2,0,0,28*T^2,0,0,1,0,2,5,0,3,36*T^2,9,0,15,13,25,15,35,35,25,55,39,70,75,61,88,105,131,176,252},{0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,1,0,0,1,1,2,1,5,1,5,5,1,15,5,5+3*T^3,17,5,17,39,17,17,45,45,45,100},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,0,5,0,5,9,15,5,25,15,15,35,17,35,55,39,45,70,88,100,176},{0,0,6*T^2,0,10*T^2,0,0,0,15*T^2,0,0,21*T^2,0,0,0,0,0,1,0,0,28*T^2,2,0,5,3,9,5,13,15,9,25,15,35,35,25,39,55,61,88,131},{3*T^3,0,7*T^3,T^3,2*T^3,0,0,0,0,6*T^3,0,0,0,14*T^3,0,0,2*T^3,0,1,4*T^3,0,1,2,1,2,5,1+9*T^3,9,5,5+21*T^3,15,5+3*T^3,17,25,15+6*T^3,17,39,39,45,88},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,1,15,5,5,15,5,15,35,17,17,35,45,45,100},{T^4,T^4,0,0,0,0,0,0,0,2*T^4,0,0,0,0,2*T^4,0,0,0,0,0,1,0,1,0,1,1,3*T^4,5,1,1,5,1,5,17,5,5,17,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,5,1,9,5,5,15,5,15,25,15,17,35,39,45,88},{T^4,T^4,3*T^3,0,T^3,0,0,0,0,2*T^4,0,0,0,6*T^3,2*T^4,0,0,0,0,2*T^3,0,0,1,0,1,1,3*T^4,5,1,1+9*T^3,5,1,5,15,5+3*T^3,5,17,17,17,45},{0,0,3*T^2,0,6*T^2,0,0,0,10*T^2,0,0,15*T^2,0,0,0,0,0,0,0,0,21*T^2,0,0,1,0,2,1,3,5,2,9,5,15,13,9,15,25,25,39,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,1,1,5,1,5,15,5,5,15,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,5,1,5,9,5,5,15,15,17,39},{0,0,3*T^2,0,6*T^2,0,0,0,10*T^2,0,0,15*T^2,0,0,0,0,0,0,0,0,21*T^2,0,0,0,0,0,1,0,0,2,0,5,0,0,9,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,5,1,1,5,5,5,17},{0,0,T^2,0,3*T^2,0,0,0,6*T^2,T^3,0,10*T^2,0,2*T^3,0,0,0,0,0,0,15*T^2,0,0,0,0,0,2*T^3,0,1,4*T^3,2,1,5,3,2,5,9,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,1,0,1,2,1,1,5,5,5,15},{0,0,T^2,0,3*T^2,0,0,0,6*T^2,0,0,10*T^2,0,0,0,0,0,0,0,0,15*T^2,0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,9,15,25},{0,0,0,0,T^2,0,0,0,3*T^2,3*T^3,0,6*T^2,0,7*T^3,0,0,T^3,0,0,2*T^3,10*T^2,0,0,0,0,0,6*T^3,0,0,14*T^3,0,2*T^3,1,0,4*T^3,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,15},{0,0,0,0,T^2,0,0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,0,0,0,10*T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,3*T^3,T^4,0,0,0,0,T^3,0,0,0,0,0,0,2*T^4,0,0,6*T^3,0,0,0,0,2*T^3,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,6*T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,233)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 2 & 4 & 3 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 5 & 1 & 3 & 2 & 4 & 3 & 1 & 4 & 3 & 2 & 0 & 2 & 1 & 3 & 1 & 2 & 0 & 3 & 2 & 1 & 0 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -2}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,4,0},{0,1,-1},{0,0,1},{1,2,2}},{{1,4,5},{1,2,5},{0,2,3},{0,2,5},{1,2,3},{0,4,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,-1},{1,2,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,4,5},{1,4,4},{1,3,5},{1,4,3},{1,3,4},{1,4,2},{1,2,5},{1,4,1},{1,3,3},{1,3,2},{1,2,4},{1,2,3},{1,3,1},{1,1,4},{0,2,3},{1,2,2},{1,3,0},{0,2,2},{1,2,1},{1,1,3},{0,2,1},{1,1,2},{1,2,0},{0,1,3},{0,1,2},{1,1,1},{0,2,0},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,6,10,18,20,21,35,40,75,52,105,126,121,106,186,196,190,301,226,311,381,456,232,399,596,476,452,881,636,748,956,1161,1712},{0,1,1,4,6,10,6,20,18,40,21,52,75,56,52,105,126,106,186,121,190,226,301,122,232,381,311,252,596,399,452,636,748,1161},{0,0,1,0,4,0,6,0,10,20,18,40,35,52,40,75,56,75,126,105,126,186,196,106,190,301,196,232,456,311,399,476,636,956},{0,0,0,1,1,4,1,10,6,18,6,21,40,21,21,52,75,52,105,56,106,121,186,56,122,226,190,127,381,232,252,399,452,748},{0,0,0,0,1,0,1,0,4,10,6,18,20,21,18,40,35,40,75,52,75,105,126,52,106,186,126,122,301,190,232,311,399,636},{0,0,0,0,0,1,0,4,1,6,1,6,18,6,6,21,40,21,52,21,52,56,105,21,56,121,106,56,226,122,127,232,252,452},{0,0,0,0,0,0,1,0,0,0,4,10,0,18,10,20,0,20,35,40,35,75,56,40,75,126,56,106,196,126,190,196,311,476},{T^3,0,2*T^3,0,0,0,3*T^3,1,0,1,0,1,6,1,1+T^3,6,18,6,21,6,21,21,52,6+2*T^3,21,56,52,21+3*T^3,121,56,56,122,127,252},{0,0,0,0,0,0,0,0,1,4,1,6,10,6,6,18,20,18,40,21,40,52,75,21,52,105,75,56,186,106,122,190,232,399},{0,0,0,0,0,0,0,0,0,1,0,1,4,1,1,6,10,6,18,6,18,21,40,6,21,52,40,21,105,52,56,106,122,232},{0,0,0,0,0,0,0,0,0,0,1,4,0,6,4,10,0,10,20,18,20,40,35,18,40,75,35,52,126,75,106,126,190,311},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,0,4,10,6,10,18,20,6,18,40,20,21,75,40,52,75,106,190},{0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,1,0,0,1,4,1,6,1,6,6,18,1+T^3,6,21,18,6+2*T^3,52,21,21,52,56,122},{0,0,0,T^2,0,4*T^2,0,10*T^2,0,0,0,0,0,1,0,0,0,0,0,4,T^2,10,0,4,10,20,4*T^2,18,35,20,40,35,75,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,0,6,18,0,20,21,0,40,52,75,105,186},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,4,6,10,1,6,18,10,6,40,18,21,40,52,106},{0,0,4*T^3,0,T^3,0,9*T^3,0,0,0,2*T^3,0,0,3*T^3,0,0,1,0,1,0,1,1,6,4*T^3,1+T^3,6,6,1+9*T^3,21,6,6+2*T^3,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,1,6,0,10,6,0,18,21,40,52,105},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,0,1,6,4,1+T^3,18,6,6,18,21,52},{0,0,0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,4,10,T^2,6,20,10,18,20,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,0,6,6,18,21,52},{T^5,0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^5,0,0,0,0,0,0,1,0,0,1,4,0,1,10,4,6,10,18,40},{0,0,0,0,0,0,4*T^3,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,0,1,0,0,1,1,4*T^3,6,1,1+T^3,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,6,0,10,18,20,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,6,10,18,40},{4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,1,0,0,4,1,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{10*T^5,4*T^5,0,T^5,0,0,0,0,0,0,0,0,0,T^3,10*T^5,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,292)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 5 & 3 & 5 & 4 & 2 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {3, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1},{1,1,2}},{{1,2,4},{0,1,3},{0,2,4},{1,3,4},{0,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{1,1,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,3,6},{2,2,6},{2,3,5},{2,2,5},{2,3,4},{2,2,4},{1,2,5},{2,3,3},{1,1,5},{1,2,4},{2,3,2},{2,2,3},{1,1,4},{2,2,2},{1,2,3},{1,1,3},{1,2,2},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,20,9,20,14,25,35,40,40,70,54,88,100,93,167,165,132,278,180,260,312,457,499,739},{0,1,0,4,0,10,4,0,9,10,0,20,25,35,20,54,35,54,56,100,93,167,100,180,167,312,259,499},{0,0,1,2,4,8,2,10,3,9,20,20,14,40,25,40,54,41,100,88,57,165,93,132,180,260,312,457},{0,0,0,1,0,4,1,0,2,4,0,10,9,20,10,25,20,25,35,54,41,100,54,93,100,180,167,312},{0,0,0,0,1,2,0,4,0,2,10,8,3,20,9,14,25,14,54,40,19,88,41,57,93,132,180,260},{0,0,0,0,0,1,0,0,0,1,0,4,2,10,4,9,10,9,20,25,14,54,25,41,54,93,100,180},{0,0,0,0,0,0,1,0,2,4,0,0,8,0,10,20,20,25,35,40,40,70,54,88,100,165,167,278},{0,0,0,0,0,0,T^3,1,2*T^3,0,4,2,0,8,2,3,9,3+T^3,25,14,4+2*T^3,40,14,19,41,57,93,132},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,10,0,20,25,35,20,54,35,100,56,167},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,9,20,20,14,40,25,40,54,88,100,165},{T^3,2*T^3,0,0,0,0,5*T^3,0,10*T^3,T^3,1,0,2*T^3,2,0,0,2,5*T^3,9,3,10*T^3,14,3+T^3,4+2*T^3,14,19,41,57},{0,0,0,0,0,0,0,0,T^3,0,0,1,0,4,1,2,4,2,10,9,3+T^3,25,9,14,25,41,54,93},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,9,20,10,25,20,54,35,100},{0,T^3,0,0,0,0,0,0,5*T^3,0,0,0,T^3,1,0,0,1,0,4,2,5*T^3,9,2,3+T^3,9,14,25,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,2,10,8,3,20,9,14,25,40,54,88},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,9,10,25,20,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,0,8,2,3,9,14,25,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{0,0,0,0,0,0,T^3,0,2*T^3,0,0,0,0,0,0,0,0,T^3,1,0,2*T^3,2,0,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,2,4,9,10,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,1,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,361)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 5 & 4 & 3 & 5 & 4 & 3 & 3 & 2 & 4 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 5}, {4, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1},{0,1,2}},{{0,2,5},{0,3,5},{0,1,3},{2,4,5},{1,3,4},{3,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{-1,1,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,6},{0,2,6},{1,2,5},{0,2,5},{1,2,4},{1,1,5},{0,2,4},{1,2,3},{0,1,5},{1,1,4},{1,1,3},{0,2,3},{1,2,2},{0,1,4},{0,2,2},{1,1,2},{0,1,3},{1,0,3},{0,1,2},{1,0,2},{1,1,1},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,6,20,20,11,19,44,40,35,34,70,85,78,58,150,124,146,97,204,230,257,375,386,626},{0,1,0,4,0,1,10,0,6,4,10,20,0,19,35,20,44,19,85,44,35,58,124,85,146,230,146,386},{0,0,1,2,4,1,8,10,2,6,19,20,20,11,40,44,34,22,78,58,85,38,97,124,150,204,230,375},{0,0,0,1,0,0,4,0,1,1,4,10,0,6,20,10,19,6,44,19,20,22,58,44,85,124,85,230},{0,0,0,0,1,0,2,4,0,1,6,8,10,2,20,19,11,6,34,22,44,11,38,58,78,97,124,204},{0,0,0,0,0,1,0,0,2,4,10,0,0,8,0,20,20,19,40,44,35,34,78,85,70,150,146,257},{0,0,0,0,0,0,1,0,0,0,1,4,0,1,10,4,6,1,19,6,10,6,22,19,44,58,44,124},{0,0,0,0,0,T^3,0,1,2*T^3,0,1,2,4,0,8,6,2,1+T^3,11,6,19,2+2*T^3,11,22,34,38,58,97},{0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,4,20,10,0,19,44,20,35,85,35,146},{0,0,0,0,0,0,0,0,0,1,4,0,0,2,0,10,8,6,20,19,20,11,34,44,40,78,85,150},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,2,1,8,6,10,2,11,19,20,34,44,78},{0,0,0,0,0,0,0,0,T^3,0,0,1,0,0,4,1,1,0,6,1,4,1+T^3,6,6,19,22,19,58},{T^3,2*T^3,0,0,0,6*T^3,0,0,11*T^3,T^3,0,0,1,2*T^3,2,1,0,6*T^3,2,1+T^3,6,11*T^3,2+2*T^3,6,11,11,22,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,10,4,0,6,19,10,20,44,20,85},{0,T^3,0,0,0,T^3,0,0,6*T^3,0,0,0,0,T^3,1,0,0,T^3,1,0,1,6*T^3,1+T^3,1,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,4,0,2,6,8,11,19,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,1,6,4,10,19,10,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,4,6,4,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,0,T^3,0,0,1,2*T^3,0,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,365)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 5 & 0 & 2 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 4 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 12 & 11 & 10 & 10 & 9 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 6 & 7 & 5 & 6 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,2,5},{2,5,10}},{{2,3,4},{0,4,5},{3,4,5},{0,1,5},{0,2,4},{1,3,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,2},{1,2,5},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (38): {{1,4,12},{1,4,11},{1,4,10},{1,3,10},{1,4,9},{1,3,9},{1,4,8},{1,3,8},{1,4,7},{1,2,8},{1,3,7},{1,2,7},{1,3,6},{0,2,7},{1,3,5},{1,2,6},{0,2,6},{1,2,5},{1,1,6},{0,2,5},{1,2,4},{1,1,5},{0,2,4},{0,1,5},{1,1,4},{1,2,3},{0,2,3},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,12,20,28,35,55,56,58,96,108,154,109,232,184,188,292,188,302,438,308,458,320,478,628,663,506,708,763,1008,786,1388,1104,1166,1542,1672,2325},{0,1,4,4,10,12,20,28,35,28,55,58,96,58,154,108,109,184,108,188,292,188,302,192,308,438,458,320,478,506,708,511,1008,763,786,1104,1166,1672},{0,0,1,1,4,4,10,12,20,12,28,28,55,28,96,58,58,108,58,109,184,108,188,109,188,292,302,192,308,320,478,320,708,506,511,763,786,1166},{0,0,0,1,0,4,0,10,0,12,20,28,35,28,56,55,55,96,58,96,154,108,154,109,184,232,232,188,292,302,438,320,628,458,506,663,763,1104},{0,0,0,0,1,1,4,4,10,4,12,12,28,12,55,28,28,58,28,58,108,58,109,58,108,184,188,109,188,192,308,192,478,320,320,506,511,786},{0,0,0,0,0,1,0,4,0,4,10,12,20,12,35,28,28,55,28,55,96,58,96,58,108,154,154,109,184,188,292,192,438,302,320,458,506,763},{T^3,0,0,2*T^3,0,0,1,1,4,1+3*T^3,4,4,12,4+T^3,28,12,12,28,12+4*T^3,28,58,28,58,28+2*T^3,58,108,109,58,108,109,188,109+3*T^3,308,192,192,320,320,511},{0,0,0,0,0,0,0,1,0,1,4,4,10,4,20,12,12,28,12,28,55,28,55,28,58,96,96,58,108,109,184,109,292,188,192,302,320,506},{4*T^3,T^3,0,8*T^3,0,2*T^3,0,0,1,12*T^3,1,1+3*T^3,4,1+7*T^3,12,4,4+T^3,12,4+16*T^3,12,28,12+4*T^3,28,12+12*T^3,28,58,58,28+2*T^3,58,58,108,58+17*T^3,188,109,109+3*T^3,192,192,320},{0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,10,20,12,20,35,28,35,28,55,56,56,55,96,96,154,109,232,154,188,232,302,458},{0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,12,4,12,28,12,28,12,28,55,55,28,58,58,108,58,184,109,109,188,192,320},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,4,10,20,12,20,12,28,35,35,28,55,55,96,58,154,96,109,154,188,302},{0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,0,4,1,1,4,1+3*T^3,4,12,4,12,4+T^3,12,28,28,12,28,28,58,28+2*T^3,108,58,58,109,109,192},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,0,20,12,0,0,35,28,0,55,0,58,0,96,108,154,184,292},{0,0,0,4*T^3,0,T^3,0,0,0,8*T^3,0,2*T^3,0,2*T^3,1,0,0,1,12*T^3,1,4,1+3*T^3,4,1+7*T^3,4,12,12,4+T^3,12,12,28,12+12*T^3,58,28,28+2*T^3,58,58,109},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,4,10,4,10,4,12,20,20,12,28,28,55,28,96,55,58,96,109,188},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,4,0,0,20,12,0,28,0,28,0,55,58,96,108,184},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,4,1,4,10,10,4,12,12,28,12,55,28,28,55,58,109},{0,0,T^2,0,4*T^2,0,10*T^2,0,20*T^2,0,0,0,0,0,0,0,0,0,1,T^2,0,4,4*T^2,4,10,0,10*T^2,10,20,20,35,28,56,35,55,56,96,154},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,0,10,4,0,12,0,12,0,28,28,55,58,108},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,1,0,1,0,1,4,4,1,4,4,12,4+T^3,28,12,12,28,28,58},{0,0,0,0,T^2,0,4*T^2,0,10*T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,T^2,1,4,0,4*T^2,4,10,10,20,12,35,20,28,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,4,0,4,0,12,12,28,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,12,0,20,28,35,55,96},{T^5,0,0,0,0,0,T^2,0,4*T^2,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,1,0,T^2,1,4,4,10,4,20,10,12,20,28,55},{0,0,0,0,0,0,0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,8*T^3,0,0,2*T^3,0,2*T^3,0,1,1,0,1,1,4,1+7*T^3,12,4,4+T^3,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,1,0,0,1,0,1+3*T^3,0,4,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,12,20,28,55},{4*T^5,T^5,0,0,0,0,0,0,T^2,0,0,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,12,28},{10*T^5,4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,10*T^5,0,0,4*T^5,0,T^3,T^5,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{20*T^5,10*T^5,4*T^5,0,T^5,0,0,0,0,0,0,0,0,20*T^5,0,0,10*T^5,0,4*T^3,4*T^5,0,T^3,T^5,T^3,0,0,0,0,0,0,0,2*T^3,1,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,410)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 2 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 7 & 5 & 4 & 6 & 5 & 3 & 5 & 2 & 4 & 4 & 3 & 5 & 2 & 3 & 2 & 4 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 5, 6}, {4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,3,0},{0,1,-1},{0,0,1},{1,1,2}},{{1,4,5},{1,2,5},{0,2,5},{0,4,5},{0,2,3},{1,2,3}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,2},{0,1,-1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,3,7},{2,3,6},{2,2,7},{2,3,5},{2,3,4},{2,2,6},{2,2,5},{2,3,3},{1,2,5},{2,3,2},{2,2,4},{1,2,4},{2,2,3},{1,1,5},{2,2,2},{1,2,3},{1,2,2},{1,1,4},{1,1,3},{1,2,1},{0,1,3},{1,2,0},{1,1,2},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,20,14,30,35,32,56,55,63,91,75,140,111,180,139,235,274,238,397,370,382,551,440,785,581,689,845,1029,1476},{0,1,1,4,10,5,14,20,14,35,30,32,55,36,91,63,111,75,139,180,139,274,235,238,370,266,551,382,440,581,689,1029},{0,0,1,0,0,4,10,0,10,0,20,20,35,32,56,35,56,63,111,84,111,120,180,180,274,238,397,274,382,397,581,845},{0,0,0,1,4,1,5,10,5,20,14,14,30,15,55,32,63,36,75,111,75,180,139,139,235,151,370,238,266,382,440,689},{0,0,0,0,1,0,1,4,1,10,5,5,14,5,30,14,32,15,36,63,36,111,75,75,139,79,235,139,151,238,266,440},{0,0,0,0,0,1,4,0,4,0,10,10,20,14,35,20,35,32,63,56,63,84,111,111,180,139,274,180,238,274,382,581},{0,0,0,0,0,0,1,0,1,0,4,4,10,5,20,10,20,14,32,35,32,56,63,63,111,75,180,111,139,180,238,382},{T^3,0,T^3,0,0,0,0,1,2*T^3,4,1,1,5,1+2*T^3,14,5,14,5,15,32,15+3*T^3,63,36,36,75,37+3*T^3,139,75,79,139,151,266},{0,0,0,0,0,0,0,0,1,0,0,4,0,5,0,10,20,14,30,35,32,56,55,63,91,75,140,111,139,180,235,370},{4*T^3,T^3,5*T^3,0,0,T^3,0,0,8*T^3,1,0,2*T^3,1,10*T^3,5,1,5,1+2*T^3,5,14,5+12*T^3,32,15,15+3*T^3,36,15+15*T^3,75,36,37+3*T^3,75,79,151},{0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,10,5,14,20,14,35,32,32,63,36,111,63,75,111,139,238},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,10,5,14,20,14,35,30,32,55,36,91,63,75,111,139,235},{0,0,T^3,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,4,1,5,10,5,20,14,14,32,15+3*T^3,63,32,36,63,75,139},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,10,0,20,20,35,32,56,35,63,56,111,180},{0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,0,8*T^3,1,0,1,2*T^3,1,4,1,10,5,5,14,5+12*T^3,32,14,15+3*T^3,32,36,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,5,10,5,20,14,14,30,15,55,32,36,63,75,139},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,5,5,14,5,30,14,15,32,36,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,10,20,14,35,20,32,35,63,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,5,20,10,14,20,32,63},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,1,2*T^3,4,1,1,5,1+2*T^3,14,5,5,14,15,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,30,55},{0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,5*T^3,0,0,0,T^3,0,0,8*T^3,1,0,2*T^3,1,10*T^3,5,1,1+2*T^3,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,14,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,0,T^3,0,0,0,0,0,0,0,8*T^3,1,0,2*T^3,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,436)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 3 & 0 & 2 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 11 & 10 & 9 & 9 & 8 & 8 & 7 & 8 & 6 & 7 & 6 & 7 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 5 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,3},{2,3,6}},{{2,3,4},{0,2,4},{1,3,5},{0,1,5},{0,4,5},{3,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,1,3},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,3,11},{2,3,10},{2,3,9},{2,2,9},{2,3,8},{2,2,8},{2,3,7},{1,2,8},{2,3,6},{2,2,7},{2,2,6},{1,2,7},{1,2,6},{2,2,5},{1,1,6},{2,2,4},{1,2,5},{1,1,5},{1,2,4},{0,1,5},{1,2,3},{1,1,4},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,11,20,24,35,26,56,45,76,53,96,119,102,176,159,177,246,180,361,286,436,298,466,634,487,887,694,746,992,1097,1556},{0,1,4,4,10,11,20,11,35,24,45,26,53,76,54,119,96,102,159,102,246,177,286,180,298,436,304,634,466,487,694,746,1097},{0,0,1,1,4,4,10,4,20,11,24,11,26,45,26,76,53,54,96,54,159,102,177,102,180,286,181,436,298,304,466,487,746},{0,0,0,1,0,4,0,4,0,10,20,10,20,35,26,56,35,53,56,53,84,96,159,96,159,246,180,361,246,298,361,466,694},{0,0,0,0,1,1,4,1,10,4,11,4,11,24,11,45,26,26,53,26,96,54,102,54,102,177,102,286,180,181,298,304,487},{0,0,0,0,0,1,0,1,0,4,10,4,10,20,11,35,20,26,35,26,56,53,96,53,96,159,102,246,159,180,246,298,466},{T^3,0,0,T^3,0,0,1,2*T^3,4,1,4,1,4,11,4+2*T^3,24,11,11,26,11+3*T^3,53,26,54,26,54,102,54+3*T^3,177,102,102,180,181,304},{0,0,0,0,0,0,0,1,0,0,0,4,10,0,11,0,20,24,35,26,56,45,76,53,96,119,102,176,159,177,246,286,436},{4*T^3,T^3,0,4*T^3,0,T^3,0,9*T^3,1,0,1,2*T^3,1,4,1+9*T^3,11,4,4+2*T^3,11,4+14*T^3,26,11,26,11+3*T^3,26,54,26+14*T^3,102,54,54+3*T^3,102,102,181},{0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,11,20,11,35,26,53,26,53,96,54,159,96,102,159,180,298},{0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,10,4,20,11,26,11,26,53,26,96,53,54,96,102,180},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,11,20,11,35,24,45,26,53,76,54,119,96,102,159,177,286},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,4,20,11,24,11,26,45,26,76,53,54,96,102,177},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,1,4,1,10,4,11,4,11,26,11+3*T^3,53,26,26,53,54,102},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,20,10,20,35,26,56,35,53,56,96,159},{0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,0,0,9*T^3,1,0,2*T^3,1,2*T^3,4,1,4,1,4,11,4+14*T^3,26,11,11+3*T^3,26,26,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,11,4,11,24,11,45,26,26,53,54,102},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,10,4,10,20,11,35,20,26,35,53,96},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,1,2*T^3,4,1,4,1,4,11,4+2*T^3,24,11,11,26,26,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,11,0,20,24,35,45,76},{0,0,0,0,0,0,0,4*T^3,0,0,0,T^3,0,0,4*T^3,0,0,T^3,0,9*T^3,1,0,1,2*T^3,1,4,1+9*T^3,11,4,4+2*T^3,11,11,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,11,20,26,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,10,11,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,11,20,24,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,2*T^3,4,1,1,4,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,T^3,0,0,0,0,0,0,9*T^3,1,0,2*T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,459)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 7 & 7 & 6 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 3 & 5 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1},{1,1,1},{0,1,2},{2,1,2}},{{2,3,7},{0,1,6},{4,5,7},{1,4,5},{0,3,8},{0,6,8},{4,6,7,8},{2,5,7},{3,7,8},{1,4,6}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,1,1},{1,0,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,2,7},{0,2,7},{1,2,6},{0,2,6},{1,2,5},{1,1,6},{0,2,5},{1,2,4},{1,1,5},{1,1,4},{1,2,3},{0,1,5},{0,2,4},{0,1,4},{0,2,3},{1,0,4},{1,1,3},{0,2,2},{0,1,3},{1,1,2},{1,0,3},{0,0,3},{0,1,2},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,5,10,5,14,20,16,38,35,20,30,50,55,44,75,91,103,131,96,124,186,210,183,241,315,306,423,686},{0,1,0,4,0,1,10,0,4,10,0,16,20,38,35,16,20,56,75,35,38,96,131,56,75,183,131,210,315,502},{0,0,1,1,4,1,5,10,5,16,20,6,14,20,30,17,38,55,50,75,44,56,103,131,96,124,183,186,241,423},{0,0,0,1,0,0,4,0,1,4,0,5,10,16,20,5,10,35,38,20,16,44,75,35,38,96,75,131,183,315},{0,0,0,0,1,0,1,4,1,5,10,1,5,6,14,5,16,30,20,38,17,21,50,75,44,56,96,103,124,241},{0,0,0,0,0,1,0,0,4,10,0,5,0,14,0,16,20,0,30,35,38,50,55,56,75,103,131,91,186,306},{0,0,0,0,0,0,1,0,0,1,0,1,4,5,10,1,4,20,16,10,5,17,38,20,16,44,38,75,96,183},{0,T^3,0,0,0,2*T^3,0,1,0,1,4,2*T^3,1,1,5,1+3*T^3,5,14,6,16,5,6+3*T^3,20,38,17,21,44,50,56,124},{0,0,0,0,0,0,0,0,1,4,0,1,0,5,0,5,10,0,14,20,16,20,30,35,38,50,75,55,103,186},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,4,0,5,10,5,6,14,20,16,20,38,30,50,103},{T^3,5*T^3,0,T^3,0,9*T^3,0,0,2*T^3,0,1,10*T^3,0,2*T^3,1,14*T^3,1,5,1,5,1+3*T^3,1+15*T^3,6,16,5,6+3*T^3,17,20,21,56},{0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,0,0,10,0,4,16,20,0,10,38,20,35,75,131},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,1,10,5,4,1,5,16,10,5,17,16,38,44,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,1,5,10,0,4,16,10,20,38,75},{0,T^3,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,2*T^3,0,4,1,1,0,1+3*T^3,5,4,1,5,5,16,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,5,0,0,10,14,20,0,30,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,1,5,10,5,6,16,14,20,50},{0,4*T^3,0,T^3,0,4*T^3,0,0,T^3,0,0,9*T^3,0,2*T^3,0,9*T^3,0,1,0,0,2*T^3,14*T^3,1,1,0,1+3*T^3,1,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,1,5,4,10,16,38},{0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,1,0,2*T^3,1,4,1,1,5,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,5,16},{0,0,0,0,0,4*T^3,0,0,T^3,0,0,5*T^3,0,T^3,0,9*T^3,0,0,0,0,2*T^3,10*T^3,0,1,0,2*T^3,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,477)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & -1 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 6 & 4 & 3 & 5 & 2 & 3 & 4 & 2 & 3 & 4 & 1 & 5 & 3 & 0 & 2 & 4 & 1 & 2 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2},{2,1,2}},{{3,4,5},{2,3,4},{0,1,6},{1,5,6},{0,1,2},{4,5,6},{0,4,6},{0,2,4}},{3,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,-1,-1},{1,0,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (31): {{2,1,6},{2,1,5},{2,0,5},{2,1,4},{1,1,6},{2,0,4},{2,1,3},{1,1,5},{2,1,2},{2,0,3},{1,1,4},{2,0,2},{1,1,3},{1,0,4},{2,0,1},{0,1,5},{1,0,3},{2,0,0},{1,1,2},{0,1,4},{1,1,1},{1,0,2},{0,1,3},{1,0,1},{0,0,3},{1,0,0},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,4,10,5,11,20,16,35,24,38,45,75,39,76,44,81,119,131,96,210,149,183,250,189,391,315,336,502,554,859},{0,1,1,4,1,4,10,5,20,11,16,24,38,16,45,17,39,76,75,44,131,81,96,149,97,250,183,189,315,336,554},{0,0,1,0,1,4,0,4,0,10,10,20,20,16,35,16,38,56,35,38,56,75,75,131,96,210,131,183,210,315,502},{0,0,0,1,0,1,4,1,10,4,5,11,16,5,24,5,16,45,38,17,75,39,44,81,44,149,96,97,183,189,336},{0,0,0,0,1,0,0,4,0,0,10,0,20,11,0,16,24,0,35,38,56,45,75,76,81,119,131,149,210,250,391},{0,0,0,0,0,1,0,1,0,4,4,10,10,5,20,5,16,35,20,16,35,38,38,75,44,131,75,96,131,183,315},{0,0,T^3,0,2*T^3,0,1,0,4,1,1,4,5,1+2*T^3,11,1+3*T^3,5,24,16,5,38,16,17,39,17+3*T^3,81,44,44,96,97,189},{0,0,0,0,0,0,0,1,0,0,4,0,10,4,0,5,11,0,20,16,35,24,38,45,39,76,75,81,131,149,250},{T^3,0,4*T^3,0,9*T^3,T^3,0,2*T^3,1,0,0,1,1,9*T^3,4,14*T^3,1+2*T^3,11,5,1+3*T^3,16,5,5,16,5+14*T^3,39,17,17+3*T^3,44,44,97},{0,0,0,0,0,0,0,0,0,1,1,4,4,1,10,1,5,20,10,5,20,16,16,38,17,75,38,44,75,96,183},{0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,1,4,0,10,5,20,11,16,24,16,45,38,39,75,81,149},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,0,1,10,4,1,10,5,5,16,5,38,16,17,38,44,96},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,10,4,5,11,5,24,16,16,38,39,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,0,10,10,20,16,35,20,38,35,75,131},{0,0,T^3,0,T^3,0,0,0,0,0,0,0,0,2*T^3,1,2*T^3,0,4,1,0,4,1,1,5,1+3*T^3,16,5,5,16,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,11,0,20,24,35,45,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,10,5,20,10,16,20,38,75},{0,0,4*T^3,0,4*T^3,T^3,0,T^3,0,0,0,0,0,9*T^3,0,9*T^3,2*T^3,1,0,2*T^3,1,0,0,1,14*T^3,5,1,1+3*T^3,5,5,17},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,2*T^3,0,0,1,0,4,1,1,4,1+2*T^3,11,5,5,16,16,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,11,20,24,45},{0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,4*T^3,0,9*T^3,T^3,0,0,2*T^3,1,0,0,1,9*T^3,4,1,1+2*T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,478)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 4 & 0 & 1 & 2 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 3 & 4 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 9 & 8 & 8 & 7 & 7 & 6 & 7 & 6 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 5 & 5 & 4 & 4 & 3 & 2 & 3 & 3 & 4 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -2, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{0,1,2},{1,2,4},{1,4,4}},{{2,4,5},{1,3,6},{0,1,6},{3,4,5},{0,5,6},{3,5,6},{0,2,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,2,4},{1,0,0},{0,1,1},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (36): {{1,4,10},{1,4,9},{1,3,9},{1,4,8},{1,3,8},{1,4,7},{1,3,7},{1,4,6},{1,2,7},{1,3,6},{1,2,6},{1,3,5},{0,2,6},{1,3,4},{1,2,5},{0,2,5},{1,2,4},{1,1,5},{0,1,5},{0,2,4},{1,1,4},{1,2,3},{1,2,2},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,2,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,15,20,34,35,39,65,80,111,81,175,145,149,240,160,165,250,275,371,544,391,440,290,474,665,579,514,960,730,815,1071,1230,1780},{0,1,1,4,5,10,15,20,16,34,39,65,39,111,80,81,145,85,86,149,160,240,371,250,275,165,290,440,391,306,665,474,514,730,815,1230},{0,0,1,0,4,0,10,0,15,20,34,35,34,56,65,65,111,80,81,111,145,175,260,175,240,149,250,371,260,290,544,391,474,579,730,1071},{0,0,0,1,1,4,5,10,5,15,16,34,16,65,39,39,80,40,40,81,85,145,240,149,160,86,165,275,250,170,440,290,306,474,514,815},{0,0,0,0,1,0,4,0,5,10,15,20,15,35,34,34,65,39,39,65,80,111,175,111,145,81,149,240,175,165,371,250,290,391,474,730},{0,0,T^3,0,0,1,1,4,1+T^3,5,5,15,5,34,16,16,39,16+T^3,16+2*T^3,39,40,80,145,81,85,40,86,160,149,87+2*T^3,275,165,170,290,306,514},{0,0,0,0,0,0,1,0,1,4,5,10,5,20,15,15,34,16,16,34,39,65,111,65,80,39,81,145,111,86,240,149,165,250,290,474},{T^3,0,5*T^3,0,T^3,0,0,1,5*T^3,1,1+T^3,5,1+2*T^3,15,5,5,16,5+5*T^3,5+10*T^3,16,16+T^3,39,80,39,40,16+2*T^3,40,85,81,40+10*T^3,160,86,87+2*T^3,165,170,306},{0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,10,20,15,15,20,34,35,56,35,65,34,65,111,56,81,175,111,149,175,250,391},{0,0,0,0,0,0,0,0,0,1,1,4,1,10,5,5,15,5,5,15,16,34,65,34,39,16,39,80,65,40,145,81,86,149,165,290},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,5,5,10,15,20,35,20,34,15,34,65,35,39,111,65,81,111,149,250},{0,0,T^3,0,0,0,0,0,T^3,0,0,1,0,4,1,1,5,1+T^3,1+2*T^3,5,5,15,34,15,16,5,16,39,34,16+2*T^3,80,39,40,81,86,165},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,5,10,0,0,0,20,0,15,34,0,35,39,0,65,80,111,145,240},{0,0,4*T^3,0,T^3,0,0,0,5*T^3,0,T^3,0,T^3,1,0,0,1,5*T^3,9*T^3,1,1+T^3,5,15,5,5,1+2*T^3,5,16,15,5+10*T^3,39,16,16+2*T^3,39,40,86},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,1,4,5,10,20,10,15,5,15,34,20,16,65,34,39,65,81,149},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,0,0,10,0,5,15,0,20,16,0,34,39,65,80,145},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,10,4,5,1,5,15,10,5,34,15,16,34,39,81},{0,0,0,T^2,0,4*T^2,0,10*T^2,0,0,0,0,0,0,0,0,0,1,1,T^2,4,0,0,4*T^2,10,4,10,20,10*T^2,15,35,20,34,35,65,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,10,0,0,15,0,20,34,35,65,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,1,5,0,10,5,0,15,16,34,39,80},{0,0,0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,T^2,4,1,4,10,4*T^2,5,20,10,15,20,34,65},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,T^3,0,0,1,4,1,1,0,1,5,4,1+2*T^3,15,5,5,15,16,39},{0,0,0,0,0,0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,5*T^3,5*T^3,0,T^3,0,1,0,0,T^3,0,1,1,9*T^3,5,1,1+2*T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,1,0,4,1+T^3,0,5,5,15,16,39},{T^5,0,0,0,0,0,0,T^2,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,T^2,1,10,4,5,10,15,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,5,0,10,15,20,34,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,5,10,15,34},{4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,4*T^5,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,5*T^3,0,0,0,0,0,0,T^3,0,0,1,5*T^3,0,1,1+T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{10*T^5,4*T^5,0,T^5,0,0,0,0,0,0,0,0,10*T^5,0,0,4*T^5,0,T^3,T^3,T^5,0,0,0,0,0,0,0,0,0,T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,518)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, -1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{0,1,2}},{{0,2,5},{0,4,5},{2,3,5},{3,4,5},{1,3,4},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,6},{0,2,6},{1,2,5},{1,1,5},{0,2,5},{0,1,5},{1,2,4},{1,1,4},{0,2,4},{1,2,3},{0,1,4},{1,1,3},{0,2,3},{0,1,3},{1,0,3},{1,2,2},{0,2,2},{1,1,2},{0,0,3},{0,1,2},{1,0,2},{0,0,2},{1,1,1},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,6,9,11,15,21,25,35,36,55,55,89,61,70,105,120,100,185,141,221,231,286,342,431,526,766},{0,1,1,1,5,6,5,6,15,15,21,21,35,55,22,35,70,55,61,120,61,141,120,141,231,286,286,526},{0,0,1,1,2,2,5,6,9,15,11,21,25,36,22,35,55,55,38,89,61,100,120,141,185,221,286,431},{0,0,0,1,0,2,0,5,0,0,9,15,0,25,21,0,0,35,36,55,55,89,70,120,105,185,231,342},{0,0,0,0,1,1,1,1,5,5,6,6,15,21,6,15,35,21,22,55,22,61,55,61,120,141,141,286},{0,0,0,0,0,1,0,1,0,0,5,5,0,15,6,0,0,15,21,35,21,55,35,55,70,120,120,231},{0,0,0,0,0,0,1,1,2,5,2,6,9,11,6,15,25,21,11,36,22,38,55,61,89,100,141,221},{0,0,0,0,0,0,0,1,0,0,2,5,0,9,6,0,0,15,11,25,21,36,35,55,55,89,120,185},{0,0,0,0,0,0,0,0,1,1,1,1,5,6,1,5,15,6,6,21,6,22,21,22,55,61,61,141},{0,0,0,0,0,T^3,0,0,0,1,0,1,2,2,1,5,9,6,2+T^3,11,6,11,21,22,36,38,61,100},{0,0,0,0,0,0,0,0,0,0,1,1,0,5,1,0,0,5,6,15,6,21,15,21,35,55,55,120},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,5,2,9,6,11,15,21,25,36,55,89},{0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,T^4,1,5,1,1,6,1,6,6,6,21,22,22,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,1,6,5,6,15,21,21,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,5,9,0,15,0,25,35,55},{0,T^3,0,T^4,0,4*T^3,0,0,0,0,T^3,0,0,0,T^4,1,2,1,4*T^3,2,1,2+T^3,6,6,11,11,22,38},{T^4,0,0,6*T^4,0,T^4,0,T^4,0,0,0,0,0,0,6*T^4,0,1,0,T^4,1,T^4,1,1,1,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,5,6,9,11,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,556)$ |
3 |
25 |
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9: $\begin{pmatrix}0 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 3 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 7 & 8 & 6 & 7 & 7 & 5 & 6 & 5 & 4 & 6 & 4 & 5 & 3 & 5 & 3 & 5 & 4 & 3 & 4 & 2 & 3 & 2 & 3 & 1 & 3 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -1, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {3, 5, 6, 7}, {0, 1, 2, 8}, {0, 1, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2},{-1,1,2}},{{3,4,5},{3,5,6},{0,4,5},{0,1,5},{1,5,6},{0,1,2},{0,2,4},{2,3,4}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,2},{0,1,2},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,2,7},{0,3,8},{1,2,6},{0,3,7},{0,2,7},{1,2,5},{0,3,6},{1,1,5},{1,2,4},{0,2,6},{1,1,4},{0,3,5},{1,2,3},{0,2,5},{1,1,3},{0,1,5},{0,2,4},{1,0,3},{0,1,4},{1,1,2},{0,2,3},{1,0,2},{0,1,3},{1,1,1},{0,0,3},{1,0,1},{0,1,2},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,4,5,10,10,13,20,16,32,20,35,38,65,41,75,71,90,116,131,140,173,189,179,249,300,328,408,481,557,886},{0,1,1,4,4,4,10,4,10,13,13,20,20,32,32,32,65,32,71,65,116,71,140,116,140,140,249,259,249,408,448,727},{0,0,1,1,1,4,4,4,10,5,13,10,20,16,32,16,38,32,41,65,75,71,90,116,90,140,173,179,249,300,328,557},{0,0,0,1,1,1,4,1,4,4,4,10,10,13,13,13,32,13,32,32,65,32,71,65,71,71,140,140,140,249,259,448},{0,0,0,0,1,0,0,1,0,4,4,0,0,10,10,13,20,13,32,20,35,32,65,35,71,65,116,140,116,189,249,408},{0,0,0,0,0,1,1,1,4,1,4,4,10,5,13,5,16,13,16,32,38,32,41,65,41,71,90,90,140,173,179,328},{0,0,0,0,0,0,1,0,1,1,1,4,4,4,4,4,13,4,13,13,32,13,32,32,32,32,71,71,71,140,140,259},{0,0,0,0,0,0,0,1,0,1,4,0,0,4,10,5,10,13,16,20,20,32,38,35,41,65,75,90,116,131,173,300},{0,0,0,0,2*T^3,0,0,0,1,0,1,1,4,1,4,1+3*T^3,5,4,5,13,16,13,16,32,16+4*T^3,32,41,41,71,90,90,179},{0,0,0,0,0,0,0,0,0,1,1,0,0,4,4,4,10,4,13,10,20,13,32,20,32,32,65,71,65,116,140,249},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,4,4,5,10,10,13,16,20,16,32,38,41,65,75,90,173},{T^3,0,0,0,3*T^3,0,0,3*T^3,0,0,0,1,1,1,1,1+6*T^3,4,1+6*T^3,4,4,13,4,13,13,13+10*T^3,13,32,32,32,71,71,140},{T^3,T^3,0,0,9*T^3,0,0,3*T^3,0,2*T^3,0,0,1,0,1,15*T^3,1,1+6*T^3,1+3*T^3,4,5,4,5,13,5+22*T^3,13,16,16+4*T^3,32,41,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,1,4,4,10,4,13,10,13,13,32,32,32,65,71,140},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,4,4,4,5,10,5,13,16,16,32,38,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,10,0,13,10,20,32,20,35,65,116},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,4,4,4,4,13,13,13,32,32,71},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,4,4,0,5,10,10,16,20,20,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,4,10,13,10,20,32,65},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,1,1,4,1+3*T^3,4,5,5,13,16,16,41},{0,0,0,0,T^3,0,0,T^3,0,0,0,0,0,0,0,3*T^3,0,3*T^3,0,0,1,0,1,1,1+6*T^3,1,4,4,4,13,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,4,5,10,10,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,4,10,13,32},{0,0,0,0,4*T^3,0,0,T^3,0,T^3,0,0,0,0,0,9*T^3,0,3*T^3,2*T^3,0,0,0,0,1,15*T^3,1,1,1+3*T^3,4,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,593)$ |
3 |
25 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -1 & 0 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}3 & 2 & 2 & 3 & 1 & 2 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 3 & 3 & 1 & 4 & 2 & 2 & 0 & 3 & 1 & -1 & 1 & 3 & 4 & 2 & 0 & 0 & 2 & 3 & 1 & -1 & 3 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (25): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 1, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,0,-1},{1,-1,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,5,7},{0,4,5},{0,2,3},{0,2,6,7},{1,6,8},{6,7,8},{1,2,3},{1,2,6},{0,3,4},{5,7,8}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-1},{1,0,0},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (31): {{3,0,2},{2,1,3},{2,0,3},{3,0,1},{1,1,4},{2,1,2},{2,0,2},{3,0,0},{1,1,3},{2,1,1},{3,0,-1},{2,0,1},{1,0,3},{0,1,4},{1,1,2},{2,1,0},{2,0,0},{1,0,2},{0,1,3},{1,1,1},{2,0,-1},{0,0,3},{1,0,1},{0,1,2},{1,1,0},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{1,0,-1},{0,0,0}}
Ext matrix: {{1,1,2,4,2,4,10,10,10,10,20,28,16,16,28,20,60,49,49,60,110,70,112,112,110,168,215,215,336,368,594},{0,1,1,1,2,4,5,4,10,10,10,16,11,16,28,20,38,34,49,60,75,55,81,112,110,133,162,215,271,287,489},{0,0,1,0,1,0,4,0,4,0,0,10,10,10,10,0,20,28,28,20,35,49,60,60,35,112,110,110,215,182,368},{0,0,0,1,0,1,2,4,2,4,10,10,3,3,10,10,28,16,16,28,60,22,49,49,60,70,112,112,168,215,336},{0,0,0,0,1,0,1,0,4,0,0,4,5,10,10,0,10,16,28,20,20,34,38,60,35,81,75,110,162,131,287},{0,0,0,0,0,1,1,1,2,4,4,5,2,3,10,10,16,11,16,28,38,17,34,49,60,55,81,112,133,162,271},{0,0,0,0,0,0,1,0,1,0,0,4,2,2,4,0,10,10,10,10,20,16,28,28,20,49,60,60,112,110,215},{0,0,0,0,0,0,0,1,0,1,4,2,0,0,2,4,10,3,3,10,28,4,16,16,28,22,49,49,70,112,168},{0,0,0,0,0,0,0,0,1,0,0,1,1,2,4,0,4,5,10,10,10,11,16,28,20,34,38,60,81,75,162},{0,0,2*T^3,0,0,0,0,0,0,1,1,1,3*T^3,0,2,4,5,2,3,10,16,3+4*T^3,11,16,28,17,34,49,55,81,133},{0,0,2*T^3,0,2*T^3,0,0,0,0,0,1,0,3*T^3,3*T^3,0,1,2,0,0,2,10,4*T^3,3,3,10,4,16,16,22,49,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,2,2,4,10,3,10,10,10,16,28,28,49,60,112},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,4,4,0,0,10,10,10,0,28,20,20,60,35,110},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,0,5,4,10,0,16,10,20,38,20,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,2,4,4,2,5,10,10,11,16,28,34,38,81},{T^3,0,9*T^3,0,2*T^3,0,2*T^3,0,0,0,0,0,14*T^3,3*T^3,0,1,1,3*T^3,0,2,5,19*T^3,2,3,10,3+4*T^3,11,16,17,34,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,2,2,4,3,10,10,16,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,4,4,0,10,10,10,28,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,0,5,4,10,16,10,38},{0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,1,1,3*T^3,1,2,4,2,5,10,11,16,34},{0,0,T^3,0,T^3,0,0,0,0,0,0,0,2*T^3,2*T^3,0,0,0,0,0,0,1,3*T^3,0,0,1,0,2,2,3,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,4,4,10,10,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,5,4,16},{0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,0,9*T^3,2*T^3,0,0,0,2*T^3,0,0,0,14*T^3,0,0,1,3*T^3,1,2,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,601)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & -1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 2 & 2 & -1 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
42: $\begin{pmatrix}1 & 0 & 2 & 1 & -1 & 0 & 2 & -1 & 0 & 1 & 0 & -1 & 2 & 1 & -1 & 2 & 1 & 0 & 0 & 2 & -1 & 1 & 0 & 2 & 1 & 0 & 1 & -1 & -1 & 0 & 2 & 1 & 1 & 0 & -1 & -1 & 0 & 1 & 0 & -1 & 1 & 0 \\ 1 & 2 & 0 & 1 & 3 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 0 & 3 & -1 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & -1 & 1 & 0 & 0 & 2 & 1 & 1 & -1 & -1 & 0 & 0 & 2 & 1 & 1 & -1 & 0 & 1 & -1 & 0 \\ 5 & 6 & 3 & 4 & 7 & 5 & 2 & 6 & 5 & 3 & 4 & 6 & 1 & 3 & 5 & 1 & 2 & 4 & 3 & 0 & 5 & 2 & 3 & 0 & 1 & 3 & 1 & 4 & 4 & 2 & -1 & 1 & 0 & 2 & 3 & 3 & 1 & 0 & 1 & 2 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {1, 2, 6, 7}, {5, 6, 7}, {0, 1, 2, 8}, {0, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2},{-1,1,2}},{{3,4,5},{0,2,4},{1,5,6},{0,4,5},{0,1,5},{0,1,2},{3,5,6},{2,3,4}},{4,1,2})
Cox degrees: {{0,0,1},{-1,1,2},{-1,1,2},{1,-1,-1},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (42): {{1,1,5},{0,2,6},{2,0,3},{1,1,4},{-1,3,7},{0,2,5},{2,0,2},{-1,3,6},{0,1,5},{1,1,3},{0,2,4},{-1,2,6},{2,0,1},{1,0,3},{-1,3,5},{2,-1,1},{1,1,2},{0,1,4},{0,2,3},{2,0,0},{-1,2,5},{1,0,2},{0,1,3},{2,-1,0},{1,1,1},{0,0,3},{1,0,1},{-1,2,4},{-1,1,4},{0,1,2},{2,-1,-1},{1,-1,1},{1,0,0},{0,0,2},{-1,2,3},{-1,1,3},{0,1,1},{1,-1,0},{0,0,1},{-1,1,2},{1,-1,-1},{0,0,0}}
Ext matrix: {{1,2,2,6,3,10,10,14,11,20,30,16,30,23,40,35,50,38,70,70,53,66,100,94,105,103,155,134,142,220,210,161,316,238,285,318,427,346,487,632,671,906},{0,1,0,2,2,6,3,10,6,10,20,11,14,10,30,14,30,23,50,40,38,35,66,47,70,66,94,100,103,155,122,94,210,161,220,238,316,219,346,487,454,671},{0,0,1,2,0,3,6,4,3,10,14,4,20,11,18,23,30,16,40,50,21,38,53,66,70,54,100,68,70,134,155,103,220,142,168,181,285,238,318,398,487,632},{0,0,0,1,0,2,2,3,2,6,10,3,10,6,14,10,20,11,30,30,16,23,38,35,50,38,66,53,54,100,94,66,155,103,134,142,220,161,238,318,346,487},{0,0,4*T^2,0,1,2,6*T^2,6,2,3,10,6,4+8*T^2,3,20,4+9*T^2,14,10,30,18+10*T^2,23,14,35,18+12*T^2,40,35,47,66,66,94,59+15*T^2,47,122,94,155,161,210,122,219,346,277,454},{0,0,0,0,0,1,0,2,1,2,6,2,3,2,10,3,10,6,20,14,11,10,23,14,30,23,35,38,38,66,47,35,94,66,100,103,155,94,161,238,219,346},{0,0,0,0,0,0,1,0,0,2,3,0,6,2,4,6,10,3,14,20,4,11,16,23,30,16,38,21,21,53,66,38,100,54,68,70,134,103,142,181,238,318},{0,0,2*T^2,0,0,0,4*T^2,1,0,0,2,1,6*T^2,0,6,6*T^2,3,2,10,4+8*T^2,6,3,10,4+9*T^2,14,10,14,23,23,35,18+12*T^2,14,47,35,66,66,94,47,94,161,122,219},{0,0,0,0,0,0,0,0,1,0,0,2,0,2,0,3,0,6,0,0,10,10,20,14,0,23,30,30,38,50,40,35,70,66,70,100,105,94,155,220,210,316},{0,0,0,0,0,0,0,0,0,1,2,0,2,1,3,2,6,2,10,10,3,6,11,10,20,11,23,16,16,38,35,23,66,38,53,54,100,66,103,142,161,238},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,1,6,3,2,2,6,3,10,6,10,11,11,23,14,10,35,23,38,38,66,35,66,103,94,161},{0,0,2*T^2,0,0,0,3*T^2,0,0,0,0,1,4*T^2,0,0,6*T^2,0,2,0,5*T^2,6,3,10,4+8*T^2,0,10,14,20,23,30,18+10*T^2,14,40,35,50,66,70,47,94,155,122,210},{0,0,0,0,0,0,0,0,T^3,0,0,2*T^3,1,0,0,1,2,0,3,6,0,2,3,6,10,3+T^3,11,4,4+2*T^3,16,23,11,38,16,21,21,53,38,54,70,103,142},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,0,0,3,6,10,10,0,11,20,14,16,30,30,23,50,38,40,53,70,66,100,134,155,220},{T^3,0,T^2+3*T^3,0,0,0,2*T^2,0,T^3,0,0,0,4*T^2,3*T^3,1,4*T^2+6*T^3,0,0,2,6*T^2,1,0,2,6*T^2,3,2+3*T^3,3,6,6,10,4+9*T^2,3+6*T^3,14,10,23,23,35,14,35,66,47,94},{0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,3*T^3,1,0,0,0,0,0,2,3,6,0,3,10,4,4,14,20,11,30,16,18,21,40,38,53,68,100,134},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,2,2,0,1,2,2,6,2,6,3,3+T^3,11,10,6,23,11,16,16,38,23,38,54,66,103},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,6,3,0,6,10,10,11,20,14,10,30,23,30,38,50,35,66,100,94,155},{0,0,T^3,0,0,0,0,0,T^4,0,0,0,0,T^3,0,3*T^3,0,0,1,0,0,0,1,0,2,1+T^3+T^4,2,2,2,6,3,2+3*T^3,10,6,11,11,23,10,23,38,35,66},{0,T^3,0,0,2*T^3,0,0,0,2*T^3,0,0,7*T^3,0,0,0,0,0,T^3,0,1,2*T^3,0,0,1,2,2*T^3,2,0,7*T^3,3,6,2,11,3+T^3,4,4+2*T^3,16,11,16,21,38,54},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,4*T^2,0,0,0,4*T^2,1,0,2,6*T^2,0,2,3,6,6,10,4+8*T^2,3,14,10,20,23,30,14,35,66,47,94},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,2,6,3,3,10,10,6,20,11,14,16,30,23,38,53,66,100},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,2,6,3,2,10,6,10,11,20,10,23,38,35,66},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,1,0,0,2,0,0,3,6,2,10,3,4,4,14,11,16,21,38,53},{T^4,0,0,0,T^3,0,0,0,3*T^4,0,0,2*T^3,0,T^4,0,T^3,0,0,0,0,T^3,0,0,0,1,3*T^4,1,0,2*T^3,2,2,1+T^3+T^4,6,2,3,3+T^3,11,6,11,16,23,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,0,6,0,10,0,10,20,30,30,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,1,6,2,3,3,10,6,11,16,23,38},{0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,2*T^2,0,0,0,3*T^2,0,0,0,4*T^2,0,0,0,1,1,2,6*T^2,0,3,2,6,6,10,3,10,23,14,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,0,1,0,4*T^2,0,0,2,0,6,0,3,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,2,6,2,6,11,10,23},{0,0,0,0,T^4,0,0,0,T^3,0,0,2*T^3,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,2*T^3,0,1,0,2,0,0,0,3,2,3,4,11,16},{0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,3,0,6,10,14,20,30},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,0,0,0,2,1,2,3,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,6,10,10,20},{0,0,T^3,0,0,0,0,0,0,0,0,0,T^2,T^3,0,T^2+3*T^3,0,0,0,2*T^2,0,0,0,2*T^2,0,T^3,0,0,0,0,4*T^2,3*T^3,0,0,1,1,2,0,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,1,0,0,2,6,3,10},{0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,T^3,0,0,0,0,1,0,1,2,2,6},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,612)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & -1 & -1 & 2 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
40: $\begin{pmatrix}2 & 3 & 1 & 0 & 1 & 2 & 1 & 0 & 3 & 2 & 1 & -1 & 0 & 2 & 0 & 3 & 1 & 2 & 0 & 1 & -1 & 0 & 2 & -1 & 0 & 1 & 2 & 1 & 0 & -1 & 1 & 1 & 2 & 0 & -1 & 1 & 0 & -1 & 1 & 0 \\ 0 & -1 & 1 & 2 & 0 & 0 & 1 & 1 & -1 & -1 & 0 & 2 & 2 & 0 & 1 & -1 & 1 & -1 & 2 & 0 & 2 & 0 & 0 & 1 & 1 & 1 & -1 & -1 & 0 & 2 & 0 & -1 & -1 & 1 & 1 & 0 & 0 & 1 & -1 & 0 \\ 2 & 0 & 3 & 4 & 3 & 1 & 2 & 4 & -1 & 1 & 2 & 5 & 3 & 0 & 3 & -2 & 1 & 0 & 2 & 1 & 4 & 3 & -1 & 4 & 2 & 0 & -1 & 1 & 2 & 3 & 0 & 0 & -2 & 1 & 3 & -1 & 1 & 2 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, -1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 6, 8}}
Primitive collections: {{1, 2, 4, 6}, {3, 5, 7}, {4, 6, 7}, {0, 1, 2, 8}, {0, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,0,-1},{1,-1,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,5,7},{0,4,5},{1,2,6},{1,6,8},{0,3,4},{1,2,3},{0,2,3},{5,7,8},{0,2,6,7},{6,7,8}},{4,1,2})
Cox degrees: {{0,0,1},{1,-1,-1},{1,-1,-1},{-1,1,2},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (40): {{2,0,2},{3,-1,0},{1,1,3},{0,2,4},{1,0,3},{2,0,1},{1,1,2},{0,1,4},{3,-1,-1},{2,-1,1},{1,0,2},{-1,2,5},{0,2,3},{2,0,0},{0,1,3},{3,-1,-2},{1,1,1},{2,-1,0},{0,2,2},{1,0,1},{-1,2,4},{0,0,3},{2,0,-1},{-1,1,4},{0,1,2},{1,1,0},{2,-1,-1},{1,-1,1},{0,0,2},{-1,2,3},{1,0,0},{1,-1,0},{2,-1,-2},{0,1,1},{-1,1,3},{1,0,-1},{0,0,1},{-1,1,2},{1,-1,-1},{0,0,0}}
Ext matrix: {{1,2,2,3,3,6,10,5,10,8,17,7,14,20,26,30,30,32,40,56,35,33,50,47,80,70,90,68,107,104,140,182,205,190,146,295,266,350,405,560},{0,1,0,3*T^2,0,2,3,0,6,3,5,3*T^2,4+5*T^2,10,7,20,14,17,18+7*T^2,26,9+6*T^2,9,30,12,35,40,56,33,47,44+9*T^2,80,107,140,104,61,190,146,185,266,350},{0,0,1,2,1,2,6,3,3,2,8,5,10,10,17,14,20,13,30,32,26,19,30,33,56,50,47,35,68,80,90,107,124,140,107,205,182,266,262,405},{0,0,0,1,0,0,2,1,0,0,2,3,6,3,8,4,10,3,20,13,17,8,14,19,32,30,18,13,35,56,47,51,62,90,68,124,107,182,146,262},{0,0,0,0,1,0,0,2,0,2,6,3,0,0,10,0,0,10,0,20,14,17,0,26,30,0,30,32,56,40,50,90,70,70,80,105,140,190,205,295},{0,0,0,0,0,1,2,0,2,1,3,0,3,6,5,10,10,8,14,17,7,6,20,9,26,30,32,19,33,35,56,68,90,80,47,140,107,146,182,266},{0,0,0,0,0,0,1,0,0,0,1,0,2,2,3,3,6,2,10,8,5,3,10,6,17,20,13,8,19,26,32,35,47,56,33,90,68,107,107,182},{0,0,0,0,0,0,0,1,0,0,2,2,0,0,6,0,0,3,0,10,10,8,0,17,20,0,14,13,32,30,30,47,40,50,56,70,90,140,124,205},{0,0,0,T^2,0,0,0,0,1,0,0,T^2+T^3,3*T^2,2,0,6,3,3,4+5*T^2,5,3*T^2,0,10,0,7,14,17,6,9,9+6*T^2,26,33,56,35,12,80,47,61,107,146},{0,0,0,2*T^2,0,0,0,0,0,1,2,3*T^2,3*T^2,0,3,0,0,6,4*T^2,10,4+5*T^2,5,0,7,14,0,20,17,26,18+7*T^2,30,56,50,40,35,70,80,104,140,190},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,2,0,6,3,3,0,5,10,0,10,8,17,14,20,32,30,30,26,50,56,80,90,140},{0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,1,0,0,2,5*T^3,0,0,0,3,6,2,0,8,10,0,4,3,13,20,14,18,18,30,32,40,47,90,62,124},{0,0,0,0,T^3,0,0,0,0,2*T^3,0,0,1,0,1,0,2,0,6,2,3,1+T^3,3,3,8,10,3,2+2*T^3,8,17,13,13,18,32,19,47,35,68,51,107},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,1,3,3,0,0,6,0,5,10,8,3,6,7,17,19,32,26,9,56,33,47,68,107},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,1,0,3,6,0,3,2,8,10,10,13,14,20,17,30,32,56,47,90},{0,0,0,T^3,0,0,0,T^3,0,0,0,5*T^3,T^2,0,0,1,0,0,3*T^2,0,T^2+T^3,0,2,T^3,0,3,3,0,0,3*T^2,5,6,17,7,0,26,9,12,33,47},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,2,1,0,0,2,0,3,6,2,1+T^3,3,5,8,8,13,17,6,32,19,33,35,68},{0,0,0,T^2,0,0,0,0,0,0,0,T^2,2*T^2,0,0,0,0,1,3*T^2,2,3*T^2,0,0,0,3,0,6,3,5,4+5*T^2,10,17,20,14,7,30,26,35,56,80},{T^3,2*T^3,0,0,3*T^3,0,0,0,0,8*T^3,T^3,0,0,0,0,0,0,2*T^3,1,0,0,3*T^3,0,0,1,2,0,8*T^3,1+T^3,3,2,2+2*T^3,3,8,3,13,8,19,13,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,2,1,3,3,6,8,10,10,5,20,17,26,32,56},{0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,0,0,1,0,0,1,2,0,0,0,2,6,3,3,4,10,8,14,13,32,18,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,2,6,0,0,10,0,0,10,0,20,30,30,50},{0,0,0,0,T^4,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^4,1,0,0,2,1,0,0,0,3,3,8,5,0,17,6,9,19,33},{0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,3,0,0,6,0,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,2,2,3,6,3,10,8,17,13,32},{0,T^3,0,0,2*T^4,0,0,T^4,0,3*T^3,0,0,0,0,0,0,0,T^3,0,0,0,2*T^4,0,T^4,0,1,0,3*T^3,0,0,1,1+T^3,2,3,0,8,3,6,8,19},{0,0,0,0,0,0,0,0,0,0,0,T^3,T^2,0,0,0,0,0,2*T^2,0,T^2,0,0,0,0,0,1,0,0,3*T^2,2,3,6,3,0,10,5,7,17,26},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,1,2,3*T^2,0,6,0,0,3,0,10,14,20,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,0,6,10,10,20},{0,T^3,0,0,T^3,0,0,0,2*T^3,2*T^3,0,0,0,0,0,3*T^3,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,1,0,0,0,2,1,3,2,8,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,0,6,3,5,8,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,1,0,0,0,0,2,3,6,10},{0,0,0,T^3,0,0,0,T^3,0,0,0,5*T^3,0,0,0,0,0,0,T^2,0,T^3,0,0,T^3,0,0,0,0,0,T^2,0,0,1,0,0,2,0,0,3,5},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,2,1,3,2,8},{0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,6,3,10},{0,0,0,0,T^4,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,649)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & -1 & -1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & -1 & -1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}3 & 2 & 1 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 0 & 2 & 1 & 1 & 3 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 & 1 & -1 & 2 & 0 & 0 & 1 & -1 & 1 & 2 & 0 & 2 & 1 & -1 & -1 & 2 & 0 & 0 & 1 & -1 & 1 & 2 & 0 & -1 & 1 & -1 & 0 & 0 & 1 & -1 & 0 & -1 & 0 \\ 2 & 3 & 4 & 1 & 2 & 1 & 3 & 2 & 0 & 3 & 0 & 1 & 4 & 1 & 2 & 2 & -1 & 1 & 3 & 2 & 0 & 3 & 0 & 1 & 2 & 1 & -1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, -1, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 6}, {4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,3,5},{0,2,3},{0,1,4},{4,5,6},{0,4,5},{1,4,6},{3,5,6},{0,1,2}},{4,1,2})
Cox degrees: {{0,0,1},{1,-1,-1},{1,-1,-1},{1,0,0},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{3,0,2},{2,1,3},{1,2,4},{3,0,1},{2,1,2},{3,-1,1},{1,2,3},{2,0,2},{3,0,0},{1,1,3},{3,-1,0},{2,1,1},{0,2,4},{2,0,1},{1,2,2},{1,1,2},{3,-1,-1},{2,-1,1},{0,2,3},{1,0,2},{2,0,0},{0,1,3},{2,-1,0},{1,1,1},{0,2,2},{1,0,1},{2,-1,-1},{0,1,2},{1,-1,1},{0,0,2},{1,0,0},{0,1,1},{1,-1,0},{0,0,1},{1,-1,-1},{0,0,0}}
Ext matrix: {{1,2,3,4,7,5,10,11,10,17,16,16,23,31,22,46,38,35,61,56,66,77,84,94,122,130,168,176,140,196,249,330,289,400,523,709},{0,1,2,1,4,1,7,5,4,11,5,10,17,16,16,31,16,17,46,35,38,56,44,66,94,84,96,130,88,140,168,249,186,289,349,523},{0,0,1,0,1,0,4,1,1,5,1,4,11,5,10,16,5,5,31,17,16,35,17,38,66,44,44,84,45,88,96,168,102,186,204,349},{0,0,0,1,2,1,3,2,4,3,5,7,4,11,10,17,16,11,23,17,31,23,35,46,61,56,84,77,56,77,130,176,140,196,289,400},{0,0,0,0,1,0,2,1,1,2,1,4,3,5,7,11,5,5,17,11,16,17,17,31,46,35,44,56,35,56,84,130,88,140,186,289},{0,0,2*T^2,0,0,1,4*T^2,2,0,3,4,0,4+3*T^2,7,6*T^2,10,10,11,13+6*T^2,17,16,23,31,22,28+9*T^2,46,66,61,56,77,94,122,130,176,249,330},{0,0,0,0,0,2*T^3,1,0,0,1,0,1,2,1,4,5,1,1+3*T^3,11,5,5,11,5,16,31,17,17,35,17+4*T^3,35,44,84,45,88,102,186},{0,0,0,0,0,0,0,1,0,2,1,0,3,4,0,7,4,5,10,11,10,17,16,16,22,31,38,46,35,56,66,94,84,130,168,249},{0,0,0,0,0,0,0,0,1,0,1,2,0,2,3,3,5,2,4,3,11,4,11,17,23,17,35,23,17,23,56,77,56,77,140,196},{0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,4,1,1,7,5,4,11,5,10,16,16,16,31,17,35,38,66,44,84,96,168},{0,0,0,0,0,0,2*T^2,0,0,0,1,0,0,2,4*T^2,3,4,2,4+3*T^2,3,7,4,11,10,13+6*T^2,17,31,23,17,23,46,61,56,77,130,176},{0,0,0,0,0,2*T^3,0,0,0,0,0,1,0,1,2,2,1,1+3*T^3,3,2,5,3,5,11,17,11,17,17,11+4*T^3,17,35,56,35,56,88,140},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,1,1,5,1,4,10,5,5,16,5,17,16,38,17,44,44,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,3,2,4,3,5,7,10,11,16,17,11,17,31,46,35,56,84,130},{T^3,0,0,0,0,9*T^3,0,2*T^3,0,0,2*T^3,0,0,0,1,1,0,14*T^3,2,1+3*T^3,1,2,1+3*T^3,5,11,5,5,11,5+19*T^3,11+4*T^3,17,35,17+4*T^3,35,45,88},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,1,2,1,4,7,5,5,11,5,11,16,31,17,35,44,84},{0,0,2*T^3,0,0,0,0,0,0,0,0,0,3*T^3,0,2*T^2,0,1,0,0,0,2,0,2,3,4+3*T^2,3,11,4,3,4,17,23,17,23,56,77},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,2*T^2,0,3*T^2,0,0,1,4*T^2,2,0,3,4,0,6*T^2,7,10,10,11,17,16,22,31,46,66,94},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,0,1,4,1,1,5,1+3*T^3,5,5,16,5,17,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,4,4,7,5,11,10,16,16,31,38,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,2,5,3,2,3,11,17,11,17,35,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,4,1,5,4,10,5,16,16,38},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,2*T^2,0,0,0,1,0,4*T^2,2,4,3,2,3,7,10,11,17,31,46},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,2,1,1,2,1+3*T^3,2,5,11,5,11,17,35},{0,0,0,0,0,4*T^3,0,T^3,0,0,T^3,0,0,0,0,0,0,9*T^3,0,2*T^3,0,0,2*T^3,0,1,0,0,1,14*T^3,1+3*T^3,1,5,1+3*T^3,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,2,4,7,5,11,16,31},{0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,1,0,0,0,2,3,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,1,2,0,0,4,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,1,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,1,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,653)$ |
3 |
28 |
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9: $\begin{pmatrix}-1 & -1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}-2 & -3 & -1 & 0 & -2 & -2 & 1 & -3 & -1 & -1 & -2 & 0 & -3 & 1 & -1 & -2 & 0 & -1 & -3 & 0 & 1 & -2 & 0 & -1 & -2 & 1 & -1 & 0 & 1 & -1 & 0 & 0 & -2 & -1 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 4 & 5 & 5 & 3 & 5 & 4 & 4 & 4 & 3 & 5 & 2 & 3 & 4 & 3 & 3 & 4 & 2 & 2 & 3 & 2 & 3 & 3 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {-1, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 2, 5}, {4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {3, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{2,5,6},{1,4,6},{4,5,6},{0,1,4},{0,4,5},{2,3,6},{1,3,6},{0,2,5}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{-1,0,1},{1,0,0},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{-2,2,6},{-3,2,6},{-1,2,5},{0,2,4},{-2,2,5},{-2,1,5},{1,2,3},{-3,2,5},{-1,2,4},{-1,1,4},{-2,2,4},{0,2,3},{-3,1,5},{1,2,2},{-1,2,3},{-2,1,4},{0,1,3},{-1,1,3},{-3,1,4},{0,2,2},{1,1,2},{-2,1,3},{0,1,2},{-1,0,3},{-2,0,3},{1,1,1},{-1,1,2},{0,0,2},{1,0,1},{-1,0,2},{0,1,1},{0,0,1},{-2,0,2},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,6,7,8,10,11,15,19,25,26,13,40,45,34,35,67,49,71,56,101,112,71,110,169,175,122,188,199,271,319,279,461,470,696},{0,1,0,0,3,3,T^3,7,6,6,15,10,8,15+T^3,26,19,10,35,34,40,15,67,56,35,71,82,112,56,82,122,169,188,199,319,269,470},{0,0,1,3,2,2,6,3,7,8,11,15,3,26,25,13,19,34,18,45,35,49,67,35,51,112,101,71,122,110,175,199,149,279,319,461},{0,0,0,1,0,0,3,0,2,2,3,7,0,15,11,3,8,13,4,25,19,18,34,13,18,67,49,35,71,51,101,110,67,149,199,279},{0,0,0,0,1,1,0,2,3,3,7,6,2,10,15,8,6,19,13,26,10,34,35,19,35,56,67,35,56,71,112,122,110,199,188,319},{0,0,0,0,0,1,T^3,0,0,3,0,0,2,T^3,0,7,6,15,11,0,10,25,26,19,34,40,45,35,56,67,71,112,101,175,169,271},{0,2*T^3,0,0,0,2*T^3,1,2*T^3,0,0,0,2,6*T^3,7,3,0,2,3,3*T^3,11,8,4,13,3+2*T^3,4+3*T^3,34,18,13,35,18,49,51,23,67,110,149},{0,0,0,0,0,0,T^3,1,0,0,3,0,1,T^3,6,3,0,6,8,10,0,19,10,6,19,15,35,10,15,35,56,56,71,122,82,188},{0,0,0,0,0,0,0,0,1,1,2,3,0,6,7,2,3,8,3,15,6,13,19,8,13,35,34,19,35,35,67,71,51,110,122,199},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,3,7,3,0,6,11,15,8,13,26,25,19,35,34,45,67,49,101,112,175},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,3,2,6,0,8,6,3,8,10,19,6,10,19,35,35,35,71,56,122},{0,0,0,0,0,T^3,0,0,0,0,0,1,2*T^3,3,2,0,1,2,0,7,3,3,8,2+T^3,3+2*T^3,19,13,8,19,13,34,35,18,51,71,110},{0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,1,7*T^3,0,3,0,6,7,T^3,T^3,15,10,6,19,15+T^3,26,10,15,35,40,56,67,112,82,169},{T^3,4*T^3,0,0,0,6*T^3,0,2*T^3,0,T^3,0,0,14*T^3,1,0,2*T^3,0,0,6*T^3,2,1,0,2,6*T^3,11*T^3,8,3,2+T^3,8,3+2*T^3,13,13,4+3*T^3,18,35,51},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,1,0,3,0,2,3,1,2+T^3,6,8,3,6,8,19,19,13,35,35,71},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,1,0,3,2,0,0,7,6,3,8,10,15,6,10,19,26,35,34,67,56,112},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,3,3,7,2,3,15,11,8,19,13,25,34,18,49,67,101},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,1,2,6,7,3,6,8,15,19,13,34,35,67},{0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,7*T^3,0,0,0,0,1,T^3,T^3,3,0,0,3,T^3,6,0,0,6,10,10,19,35,15,56},{0,T^3,0,0,0,T^3,0,0,0,0,0,0,6*T^3,0,0,T^3,0,0,2*T^3,1,0,0,1,T^3,6*T^3,3,2,1,3,2+T^3,8,8,3+2*T^3,13,19,35},{0,T^3,0,0,0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,0,2*T^3,0,1,0,2,0,0,7,3,2,8,3,11,13,4,18,34,49},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,1,0,3,0,0,3,6,6,8,19,10,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,1,3,2,7,8,3,13,19,34},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,2,0,0,3,6,7,0,15,11,25,26,45},{0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,T^3,0,0,0,1,T^3,0,0,0,3,0,6,7,15,10,26},{0,T^3,0,0,0,T^3,0,T^3,0,0,0,0,4*T^3,0,0,0,0,0,2*T^3,0,0,0,0,T^3,2*T^3,1,0,0,1,0,2,2,0,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,3,2,8,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,0,7,3,11,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,7,11},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,7,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,1,0,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,7},{0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,T^3,0,0,0,0,T^3,0,0,0,0,0,0,1,3,0,6},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,654)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 3 & 5 & 1 & 3 & 4 & 2 & 0 & 2 & 1 & 3 & 1 & 2 & 0 & 3 & 2 & 1 & 0 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,3,0},{0,1,-1},{0,0,1},{1,1,2}},{{1,4,5},{1,2,5},{1,2,3},{0,2,3},{0,4,5},{0,2,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,-1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,5},{1,3,4},{1,2,5},{1,3,3},{1,2,4},{1,3,2},{1,2,3},{1,1,5},{1,3,1},{0,2,3},{1,1,4},{1,2,2},{1,3,0},{0,2,2},{1,2,1},{1,1,3},{0,2,1},{1,1,2},{1,2,0},{0,1,3},{0,1,2},{1,1,1},{0,2,0},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,6,10,18,20,40,21,35,41,52,75,56,79,126,105,136,186,196,111,204,301,216,247,456,341,433,531,701,1067},{0,1,1,4,6,10,18,6,20,18,21,40,35,41,75,52,79,105,126,53,111,186,136,127,301,204,247,341,433,701},{0,0,1,0,4,0,10,6,0,10,18,20,0,20,35,40,35,75,56,41,79,126,56,111,196,136,204,216,341,531},{0,0,0,1,1,4,6,1,10,6,6,18,20,18,40,21,41,52,75,21,53,105,79,57,186,111,127,204,247,433},{0,0,0,0,1,0,4,1,0,4,6,10,0,10,20,18,20,40,35,18,41,75,35,53,126,79,111,136,204,341},{0,0,0,0,0,1,1,0,4,1,1,6,10,6,18,6,18,21,40,6,21,52,41,21,105,53,57,111,127,247},{0,0,0,0,0,0,1,0,0,1,1,4,0,4,10,6,10,18,20,6,18,40,20,21,75,41,53,79,111,204},{0,0,0,0,0,0,0,1,0,0,4,0,0,0,0,10,0,20,0,10,20,35,0,41,56,35,79,56,136,216},{T^3,0,2*T^3,0,0,0,0,3*T^3,1,T^3,0,1,4,1,6,1,6,6,18,1+2*T^3,6,21,18,6+3*T^3,52,21,21,53,57,127},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,0,6,18,0,20,21,0,40,52,75,105,186},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,10,0,4,10,20,0,18,35,20,41,35,79,136},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,4,6,10,1,6,18,10,6,40,18,21,41,53,111},{4*T^3,T^3,9*T^3,0,2*T^3,0,0,14*T^3,0,4*T^3,3*T^3,0,1,T^3,1,0,1,1,6,9*T^3,1+2*T^3,6,6,1+14*T^3,21,6,6+3*T^3,21,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,1,6,0,10,6,0,18,21,40,52,105},{0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,0,0,1,0,1,1,4,T^3,1,6,4,1+2*T^3,18,6,6,18,21,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,4,10,0,6,20,10,18,20,41,79},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,0,6,6,18,21,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,1,10,4,6,10,18,41},{0,0,4*T^3,0,T^3,0,0,9*T^3,0,0,2*T^3,0,0,0,0,0,0,0,1,4*T^3,T^3,1,1,9*T^3,6,1,1+2*T^3,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,6,0,10,18,20,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,6,10,18,40},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^3,4,1,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,1,0,T^3,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,659)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 0 & 1 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 5 & 5 & 4 & 4 & 3 & 2 & 3 & 3 & 4 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{0,1,2},{1,1,2},{1,2,2}},{{2,4,5},{0,1,6},{1,3,6},{3,4,5},{0,5,6},{0,2,5},{3,5,6}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,1},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,8},{1,3,7},{1,2,7},{1,3,6},{1,2,6},{1,3,5},{0,2,6},{1,3,4},{1,2,5},{0,2,5},{1,2,4},{1,1,5},{0,1,5},{0,2,4},{1,1,4},{1,2,3},{1,2,2},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,2,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,15,20,16,35,34,38,65,39,44,75,80,111,175,131,145,95,179,240,210,199,371,305,355,482,585,905},{0,1,1,4,5,10,5,20,15,16,34,16,17,38,39,65,111,75,80,44,95,145,131,101,240,179,199,305,355,585},{0,0,1,0,4,0,4,0,10,10,20,15,16,20,34,35,56,35,65,38,75,111,56,95,175,131,179,210,305,482},{0,0,0,1,1,4,1,10,5,5,15,5,5,16,16,34,65,38,39,17,44,80,75,45,145,95,101,179,199,355},{0,0,0,0,1,0,1,0,4,4,10,5,5,10,15,20,35,20,34,16,38,65,35,44,111,75,95,131,179,305},{0,0,T^3,0,0,1,0,4,1,1,5,1+T^3,1+2*T^3,5,5,15,34,16,16,5,17,39,38,17+2*T^3,80,44,45,95,101,199},{0,0,0,0,0,0,1,0,0,4,0,0,5,10,0,0,0,20,0,15,34,0,35,39,0,65,80,111,145,240},{T^3,0,5*T^3,0,T^3,0,2*T^3,1,0,0,1,5*T^3,10*T^3,1,1+T^3,5,15,5,5,1+2*T^3,5,16,16,5+10*T^3,39,17,17+2*T^3,44,45,101},{0,0,0,0,0,0,0,0,1,1,4,1,1,4,5,10,20,10,15,5,16,34,20,17,65,38,44,75,95,179},{0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,0,0,10,0,5,15,0,20,16,0,34,39,65,80,145},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,10,4,5,1,5,15,10,5,34,16,17,38,44,95},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,0,0,0,10,4,10,20,0,16,35,20,38,35,75,131},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,10,0,0,15,0,20,34,35,65,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,1,5,0,10,5,0,15,16,34,39,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,4,10,0,5,20,10,16,20,38,75},{0,0,T^3,0,0,0,0,0,0,0,0,T^3,2*T^3,0,0,1,4,1,1,0,1,5,4,1+2*T^3,15,5,5,16,17,44},{0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,5*T^3,9*T^3,0,T^3,0,1,0,0,2*T^3,0,1,1,10*T^3,5,1,1+2*T^3,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,1,0,4,1+T^3,0,5,5,15,16,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,1,10,4,5,10,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,5,0,10,15,20,34,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,5,10,15,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,4,5,16},{0,0,0,0,0,0,T^3,0,0,0,0,0,5*T^3,0,0,0,0,0,0,T^3,0,0,1,5*T^3,0,1,1+T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,662)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 5 & 4 & 3 & 5 & 4 & 3 & 3 & 2 & 4 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{0,1,2}},{{0,2,4},{0,3,4},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,6},{0,2,6},{1,2,5},{0,2,5},{1,2,4},{1,1,5},{0,2,4},{1,2,3},{0,1,5},{1,1,4},{1,1,3},{0,2,3},{1,2,2},{0,1,4},{0,2,2},{1,1,2},{0,1,3},{1,0,3},{0,1,2},{1,0,2},{1,1,1},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,5,20,20,10,15,34,40,35,30,70,65,68,39,130,80,111,78,160,145,222,290,240,480},{0,1,0,4,0,0,10,0,5,0,0,20,0,15,35,0,34,0,65,0,0,39,80,0,111,145,0,240},{0,0,1,2,4,1,8,10,2,5,15,20,20,10,40,34,30,16,68,39,65,32,78,80,130,160,145,290},{0,0,0,1,0,0,4,0,1,0,0,10,0,5,20,0,15,0,34,0,0,16,39,0,65,80,0,145},{0,0,0,0,1,0,2,4,0,1,5,8,10,2,20,15,10,5,30,16,34,10,32,39,68,78,80,160},{0,0,0,0,0,1,0,0,2,4,10,0,0,8,0,20,20,15,40,34,35,30,68,65,70,130,111,222},{0,0,0,0,0,0,1,0,0,0,0,4,0,1,10,0,5,0,15,0,0,5,16,0,34,39,0,80},{0,0,0,0,0,T^3,0,1,2*T^3,0,1,2,4,0,8,5,2,1+T^3,10,5,15,2+2*T^3,10,16,30,32,39,78},{0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,20,0,0,15,34,0,35,65,0,111},{0,0,0,0,0,0,0,0,0,1,4,0,0,2,0,10,8,5,20,15,20,10,30,34,40,68,65,130},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,2,1,8,5,10,2,10,15,20,30,34,68},{0,0,0,0,0,0,0,0,T^3,0,0,1,0,0,4,0,1,0,5,0,0,1+T^3,5,0,15,16,0,39},{T^3,2*T^3,0,0,0,5*T^3,0,0,10*T^3,T^3,0,0,1,2*T^3,2,1,0,5*T^3,2,1+T^3,5,10*T^3,2+2*T^3,5,10,10,16,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,0,5,15,0,20,34,0,65},{0,T^3,0,0,0,0,0,0,5*T^3,0,0,0,0,T^3,1,0,0,0,1,0,0,5*T^3,1+T^3,0,5,5,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,4,0,2,5,8,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,1,5,0,10,15,0,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,0,T^3,0,0,1,2*T^3,0,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,1,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,663)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 3 & 0 & 2 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 8 & 8 & 7 & 7 & 6 & 7 & 5 & 6 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,3},{2,3,6}},{{2,3,4},{0,4,5},{0,1,5},{1,3,5},{3,4,5},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,2},{1,1,3},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,3,10},{1,3,9},{1,3,8},{1,2,8},{1,3,7},{1,2,7},{1,3,6},{0,2,7},{1,3,5},{1,2,6},{0,2,6},{1,2,5},{1,1,6},{0,2,5},{1,2,4},{1,1,5},{0,2,4},{0,1,5},{1,1,4},{1,2,3},{0,2,3},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,12,20,28,35,29,56,55,59,96,58,106,154,108,174,120,184,232,267,212,292,347,438,366,628,534,586,782,892,1300},{0,1,4,4,10,12,20,12,35,28,29,55,28,59,96,58,106,62,108,154,174,120,184,212,292,216,438,347,366,534,586,892},{0,0,1,1,4,4,10,4,20,12,12,28,12,29,55,28,59,29,58,96,106,62,108,120,184,120,292,212,216,347,366,586},{0,0,0,1,0,4,0,4,0,10,10,20,12,20,35,28,35,29,55,56,56,59,96,106,154,120,232,174,212,267,347,534},{0,0,0,0,1,1,4,1,10,4,4,12,4,12,28,12,29,12,28,55,59,29,58,62,108,62,184,120,120,212,216,366},{0,0,0,0,0,1,0,1,0,4,4,10,4,10,20,12,20,12,28,35,35,29,55,59,96,62,154,106,120,174,212,347},{T^3,0,0,2*T^3,0,0,1,T^3,4,1,1,4,1+3*T^3,4,12,4,12,4+2*T^3,12,28,29,12,28,29,58,29+3*T^3,108,62,62,120,120,216},{0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,0,20,12,0,0,35,28,0,55,0,58,0,96,108,154,184,292},{4*T^3,T^3,0,8*T^3,0,2*T^3,0,6*T^3,1,0,T^3,1,12*T^3,1,4,1+3*T^3,4,1+11*T^3,4,12,12,4+2*T^3,12,12,28,12+16*T^3,58,29,29+3*T^3,62,62,120},{0,0,0,0,0,0,0,0,0,1,1,4,1,4,10,4,10,4,12,20,20,12,28,29,55,29,96,59,62,106,120,212},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,4,0,0,20,12,0,28,0,28,0,55,58,96,108,184},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,4,1,4,10,10,4,12,12,28,12,55,29,29,59,62,120},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,10,0,0,10,20,20,35,29,56,35,59,56,106,174},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,0,10,4,0,12,0,12,0,28,28,55,58,108},{0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,1,0,1,T^3,1,4,4,1,4,4,12,4+2*T^3,28,12,12,29,29,62},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,10,10,20,12,35,20,29,35,59,106},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,4,0,4,0,12,12,28,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,12,0,20,28,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,4,10,4,20,10,12,20,29,59},{0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,8*T^3,0,0,2*T^3,0,6*T^3,0,1,1,T^3,1,1,4,1+11*T^3,12,4,4+2*T^3,12,12,29},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,1,0,0,1,0,1+3*T^3,0,4,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,12,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,12,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,T^3,4,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,0,T^3,0,0,0,0,0,0,0,6*T^3,1,0,T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,669)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 3 & 5 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,2},{2,1,2}},{{2,3,4},{0,3,5},{1,4,5},{3,4,5},{0,1,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,2},{1,0,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,2,8},{1,2,7},{0,2,7},{1,2,6},{0,2,6},{1,2,5},{1,1,6},{0,2,5},{1,2,4},{1,1,5},{1,1,4},{1,2,3},{0,1,5},{0,2,4},{0,1,4},{0,2,3},{1,0,4},{1,1,3},{1,1,2},{0,1,3},{1,0,3},{0,0,3},{0,1,2},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,14,20,12,30,35,28,55,56,40,55,83,91,58,96,154,151,108,166,250,232,184,292,292,386,476,730},{0,1,1,4,5,10,4,14,20,12,28,35,16,30,40,55,28,55,96,83,58,86,151,154,108,166,184,250,292,476},{0,0,1,0,4,0,0,10,0,0,0,0,12,20,28,35,0,0,0,55,0,58,96,0,0,108,0,154,184,292},{0,0,0,1,1,4,1,5,10,4,12,20,5,14,16,30,12,28,55,40,28,40,83,96,58,86,108,151,166,292},{0,0,0,0,1,0,0,4,0,0,0,0,4,10,12,20,0,0,0,28,0,28,55,0,0,58,0,96,108,184},{0,0,0,0,0,1,0,1,4,1,4,10,1,5,5,14,4,12,28,16,12,16,40,55,28,40,58,83,86,166},{0,0,0,0,0,0,1,0,0,4,10,0,5,0,14,0,12,20,35,30,28,40,55,56,55,83,96,91,151,250},{0,0,0,0,0,0,0,1,0,0,0,0,1,4,4,10,0,0,0,12,0,12,28,0,0,28,0,55,58,108},{T^3,0,T^3,0,0,0,2*T^3,0,1,0,1,4,2*T^3,1,1,5,1+3*T^3,4,12,5,4,5+3*T^3,16,28,12,16,28,40,40,86},{0,0,0,0,0,0,0,0,0,1,4,0,1,0,5,0,4,10,20,14,12,16,30,35,28,40,55,55,83,151},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,4,10,5,4,5,14,20,12,16,28,30,40,83},{4*T^3,T^3,5*T^3,0,T^3,0,8*T^3,0,0,2*T^3,0,1,10*T^3,0,2*T^3,1,12*T^3,1,4,1,1+3*T^3,1+15*T^3,5,12,4,5+3*T^3,12,16,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,0,0,10,0,12,20,0,0,28,0,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,0,0,4,0,4,12,0,0,12,0,28,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,4,10,0,0,12,0,20,28,55},{0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,1,0,0,0,1,0,1+3*T^3,4,0,0,4,0,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,5,0,0,10,14,20,0,30,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,1,1,5,10,4,5,12,14,16,40},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,2*T^3,0,1,0,0,2*T^3,1,4,1,1,4,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,0,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,12},{0,0,0,0,0,0,4*T^3,0,0,T^3,0,0,5*T^3,0,T^3,0,8*T^3,0,0,0,2*T^3,10*T^3,0,1,0,2*T^3,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,670)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 7 & 5 & 4 & 6 & 3 & 4 & 5 & 3 & 4 & 5 & 4 & 3 & 2 & 3 & 4 & 2 & 1 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2}},{{3,4,5},{0,4,5},{0,2,4},{0,1,2},{0,1,5},{2,3,4}},{3,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,2},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,2,7},{1,2,6},{1,1,6},{1,2,5},{0,2,7},{1,1,5},{1,2,4},{0,2,6},{1,2,3},{1,1,4},{0,2,5},{1,1,3},{1,0,4},{0,1,5},{0,2,4},{1,0,3},{1,1,2},{0,2,3},{0,1,4},{1,0,2},{1,1,1},{0,1,3},{1,0,1},{0,0,3},{1,0,0},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,4,10,5,12,20,16,35,28,38,55,28,40,75,58,96,131,86,108,154,163,184,166,292,280,296,446,492,770},{0,1,1,4,1,4,10,5,20,12,16,28,12,16,38,28,55,75,40,58,96,86,108,86,184,163,166,280,296,492},{0,0,1,0,1,4,0,4,0,10,10,20,12,16,20,28,35,35,38,55,56,75,96,86,154,131,163,210,280,446},{0,0,0,1,0,1,4,1,10,4,5,12,4,5,16,12,28,38,16,28,55,40,58,40,108,86,86,163,166,296},{0,0,0,0,1,0,0,4,0,0,10,0,0,12,20,0,0,35,28,0,0,55,0,58,0,96,108,154,184,292},{0,0,0,0,0,1,0,1,0,4,4,10,4,5,10,12,20,20,16,28,35,38,55,40,96,75,86,131,163,280},{0,0,2*T^3,0,2*T^3,0,1,0,4,1,1,4,1+3*T^3,1+3*T^3,5,4,12,16,5,12,28,16,28,16+4*T^3,58,40,40,86,86,166},{0,0,0,0,0,0,0,1,0,0,4,0,0,4,10,0,0,20,12,0,0,28,0,28,0,55,58,96,108,184},{T^3,0,8*T^3,0,9*T^3,2*T^3,0,2*T^3,1,0,0,1,12*T^3,14*T^3,1,1+3*T^3,4,5,1+3*T^3,4,12,5,12,5+19*T^3,28,16,16+4*T^3,40,40,86},{0,0,0,0,0,0,0,0,0,1,1,4,1,1,4,4,10,10,5,12,20,16,28,16,55,38,40,75,86,163},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,0,10,4,0,0,12,0,12,0,28,28,55,58,108},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,4,1,4,10,5,12,5,28,16,16,38,40,86},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,0,0,4,10,0,10,20,16,35,20,38,35,75,131},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,12,0,20,28,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,0,4,0,4,0,12,12,28,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10,5,20,10,16,20,38,75},{0,0,T^3,0,T^3,0,0,0,0,0,0,0,2*T^3,2*T^3,0,0,1,1,0,1,4,1,4,1+3*T^3,12,5,5,16,16,40},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,1,0,0,0,1,0,1+3*T^3,0,4,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,12,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,5,10,16,38},{0,0,4*T^3,0,4*T^3,T^3,0,T^3,0,0,0,0,8*T^3,9*T^3,0,2*T^3,0,0,2*T^3,0,1,0,1,14*T^3,4,1,1+3*T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,672)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 5 & 4 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,2},{2,1,2}},{{2,3,4},{0,1,5},{3,4,5},{1,4,5},{0,3,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,1},{1,0,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (29): {{2,1,7},{2,1,6},{1,1,6},{2,1,5},{2,0,5},{2,1,4},{1,1,5},{1,1,4},{2,0,4},{2,1,3},{0,1,5},{1,0,4},{0,1,4},{2,0,3},{2,1,2},{1,1,3},{0,1,3},{1,1,2},{2,0,2},{1,0,3},{0,0,3},{0,1,2},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,6,10,11,20,18,40,24,35,21,46,52,45,56,75,105,126,76,93,126,186,196,166,238,271,301,406,642},{0,1,1,4,4,10,6,18,11,20,6,19,21,24,35,40,52,75,45,46,58,105,126,93,126,166,186,238,406},{0,0,1,0,0,0,4,10,0,0,6,11,18,0,0,20,40,35,0,24,46,75,56,45,93,76,126,166,271},{0,0,0,1,1,4,1,6,4,10,1,6,6,11,20,18,21,40,24,19,22,52,75,46,58,93,105,126,238},{0,0,0,0,1,0,0,0,4,0,0,6,0,10,0,0,0,0,20,18,21,0,0,40,52,75,0,105,186},{0,0,0,0,0,1,0,1,1,4,0,1,1,4,10,6,6,18,11,6,6,21,40,19,22,46,52,58,126},{0,0,0,0,0,0,1,4,0,0,1,4,6,0,0,10,18,20,0,11,19,40,35,24,46,45,75,93,166},{0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,4,6,10,0,4,6,18,20,11,19,24,40,46,93},{0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,0,0,0,10,6,6,0,0,18,21,40,0,52,105},{T^3,0,2*T^3,0,T^3,0,0,0,0,1,3*T^3,2*T^3,0,1,4,1,1,6,4,1,1+3*T^3,6,18,6,6,19,21,22,58},{0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,0,10,0,0,0,11,20,0,0,24,0,35,45,76},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,6,0,0,10,18,20,0,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,4,10,0,0,11,0,20,24,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,1,1,0,0,6,6,18,0,21,52},{4*T^3,T^3,9*T^3,0,4*T^3,0,2*T^3,0,T^3,0,14*T^3,9*T^3,3*T^3,0,1,0,0,1,1,2*T^3,14*T^3,1,6,1,1+3*T^3,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,1,1,6,10,4,6,11,18,19,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,0,4,0,10,11,24},{0,0,T^3,0,0,0,0,0,0,0,2*T^3,T^3,0,0,0,0,0,1,0,0,2*T^3,1,4,1,1,4,6,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,6,0,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,4,6,10,0,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,11},{0,0,4*T^3,0,0,0,T^3,0,0,0,9*T^3,4*T^3,2*T^3,0,0,0,0,0,0,T^3,9*T^3,0,1,0,2*T^3,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,675)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 5 & 3 & 3 & 2 & 4 & 3 & 2 & 1 & 5 & 3 & 4 & 1 & 0 & 2 & 3 & 1 & 0 & 2 & 3 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,0,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,4,6},{1,2,5},{1,2,3},{0,2,5,6},{1,5,7},{0,2,3},{4,6,7},{5,6,7}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,1,4},{1,1,5},{2,1,3},{2,0,3},{2,1,2},{1,1,4},{1,1,3},{2,0,2},{2,1,1},{0,1,5},{1,0,3},{0,1,4},{2,0,1},{2,1,0},{1,1,2},{0,1,3},{1,1,1},{2,0,0},{1,0,2},{0,0,3},{0,1,2},{1,1,0},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,5,10,6,18,16,20,6,24,21,38,35,40,52,75,75,61,73,105,126,127,161,231,186,307,527},{0,1,0,1,0,4,10,4,0,6,16,18,10,0,20,40,35,20,38,61,75,56,75,127,131,126,231,382},{0,0,1,1,4,1,6,5,10,1,7,6,16,20,18,21,40,38,24,27,52,75,61,73,127,105,161,307},{0,0,0,1,0,0,0,4,0,0,6,0,10,0,0,0,0,20,18,21,0,0,40,52,75,0,105,186},{0,0,0,0,1,0,1,1,4,0,1,1,5,10,6,6,18,16,7,7,21,40,24,27,61,52,73,161},{0,0,0,0,0,1,4,1,0,1,5,6,4,0,10,18,20,10,16,24,40,35,38,61,75,75,127,231},{0,0,0,0,0,0,1,0,0,0,1,1,1,0,4,6,10,4,5,7,18,20,16,24,38,40,61,127},{0,0,0,0,0,0,0,1,0,0,1,0,4,0,0,0,0,10,6,6,0,0,18,21,40,0,52,105},{0,2*T^3,0,2*T^3,0,0,0,0,1,3*T^3,3*T^3,0,1,4,1,1,6,5,1,1+4*T^3,6,18,7,7,24,21,27,73},{0,0,0,0,0,0,0,0,0,1,1,4,0,0,0,10,0,0,4,16,20,0,10,38,20,35,75,131},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,6,0,0,10,18,20,0,40,75},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,1,5,10,0,4,16,10,20,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,1,1,0,0,6,6,18,0,21,52},{T^3,9*T^3,0,9*T^3,0,2*T^3,0,2*T^3,0,14*T^3,14*T^3,3*T^3,0,1,0,0,1,1,3*T^3,19*T^3,1,6,1,1+4*T^3,7,6,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,1,1,6,10,5,7,16,18,24,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,1,5,4,10,16,38},{0,T^3,0,T^3,0,0,0,0,0,2*T^3,2*T^3,0,0,0,0,0,1,0,0,3*T^3,1,4,1,1,5,6,7,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,6,0,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,4,6,10,0,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,5,16},{0,4*T^3,0,4*T^3,0,T^3,0,T^3,0,9*T^3,9*T^3,2*T^3,0,0,0,0,0,0,2*T^3,14*T^3,0,1,0,3*T^3,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,676)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & -1 & -1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}-2 & -2 & -1 & 0 & -2 & -1 & -2 & -2 & 0 & -1 & 1 & -2 & -1 & 0 & -1 & -1 & -2 & 1 & 0 & -1 & -2 & 0 & 1 & 0 & 1 & -1 & 0 & 1 & -1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 5 & 4 & 5 & 5 & 3 & 4 & 2 & 5 & 4 & 3 & 4 & 4 & 2 & 3 & 4 & 1 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 0 & 1 & 2 & 3 & 0 & 1 & 2 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 2}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{-1,0,0},{0,1,0},{2,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{3,4,5},{1,2,5},{2,3,5},{0,1,4},{1,4,5}},{-1,3,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{-1,0,1},{-1,0,0},{-1,0,1},{2,1,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{-2,1,5},{-2,1,4},{-1,1,5},{0,1,5},{-2,1,3},{-1,1,4},{-2,1,2},{-2,0,5},{0,1,4},{-1,1,3},{1,1,4},{-2,0,4},{-1,1,2},{0,1,3},{-1,0,4},{-1,1,1},{-2,0,3},{1,1,3},{0,1,2},{-1,0,3},{-2,0,2},{0,1,1},{1,1,2},{0,1,0},{1,1,1},{-1,0,2},{0,0,3},{1,1,0},{-1,0,1},{0,0,2},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,1,1,10,6,20,2,6,18,6,10,40,21,12,75,31,21,52,39,72,105,56,186,121,96,42,226,196,108,231,432},{0,1,0,0,4,1,10,0,1,6,1,2,18,6,2,40,10,6,21,12,31,52,21,105,56,39,12,121,96,42,108,231},{0,0,1,1,0,4,0,1,6,10,6,6,20,18,10,35,18,21,40,31,40,75,52,126,105,72,39,186,140,96,196,352},{0,0,0,1,0,0,0,1,4,0,6,4,0,10,6,0,10,18,20,18,20,35,40,56,75,40,31,126,75,72,140,242},{0,0,0,3*T^3,1,0,4,3*T^3,0,1,4*T^3,0,6,1,4*T^3,18,2,1,6,2,10,21,6,52,21,12,2+5*T^3,56,39,12,42,108},{0,0,0,0,0,1,0,0,1,4,1,1,10,6,2,20,6,6,18,10,18,40,21,75,52,31,12,105,72,39,96,196},{0,0,2*T^3,14*T^3,0,0,1,14*T^3,3*T^3,0,19*T^3,3*T^3,1,0,19*T^3,6,0,4*T^3,1,4*T^3,2,6,1,21,6,2,24*T^3,21,12,2+5*T^3,12,42},{0,0,0,0,0,0,0,1,0,0,0,4,0,0,6,0,10,0,0,18,20,0,0,0,0,40,21,0,75,52,105,186},{0,0,0,0,0,0,0,0,1,0,1,1,0,4,1,0,4,6,10,6,10,20,18,35,40,18,10,75,40,31,72,140},{0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,10,1,1,6,2,6,18,6,40,21,10,2,52,31,12,39,96},{4*T^2,10*T^2,0,0,20*T^2,0,35*T^2,4*T^2,0,0,1,10*T^2,0,0,1,0,20*T^2,4,0,4,35*T^2,0,10,0,20,10,6,35,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,0,6,10,0,0,0,0,18,6,0,40,21,52,105},{0,0,0,2*T^3,0,0,0,2*T^3,0,0,3*T^3,0,1,0,3*T^3,4,0,0,1,0,1,6,1,18,6,2,4*T^3,21,10,2,12,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,1,4,10,6,20,18,6,2,40,18,10,31,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,0,0,10,6,0,20,18,40,75},{0,0,T^3,9*T^3,0,0,0,9*T^3,2*T^3,0,14*T^3,2*T^3,0,0,14*T^3,1,0,3*T^3,0,3*T^3,0,1,0,6,1,0,19*T^3,6,2,4*T^3,2,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,0,0,0,6,1,0,18,6,21,52},{T^2,4*T^2,0,0,10*T^2,0,20*T^2,T^2,0,0,0,4*T^2,0,0,0,0,10*T^2,1,0,1,20*T^2,0,4,0,10,4,1,20,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,6,1,0,18,6,2,10,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,1,0,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,6,1,6,21},{0,0,0,T^3,0,0,0,T^3,0,0,2*T^3,0,0,0,2*T^3,0,0,0,0,0,0,1,0,4,1,0,3*T^3,6,1,0,2,10},{0,T^2,0,0,4*T^2,0,10*T^2,0,0,0,0,T^2,0,0,0,0,4*T^2,0,0,0,10*T^2,0,1,0,4,1,0,10,4,1,6,18},{0,0,0,4*T^3,0,0,0,4*T^3,T^3,0,9*T^3,T^3,0,0,9*T^3,0,0,2*T^3,0,2*T^3,0,0,0,1,0,0,14*T^3,1,0,3*T^3,0,2},{0,0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,0,4*T^2,0,0,0,1,0,0,4,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{0,0,0,0,0,0,T^2,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,T^2,0,0,0,0,0,2*T^3,1,0,0,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,677)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & -1 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 & 1 & 0 & 0 & 2 & 1 & 1 & -1 & 0 & 0 & 2 & -1 & 1 & 1 & 0 & 0 & 2 & 1 & -1 & -1 & 1 & 0 & 0 & -1 & -1 & 1 & 0 & 0 & -1 & 1 & 0 & -1 & 0 \\ 4 & 5 & 6 & 3 & 4 & 2 & 4 & 5 & 5 & 3 & 2 & 1 & 3 & 4 & 1 & 2 & 4 & 0 & 2 & 3 & 3 & 2 & 0 & 1 & 1 & 3 & -1 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {5, 6, 7}, {0, 1, 2, 8}, {0, 1, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2},{-1,1,2}},{{3,4,5},{0,1,5},{1,5,6},{0,1,2},{0,2,4},{3,5,6},{0,4,5},{2,3,4}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,2},{1,-1,-1},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,0,4},{1,1,5},{0,2,6},{2,0,3},{1,1,4},{2,0,2},{1,0,4},{0,2,5},{0,1,5},{1,1,3},{2,-1,2},{2,0,1},{1,0,3},{0,2,4},{2,-1,1},{1,1,2},{0,1,4},{2,0,0},{1,0,2},{0,2,3},{0,1,3},{1,-1,2},{2,-1,0},{1,1,1},{1,0,1},{0,0,3},{2,-1,-1},{1,-1,1},{0,1,2},{0,0,2},{1,0,0},{1,-1,0},{0,1,1},{0,0,1},{1,-1,-1},{0,0,0}}
Ext matrix: {{1,2,3,5,9,15,10,13,15,25,17,35,32,35,45,55,47,70,79,75,113,81,100,105,165,120,196,177,230,257,307,346,418,491,620,860},{0,1,2,1,5,5,5,9,10,15,5,15,17,25,17,35,32,35,45,55,79,45,45,70,100,81,100,103,165,177,196,211,307,346,395,620},{0,0,1,0,1,1,1,5,5,5,1,5,5,15,5,15,17,15,17,35,45,17,17,35,45,45,45,45,100,103,100,103,196,211,211,395},{0,0,0,1,2,5,2,3,3,9,5,15,10,13,17,25,15,35,32,35,47,32,45,55,79,48,100,81,113,120,165,177,230,257,346,491},{0,0,0,0,1,1,1,2,2,5,1,5,5,9,5,15,10,15,17,25,32,17,17,35,45,32,45,45,79,81,100,103,165,177,211,346},{0,0,0,0,0,1,0,0,0,2,1,5,2,3,5,9,3,15,10,13,15,10,17,25,32,15,45,32,47,48,79,81,113,120,177,257},{0,0,0,0,0,0,1,0,2,0,1,0,5,0,5,0,9,0,15,0,25,17,15,0,35,32,35,45,55,79,70,100,105,165,196,307},{0,0,0,0,0,0,0,1,1,1,0,1,1,5,1,5,5,5,5,15,17,5,5,15,17,17,17,17,45,45,45,45,100,103,103,211},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,5,0,5,0,15,5,5,0,15,17,15,17,35,45,35,45,70,100,100,196},{0,0,0,0,0,0,0,0,0,1,0,1,1,2,1,5,2,5,5,9,10,5,5,15,17,10,17,17,32,32,45,45,79,81,103,177},{0,0,T^2,0,0,0,0,3*T^2,0,0,1,0,2,6*T^2,5,0,3,0,9,10*T^2,13,10,15,0,25,15,35,32,35,47,55,79,75,113,165,230},{0,0,0,0,0,0,T^3,0,2*T^3,0,0,1,0,0,1,2,0,5,2,3,3,2+T^3,5,9,10,3+2*T^3,17,10,15,15,32,32,47,48,81,120},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,0,5,0,9,5,5,0,15,10,15,17,25,32,35,45,55,79,100,165},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,5,5,1,1,5,5,5,5,5,17,17,17,17,45,45,45,103},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,1,0,0,0,2,6*T^2,3,2,5,0,9,3,15,10,13,15,25,32,35,47,79,113},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,1,1,2,2,1,1,5,5,2+T^3,5,5,10,10,17,17,32,32,45,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,1,1,0,5,5,5,5,15,17,15,17,35,45,45,100},{0,T^3,2*T^3,0,0,0,3*T^3,0,8*T^3,0,0,0,T^3,0,0,0,2*T^3,1,0,0,0,3*T^3,1,2,2,8*T^3,5,2+T^3,3,3+2*T^3,10,10,15,15,32,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,0,5,2,5,5,9,10,15,17,25,32,45,79},{T^4,0,0,0,0,0,2*T^4,0,0,0,2*T^4,0,0,0,0,0,0,0,0,1,1,3*T^4,0,1,1,1,1,1,5,5,5,5,17,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,5,5,5,5,15,17,17,45},{0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,0,0,0,10*T^2,0,1,0,0,0,2,0,5,0,9,0,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,1,0,2,0,5,2,3,3,9,10,13,15,32,47},{T^4,0,T^3,0,0,0,2*T^4,0,3*T^3,0,2*T^4,0,0,0,0,0,T^3,0,0,0,0,3*T^4,0,1,1,3*T^3,1,1,2,2+T^3,5,5,10,10,17,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,2,2,5,5,9,10,17,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,15,15,35},{0,0,T^4,0,0,0,T^3,0,2*T^3,0,0,0,0,0,0,0,0,0,0,T^2,0,T^3,0,0,0,2*T^3,1,0,0,0,2,2,3,3,10,15},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,0,0,0,0,0,1,0,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,5,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,678)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -1 & 2 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}1 & 0 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & 0 & 1 & 2 & 0 & -1 & 1 & 0 & -1 & 1 & 0 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 0 & -1 & 1 & -1 & 0 & 1 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 0 & 2 & 2 & 0 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 2 & 1 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 4 & 5 & 2 & 3 & 5 & 6 & 3 & 1 & 4 & 4 & 2 & 0 & 3 & 5 & 2 & 3 & 5 & 1 & 3 & 4 & 1 & -1 & 2 & 2 & 4 & 0 & 2 & 3 & 0 & 3 & 1 & -1 & 1 & 2 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 4, 6}, {3, 5, 7}, {4, 6, 7}, {0, 1, 2, 8}, {0, 1, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,0,-1},{1,-1,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,5,7},{0,4,5},{5,7,8},{0,2,3},{0,3,4},{6,7,8},{1,2,3},{1,6,8},{0,2,6,7},{1,2,6}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-1},{-1,1,2},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (35): {{1,1,4},{0,2,5},{2,0,2},{1,1,3},{0,1,5},{-1,2,6},{1,0,3},{2,0,1},{0,2,4},{0,1,4},{1,1,2},{2,0,0},{0,2,3},{-1,2,5},{1,0,2},{0,1,3},{-1,1,5},{1,1,1},{0,0,3},{-1,2,4},{1,0,1},{2,0,-1},{0,2,2},{0,1,2},{-1,1,4},{1,1,0},{0,0,2},{-1,2,3},{1,0,0},{-1,1,3},{0,1,1},{1,0,-1},{0,0,1},{-1,1,2},{0,0,0}}
Ext matrix: {{1,1,2,5,2,2,7,9,5,11,15,25,15,11,26,35,17,35,46,35,69,55,35,85,56,70,121,85,150,140,175,286,264,295,507},{0,1,0,2,1,2,2,3,5,7,9,13,15,11,12,26,13,25,29,35,41,35,35,69,46,55,85,85,103,121,150,215,201,264,409},{0,0,1,1,0,0,2,5,1,2,5,15,5,2,11,11,3,15,17,11,35,35,15,35,17,35,56,35,85,56,85,175,140,140,295},{0,0,0,1,0,0,1,2,1,2,5,9,5,2,7,11,3,15,13,11,26,25,15,35,17,35,46,35,69,56,85,150,121,140,264},{0,0,0,0,1,1,2,0,0,5,0,0,0,5,9,15,11,0,26,15,25,0,0,35,35,0,69,35,55,85,70,105,150,175,286},{0,0,6*T^2,0,0,1,0,10*T^2,0,2,0,15*T^2,0,5,3,9,7,0,12,15,13,21*T^2,0,25,26,0,41,35,35,69,55,75,103,150,215},{0,0,0,0,0,0,1,0,0,1,0,0,0,1,5,5,2,0,11,5,15,0,0,15,11,0,35,15,35,35,35,70,85,85,175},{0,0,0,0,0,0,0,1,0,0,1,5,1,0,2,2,0,5,3,2,11,15,5,11,3,15,17,11,35,17,35,85,56,56,140},{0,0,0,0,0,0,0,0,1,1,2,3,5,2,2,7,2,9,7,11,12,13,15,26,13,25,29,35,41,46,69,103,85,121,201},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,5,2,0,7,5,9,0,0,15,11,0,26,15,25,35,35,55,69,85,150},{0,0,0,0,0,0,0,0,0,0,1,2,1,0,1,2,0,5,2,2,7,9,5,11,3,15,13,11,26,17,35,69,46,56,121},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,2,5,1,2,0,5,3,2,11,3,11,35,17,17,56},{0,0,0,0,T^3,0,2*T^3,0,0,0,0,0,1,0,0,1,T^3,2,1+2*T^3,2,2,3,5,7,2,9,7,11,12,13,26,41,29,46,85},{0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,10*T^2,0,1,0,2,1,0,2,5,3,15*T^2,0,9,7,0,12,15,13,26,25,35,41,69,103},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,1,5,0,0,5,2,0,11,5,15,11,15,35,35,35,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,0,0,5,2,0,7,5,9,11,15,25,26,35,69},{0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,10*T^2,0,0,0,0,1,0,2,0,0,15*T^2,0,0,5,0,9,0,0,15,0,0,25,35,55},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,T^3,0,1,2,1,2,0,5,2,2,7,3,11,26,13,17,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,5,0,0,5,0,0,15,15,35},{0,0,T^2,0,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,0,0,0,1,0,10*T^2,0,2,1,0,2,5,3,7,9,13,12,26,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,1,5,2,5,15,11,11,35},{0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,0,1,0,0,2,0,2,11,3,3,17},{T^3,0,2*T^3,0,4*T^3,0,9*T^3,0,0,T^3,0,0,0,0,2*T^3,0,4*T^3,0,9*T^3,0,0,0,1,1,T^3,2,1+2*T^3,2,2,2,7,12,7,13,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,2,5,9,7,11,26},{0,0,T^2,0,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,0,0,0,0,0,10*T^2,0,0,1,0,2,0,0,5,0,0,9,15,25},{0,0,T^3,0,T^4,T^4,4*T^3,0,0,0,0,0,0,0,T^3,0,T^4,0,4*T^3,0,0,0,0,0,0,1,T^3,0,1,0,2,7,2,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,5,5,15},{0,0,0,0,T^3,0,2*T^3,T^2,0,0,0,3*T^2,0,0,0,0,T^3,0,2*T^3,0,0,6*T^2,0,0,0,0,0,1,0,1,2,3,2,7,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,2,2,11},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,6*T^2,0,0,0,0,0,0,0,1,0,0,2,5,9},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,7},{0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,679)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & -1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 4 & 5 & 3 & 4 & 3 & 2 & 4 & 3 & 2 & 5 & 3 & 1 & 4 & 3 & 1 & 2 & 4 & 2 & 0 & 3 & 2 & 1 & 3 & 3 & 1 & 2 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 6}, {4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 1, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,3,5},{4,5,6},{0,2,3},{3,5,6},{0,4,5},{0,1,4},{1,4,6},{0,1,2}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-1},{1,0,0},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,1,4},{1,2,5},{2,1,3},{1,2,4},{2,0,3},{2,1,2},{1,1,4},{1,2,3},{2,0,2},{0,2,5},{1,1,3},{2,1,1},{0,2,4},{1,0,3},{2,0,1},{1,2,2},{0,1,4},{1,1,2},{2,0,0},{0,2,3},{1,0,2},{1,1,1},{0,1,3},{0,0,3},{1,0,1},{0,2,2},{0,1,2},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,4,5,10,7,10,16,7,22,20,22,25,38,20,28,50,75,50,65,95,74,80,137,95,155,183,251,281,357,622},{0,1,1,4,1,4,5,10,5,7,16,10,22,17,16,20,25,38,38,50,44,75,65,68,96,95,137,152,183,251,297,523},{0,0,1,1,1,4,1,4,5,1,7,10,7,7,16,10,7,22,38,22,25,50,28,28,65,50,74,80,137,155,183,357},{0,0,0,1,0,1,1,4,1,1,5,4,7,5,5,10,7,16,16,22,17,38,25,25,44,50,65,68,96,137,152,297},{0,0,0,0,1,0,1,0,4,1,4,0,4,7,10,0,7,10,20,10,22,20,22,28,50,20,50,74,95,95,155,281},{0,0,0,0,0,1,0,1,1,0,1,4,1,1,5,4,1,7,16,7,7,22,7,7,25,22,28,28,65,74,80,183},{0,0,0,0,0,0,1,0,1,1,4,0,4,5,4,0,7,10,10,10,16,20,22,25,38,20,50,65,75,95,137,251},{0,0,0,0,2*T^3,0,0,1,0,0,1,1,1,1+3*T^3,1,4,1,5,5,7,5,16,7,7+4*T^3,17,22,25,25,44,65,68,152},{0,0,0,0,0,0,0,0,1,0,1,0,1,1,4,0,1,4,10,4,7,10,7,7,22,10,22,28,50,50,74,155},{0,0,0,0,0,0,0,0,0,1,1,0,4,1,1,0,5,4,4,10,5,10,16,17,16,20,38,44,38,75,96,183},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,1,4,4,4,5,10,7,7,16,10,22,25,38,50,65,137},{0,0,0,0,2*T^3,0,0,0,0,0,0,1,0,3*T^3,1,1,0,1,5,1,1,7,1,1+4*T^3,7,7,7,7,25,28,28,80},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,4,1,4,5,5,5,10,16,17,16,38,44,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,4,0,4,7,10,0,10,22,20,20,50,95},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,1,4,1,1,7,4,7,7,22,22,28,74},{T^3,0,0,0,9*T^3,0,2*T^3,0,2*T^3,0,0,0,0,14*T^3,0,1,3*T^3,1,1,1,1+3*T^3,5,1,1+19*T^3,5,7,7,7+4*T^3,17,25,25,68},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,5,4,0,10,16,10,20,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,4,1,1,5,4,7,7,16,22,25,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,1,1,7,7,7,28},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,0,1,1,1+3*T^3,1,4,5,5,5,16,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,0,4,7,10,10,22,50},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,0,3*T^3,1,1,1,1,5,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,4,5,4,10,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,7,22},{0,0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,9*T^3,0,0,2*T^3,0,0,0,2*T^3,0,0,14*T^3,0,1,1,1+3*T^3,1,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,680)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & -1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}-1 & 0 & -2 & 1 & -1 & -1 & -2 & 0 & 0 & 1 & -1 & -2 & -1 & -2 & 1 & 0 & -2 & 0 & -1 & 1 & 0 & 1 & -1 & 0 & -2 & -1 & 0 & 1 & 1 & -1 & 0 & 1 & -1 & 0 & 0 & -1 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 5 & 5 & 4 & 4 & 3 & 4 & 5 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 2 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 5}, {4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 3, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{2,5,6},{0,2,5},{1,3,6},{4,5,6},{0,1,4},{2,3,6},{0,4,5},{1,4,6}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{-1,0,1},{1,0,0},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (38): {{-1,2,6},{0,2,5},{-2,2,6},{1,2,4},{-1,2,5},{-1,1,5},{-2,2,5},{0,2,4},{0,1,4},{1,2,3},{-1,2,4},{-2,1,5},{-1,1,4},{-2,2,4},{1,1,3},{0,2,3},{-2,1,4},{0,1,3},{-1,2,3},{1,2,2},{0,2,2},{1,1,2},{-1,1,3},{0,0,3},{-2,1,3},{-1,0,3},{0,1,2},{1,0,2},{1,1,1},{-1,1,2},{0,0,2},{1,0,1},{-1,0,2},{0,1,1},{0,0,1},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,3,6,7,10,10,13,14,20,12,28,30,19,30,43,46,50,40,70,64,80,49,114,88,120,70,160,185,138,190,218,260,320,465,425,647},{0,1,0,2,2,2,3,6,7,10,10,3,12,14,13,20,17,28,30,30,50,46,43,29,58,45,80,49,120,114,88,138,127,185,218,298,320,465},{0,0,1,0,2,2,6,3,3,4,10,7,13,20,4,14,28,19,30,18,40,25,46,19,80,49,64,25,82,120,70,91,138,160,190,320,242,425},{0,0,5*T^2,1,0,0,7*T^2,2,2,6,3,9*T^2,3,4+9*T^2,7,10,4+12*T^2,12,14,20,30,28,17,12,22+15*T^2,17,43,29,80,58,45,88,61,114,127,166,218,298},{0,0,0,0,1,1,2,2,2,3,6,2,7,10,3,10,12,13,20,14,30,19,28,13,43,29,46,19,64,80,49,70,88,120,138,218,190,320},{0,0,0,0,0,1,0,0,2,0,0,2,6,0,3,0,10,10,0,0,0,14,20,13,30,28,30,19,40,50,46,64,80,70,120,185,160,260},{0,0,0,0,0,0,1,0,0,0,2,1,2,6,0,3,7,3,10,4,14,4,13,3,28,13,19,4,25,46,19,25,49,64,70,138,91,190},{0,0,0,0,0,0,0,1,1,2,2,0,2,3,2,6,3,7,10,10,20,13,12,7,17,12,28,13,46,43,29,49,45,80,88,127,138,218},{0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,0,3,6,0,0,0,10,10,7,14,12,20,13,30,30,28,46,43,50,80,114,120,185},{0,0,3*T^2,0,0,2*T^3,5*T^2,0,0,1,0,6*T^2+3*T^3,0,7*T^2,1,2,9*T^2,2,3,6,10,7,3,2+2*T^3,4+12*T^2,3+3*T^3,12,7,28,17,12,29,17,43,45,61,88,127},{0,0,0,0,0,0,0,0,0,0,1,0,1,2,0,2,2,2,6,3,10,3,7,2,12,7,13,3,19,28,13,19,29,46,49,88,70,138},{0,0,0,T^3,0,0,0,0,0,2*T^3,0,1,2,0,0,0,6,3,0,3*T^3,0,4,10,3,20,13,14,4,18,30,19,25,46,40,64,120,82,160},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,0,0,3,6,2,10,7,10,3,14,20,13,19,28,30,46,80,64,120},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,2,0,3,0,2,0,7,2,3,0,4,13,3,4,13,19,19,49,25,70},{0,0,2*T^2,0,0,0,3*T^2,0,0,0,0,5*T^2,0,4*T^2,1,0,7*T^2,2,0,0,0,6,3,2,4+9*T^2,3,10,7,20,14,12,28,17,30,43,58,80,114},{0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,0,1,0,1,2,2,6,2,2,1+T^3,3,2+2*T^3,7,2,13,12,7,13,12,28,29,45,49,88},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,0,2*T^3,0,0,2,0,6,2,3,0,4,10,3,4,13,14,19,46,25,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,1,3,2,6,2,10,10,7,13,12,20,28,43,46,80},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,2,0,1,0,2,1+T^3,2,0,3,7,2,3,7,13,13,29,19,49},{T^3,0,T^2+2*T^3,0,0,7*T^3,3*T^2,0,T^3,0,0,3*T^2+12*T^3,2*T^3,5*T^2,0,0,6*T^2+3*T^3,0,0,1,2,1,0,7*T^3,9*T^2,12*T^3,2,1+T^3,7,3,2+2*T^3,7,3+3*T^3,12,12,17,29,45},{0,0,T^3,0,0,2*T^3,0,0,0,0,0,7*T^3,T^3,0,0,0,2*T^3,0,0,0,1,0,0,2*T^3,0,7*T^3,1,0,2,2,1+T^3,2,2+2*T^3,7,7,12,13,29},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,3*T^2,0,3*T^2,0,0,5*T^2,0,0,0,0,1,0,0,7*T^2,0,2,1,6,3,2,7,3,10,12,17,28,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,0,3,6,2,3,7,10,13,28,19,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,0,0,6,10,10,0,20,30,30,50},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,0,0,2,0,0,2,3,3,13,4,19},{0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,1,0,0,0,0,2,3,6,0,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,1,2,2,6,7,12,13,28},{0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,0,4*T^2,0,0,1,0,0,2,6,3,0,10,14,20,30},{0,0,0,0,0,T^3,T^2,0,0,0,0,T^2+2*T^3,0,2*T^2,0,0,3*T^2,0,0,0,0,0,0,T^3,5*T^2,2*T^3,0,0,1,0,0,1,0,2,2,3,7,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,7,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,6,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,1,0,0,2,3,6,10},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,681)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 6 & 5 & 4 & 5 & 3 & 4 & 5 & 4 & 2 & 3 & 3 & 4 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{3, 6}, {4, 5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,2,4},{1,3,5},{0,1,3},{3,4,5},{0,3,4},{2,4,5}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,6},{1,2,5},{0,2,6},{1,1,5},{1,2,4},{0,2,5},{1,2,3},{1,1,4},{0,1,5},{0,2,4},{1,2,2},{1,1,3},{0,2,3},{0,1,4},{1,1,2},{1,0,3},{0,2,2},{0,1,3},{1,0,2},{1,1,1},{0,1,2},{0,0,3},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,2,5,10,8,20,16,10,20,35,38,40,31,75,44,70,72,96,131,140,83,183,176,242,315,328,555},{0,1,0,1,4,2,10,5,2,8,20,16,20,10,38,17,40,31,44,75,72,33,96,83,140,183,176,328},{0,0,1,0,0,4,0,1,5,10,0,4,20,16,10,5,35,38,16,20,75,44,38,96,131,75,183,315},{0,0,0,1,0,0,0,4,2,0,0,10,0,8,20,16,0,20,38,35,40,31,75,72,70,131,140,242},{0,0,0,0,1,0,4,1,0,2,10,5,8,2,16,5,20,10,17,38,31,10,44,33,72,96,83,176},{0,0,0,0,0,1,0,0,1,4,0,1,10,5,4,1,20,16,5,10,38,17,16,44,75,38,96,183},{0,0,0,2*T^3,0,0,1,0,3*T^3,0,4,1,2,0,5,1+3*T^3,8,2,5,16,10,2+4*T^3,17,10,31,44,33,83},{0,0,0,0,0,0,0,1,0,0,0,4,0,2,10,5,0,8,16,20,20,10,38,31,40,75,72,140},{0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,1,0,10,4,0,20,16,10,38,35,20,75,131},{0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,0,10,5,1,4,16,5,5,17,38,16,44,96},{T^3,0,2*T^3,9*T^3,0,0,0,2*T^3,14*T^3,0,1,0,0,3*T^3,1,14*T^3,2,0,1+3*T^3,5,2,19*T^3,5,2+4*T^3,10,17,10,33},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,2,5,10,8,2,16,10,20,38,31,72},{0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,1,0,0,2*T^3,4,1,0,1,5,1+3*T^3,1,5,16,5,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,10,5,4,16,20,10,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,2,0,5,2,8,16,10,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,2,10,8,0,20,20,40},{0,0,T^3,4*T^3,0,0,0,T^3,9*T^3,0,0,0,0,2*T^3,0,9*T^3,1,0,2*T^3,0,1,14*T^3,0,1+3*T^3,5,1,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,5,10,4,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,0,10,8,20},{0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,0,0,2*T^3,0,0,0,1,0,3*T^3,1,0,2,5,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,686)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & -1 & -1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 4 & 2 & 1 & 3 & 2 & 4 & 0 & -1 & 1 & 3 & 4 & 0 & 2 & -1 & 1 & 3 & 2 & 1 & 3 & 0 & 2 & 1 & 2 & -1 & 0 & -1 & 1 & 3 & 0 & 2 & 0 & -1 & 1 & 0 \\ 4 & 3 & 4 & 4 & 3 & 3 & 2 & 4 & 4 & 3 & 2 & 1 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 2 & 2 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}, {0, 0, 0, 1, 1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 1, 2, 7}, {3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,2},{1,0,3}},{{1,2,4},{0,1,4},{2,3,5},{0,4,5},{2,4,5},{0,3,5}},{1,1,2})
Cox degrees: {{0,1,0},{0,1,0},{0,1,0},{0,-1,1},{0,-1,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (35): {{1,3,4},{1,4,3},{1,2,4},{1,1,4},{1,3,3},{1,2,3},{1,4,2},{1,0,4},{1,-1,4},{1,1,3},{1,3,2},{1,4,1},{1,0,3},{1,2,2},{1,-1,3},{1,1,2},{1,3,1},{0,2,2},{0,1,2},{0,3,1},{1,0,2},{1,2,1},{1,1,1},{0,2,1},{1,-1,2},{0,0,2},{0,-1,2},{0,1,1},{0,3,0},{1,0,1},{0,2,0},{0,0,1},{0,-1,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,10,9,24,14,20,35,50,39,54,90,84,147,155,119,85,159,121,258,224,379,233,399,268,419,403,308,594,543,644,969,883,1349},{0,1,0,0,4,10,9,0,0,20,24,39,35,50,56,90,84,50,90,85,147,155,258,159,224,147,224,268,233,399,403,419,619,644,969},{0,0,1,4,2,9,3,10,20,24,14,19,50,39,90,84,54,39,85,54,155,119,224,121,258,159,268,233,157,379,308,403,644,543,883},{0,0,0,1,0,2,0,4,10,9,3,4,24,14,50,39,19,14,39,19,84,54,119,54,155,85,159,121,69,224,157,233,403,308,543},{0,0,0,0,1,4,2,0,0,10,9,14,20,24,35,50,39,24,50,39,90,84,155,85,147,90,147,159,121,258,233,268,419,403,644},{0,0,0,0,0,1,0,0,0,4,2,3,10,9,20,24,14,9,24,14,50,39,84,39,90,50,90,85,54,155,121,159,268,233,403},{0,0,0,0,0,0,1,0,0,0,4,9,0,10,0,20,24,10,20,24,35,50,90,50,56,35,56,90,85,147,159,147,224,268,419},{0,T^3,0,0,0,0,T^3,1,4,2,0,T^3,9,3,24,14,4,3,14,4+T^3,39,19,54,19,84,39,85,54,24+T^3,119,69,121,233,157,308},{T^3,6*T^3,0,0,T^3,0,6*T^3,0,1,0,T^3,6*T^3,2,0,9,3,T^3,T^3,3,7*T^3,14,4,19,4+T^3,39,14,39,19,5+7*T^3,54,24+T^3,54,121,69,157},{0,0,0,0,0,0,0,0,0,1,0,0,4,2,10,9,3,2,9,3,24,14,39,14,50,24,50,39,19,84,54,85,159,121,233},{0,0,0,0,0,0,0,0,0,0,1,2,0,4,0,10,9,4,10,9,20,24,50,24,35,20,35,50,39,90,85,90,147,159,268},{0,0,T^2,4*T^2,0,0,0,10*T^2,20*T^2,0,0,1,0,0,0,0,4,0,T^2,4,0,10,20,10,0,4*T^2,10*T^2,20,24,35,50,35,56,90,147},{0,T^3,0,0,0,0,T^3,0,0,0,0,T^3,1,0,4,2,0,0,2,T^3,9,3,14,3,24,9,24,14,4+T^3,39,19,39,85,54,121},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,1,4,2,10,9,24,9,20,10,20,24,14,50,39,50,90,85,159},{0,4*T^3,0,0,T^3,0,6*T^3,0,0,0,T^3,6*T^3,0,0,1,0,T^3,0,0,5*T^3,2,0,3,T^3,9,2,9,3,7*T^3,14,4+T^3,14,39,19,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,2,9,2,10,4,10,9,3,24,14,24,50,39,85},{0,0,0,T^2,0,0,0,4*T^2,10*T^2,0,0,0,0,0,0,0,1,0,0,1,0,4,10,4,0,T^2,4*T^2,10,9,20,24,20,35,50,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,0,0,0,9,0,10,20,24,14,0,39,50,90,84,155},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,4,10,9,3,0,14,24,50,39,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,10,9,0,24,20,35,50,90},{0,0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,0,2,0,4,1,4,2,T^3,9,3,9,24,14,39},{0,0,0,0,0,0,0,T^2,4*T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,0,T^2,4,2,10,9,10,20,24,50},{T^5,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^5,0,0,0,0,1,0,0,0,0,1,0,4,2,4,10,9,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,0,9,10,20,24,50},{0,0,0,0,0,0,4*T^3,0,0,0,T^3,6*T^3,0,0,0,0,T^3,0,0,T^3,0,0,0,0,1,0,1,0,5*T^3,2,T^3,2,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,0,0,3,9,24,14,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,T^3,0,0,2,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,10,9,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{4*T^5,0,T^5,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,1,0,1,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,743)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 2 & 4 & 3 & 1 & 3 & 2 & 0 & 4 & 2 & 1 & 3 & 0 & 1 & 3 & 0 & 2 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {3, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,5,6},{0,2,6},{2,3,4},{2,3,6},{0,2,4},{0,5,6},{1,3,4},{1,3,6}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,-1},{1,1,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,3,4},{2,3,3},{2,2,4},{2,3,2},{1,2,4},{2,2,3},{2,3,1},{1,2,3},{2,2,2},{2,3,0},{1,1,4},{1,2,2},{2,2,1},{1,1,3},{2,2,0},{1,2,1},{0,1,3},{1,2,0},{1,1,2},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,6,14,20,19,30,35,21,44,55,53,91,85,58,146,109,124,196,138,321,230,269,386,470,757},{0,1,1,4,1,5,10,6,14,20,6,19,30,21,55,44,22,85,53,58,109,61,196,124,138,230,269,470},{0,0,1,0,1,4,0,4,10,0,6,10,20,19,35,20,19,35,44,44,85,58,146,85,124,146,230,386},{0,0,0,1,0,1,4,1,5,10,1,6,14,6,30,19,6,44,21,22,53,22,109,58,61,124,138,269},{0,0,0,0,1,0,0,4,0,0,5,10,0,14,0,20,19,35,30,44,55,53,91,85,109,146,196,321},{0,0,0,0,0,1,0,1,4,0,1,4,10,6,20,10,6,20,19,19,44,22,85,44,58,85,124,230},{0,0,0,0,T^3,0,1,0,1,4,T^3,1,5,1,14,6,1+T^3,19,6,6,21,6+T^3,53,22,22,58,61,138},{0,0,0,0,0,0,0,1,0,0,1,4,0,5,0,10,6,20,14,19,30,21,55,44,53,85,109,196},{0,0,0,0,0,0,0,0,1,0,0,1,4,1,10,4,1,10,6,6,19,6,44,19,22,44,58,124},{T^3,0,T^3,0,6*T^3,0,0,T^3,0,1,7*T^3,0,1,T^3,5,1,6*T^3,6,1,1+T^3,6,1+7*T^3,21,6,6+T^3,22,22,61},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,4,0,10,10,20,19,35,20,44,35,85,146},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,1,10,5,6,14,6,30,19,21,44,53,109},{0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,4,1,0,4,1,1,6,1+T^3,19,6,6,19,22,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,10,6,20,10,19,20,44,85},{0,0,T^3,0,T^3,0,0,0,0,0,6*T^3,0,0,T^3,1,0,T^3,1,0,0,1,6*T^3,6,1,1+T^3,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,5,1,14,6,6,19,21,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,30,55},{0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,T^3,1,0,0,1,T^3,5,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,6,10,19,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,858)$ |
3 |
25 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 1 & 3 & 2 & 2 & 1 & 1 & 3 & 2 & 2 & 0 & 3 & 1 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 0 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, -1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (25): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{3, 4}, {2, 5, 6, 7}, {4, 5, 6, 7}, {0, 1, 2, 8}, {0, 1, 3, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{3,4,5},{2,5,6},{0,1,4},{3,5,6},{0,2,5},{0,4,5},{1,3,4}},{2,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,1},{1,-1,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{1,2,4},{1,1,4},{0,3,4},{1,2,3},{0,2,4},{0,1,4},{1,1,3},{0,3,3},{0,2,3},{1,2,2},{1,0,3},{0,3,2},{1,1,2},{0,1,3},{0,0,3},{0,2,2},{1,0,2},{1,2,1},{1,1,1},{0,1,2},{0,0,2},{1,0,1},{0,2,1},{1,1,0},{0,1,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,1,4,3,5,10,4,13,10,16,10,28,24,35,34,49,20,60,67,103,112,70,110,144,231,215,265,439},{0,1,0,0,1,3,4,0,4,0,10,0,10,13,24,10,28,0,20,34,67,60,20,35,70,144,110,125,265},{0,0,1,1,2,3,2,4,10,4,3,10,10,16,22,28,16,10,28,49,70,49,60,60,112,168,112,215,336},{0,0,0,1,0,0,2,1,3,4,3,4,10,5,7,13,16,10,28,24,35,49,34,60,67,103,112,144,231},{0,0,0,0,1,2,1,0,4,0,2,0,4,10,16,10,10,0,10,28,49,28,20,20,60,112,60,110,215},{0,0,0,0,0,1,0,0,0,0,1,0,0,4,10,0,4,0,0,10,28,10,0,0,20,60,20,35,110},{0,0,0,0,0,0,1,0,1,0,2,0,4,3,5,4,10,0,10,13,24,28,10,20,34,67,60,70,144},{0,0,0,0,0,0,0,1,2,1,0,4,2,3,4,10,3,4,10,16,22,16,28,28,49,70,49,112,168},{0,0,0,0,0,0,0,0,1,0,0,0,1,2,3,4,2,0,4,10,16,10,10,10,28,49,28,60,112},{0,0,0,0,0,T^3,0,0,0,1,0,1,2,0,T^3,3,3,4,10,5,7,16,13,28,24,35,49,67,103},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,4,0,0,4,13,10,0,0,10,34,20,20,70},{0,2*T^3,0,0,0,3*T^3,0,0,0,0,3*T^3,1,0,0,4*T^3,2,0,1,2,3,4,3,10,10,16,22,16,49,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,0,4,3,5,10,4,10,13,24,28,34,67},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,0,0,4,10,4,0,0,10,28,10,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,10,0,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,3,2,4,4,10,16,10,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,4,0,0,4,13,10,10,34},{0,2*T^3,0,0,T^3,8*T^3,0,0,0,0,3*T^3,0,0,T^3,9*T^3,0,0,1,2,0,T^3,3,3,10,5,7,16,24,35},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,1,0,0,2,1,4,3,5,10,13,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,0,0,4,10,4,10,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,4,4,13},{0,T^3,0,0,0,2*T^3,0,0,0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,1,1,2,3,2,10,16},{0,T^3,0,0,T^3,7*T^3,0,0,0,0,2*T^3,0,0,T^3,8*T^3,0,0,0,0,0,T^3,0,0,1,0,0,2,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,1,3},{0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,912)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & -1 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 0 & 2 & 0 & 1 & 1 & 0 & -1 & 2 & -1 & 0 & 2 & 1 & 2 & -1 & 0 & 1 & 1 & -1 & 2 & 0 & 1 & 0 & -1 & 2 & 1 & 0 & -1 & -1 & 0 & 1 & 0 & -1 & 0 \\ 2 & 3 & 1 & 2 & 2 & 1 & 3 & 3 & 1 & 2 & 2 & 0 & 2 & 1 & 3 & 1 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 3 & 4 & 2 & 4 & 3 & 2 & 2 & 1 & 3 & 3 & 2 & 2 & 3 & 1 & 2 & 1 & 2 & 3 & 0 & 1 & 2 & 2 & 2 & 1 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {1, 2, 6, 7}, {3, 5, 6, 7}, {0, 1, 2, 8}, {0, 4, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{3,4,5},{3,5,6},{2,5,6},{1,3,4},{0,2,5},{0,4,5},{0,1,4}},{2,1,2})
Cox degrees: {{0,0,1},{-1,1,1},{-1,1,1},{1,0,0},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,2,4},{0,3,4},{2,1,3},{0,2,4},{1,2,3},{1,1,3},{0,3,3},{-1,3,4},{2,1,2},{-1,2,4},{0,2,3},{2,0,2},{1,2,2},{2,1,1},{-1,3,3},{0,1,3},{1,1,2},{1,0,2},{-1,2,3},{2,0,1},{0,2,2},{1,1,1},{0,1,2},{-1,1,3},{2,0,0},{1,0,1},{0,0,2},{-1,2,2},{-1,1,2},{0,1,1},{1,0,0},{0,0,1},{-1,1,1},{0,0,0}}
Ext matrix: {{1,1,2,3,4,9,4,3,7,6,13,15,10,16,13,21,28,42,27,43,34,62,64,38,90,110,84,73,115,142,223,212,257,425},{0,1,0,1,2,2,4,3,3,3,9,3,7,10,13,9,15,15,21,21,28,43,42,21,58,63,42,64,84,110,156,140,212,323},{0,0,1,0,1,3,1,0,4,0,3,9,4,10,3,6,13,21,6,28,13,34,27,10,62,64,38,27,46,73,142,115,127,257},{0,0,0,1,0,2,0,1,0,3,4,3,0,0,4,9,7,15,13,10,10,16,28,21,22,43,42,34,64,62,90,110,142,223},{0,0,0,0,1,1,1,0,2,0,3,2,4,7,3,3,9,9,6,15,13,28,21,6,43,42,21,27,38,64,110,84,115,212},{0,0,0,0,0,1,0,0,0,0,1,2,0,0,1,3,4,9,3,7,4,10,13,6,16,28,21,13,27,34,62,64,73,142},{0,0,0,0,0,0,1,0,0,0,1,0,2,3,3,1,2,2,3,3,9,15,9,3,21,15,9,21,21,42,63,42,84,140},{0,0,3*T^2,0,0,0,0,1,5*T^2,1,2,6*T^2,0,7*T^2,4,2,3,3,9,4+9*T^2,7,10,15,9,13+12*T^2,21,15,28,42,43,58,63,110,156},{0,0,0,0,0,0,0,0,1,T^3,0,1,1,4,0,0,3,3,0,9,3,13,6,T^3,28,21,6,6,10,27,64,38,46,115},{0,0,2*T^2,0,0,0,0,0,3*T^2,1,0,5*T^2,0,4*T^2,0,2,0,3,4,7*T^2,0,0,7,9,9*T^2,10,15,10,28,16,22,43,62,90},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,2,2,3,3,4,7,9,3,10,15,9,13,21,28,43,42,64,110},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,0,4,1,4,3,0,10,13,6,3,6,13,34,27,27,73},{0,0,0,0,0,0,0,0,0,T^3,0,0,1,2,0,0,1,1,0,2,3,9,3,T^3,15,9,3,6,6,21,42,21,38,84},{0,0,0,T^3,0,0,0,T^3,0,7*T^3,0,0,0,1,0,T^3,0,0,T^3,1,0,3,0,7*T^3,9,3,T^3,0,T^3,6,21,6,10,38},{0,0,T^2,0,0,0,0,0,3*T^2,0,0,3*T^2,0,5*T^2,1,0,0,0,1,6*T^2,2,3,2,1,4+9*T^2,3,2,9,9,15,21,15,42,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,0,4,3,0,7,9,4,13,10,16,28,34,62},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,1,4,3,0,7,9,3,3,6,13,28,21,27,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,4,3,1,3,4,10,13,13,34},{0,0,T^2,0,0,0,0,0,2*T^2,0,0,3*T^2,0,3*T^2,0,0,0,0,1,5*T^2,0,0,2,1,7*T^2,3,2,4,9,7,10,15,28,43},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,1,0,T^3,4,3,0,0,0,3,13,6,6,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,0,3,2,1,3,3,9,15,9,21,42},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,T^3,2,1,0,0,0,3,9,3,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,1,3,4,7,9,13,28},{0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,1,4*T^2,0,2,0,4,0,0,7,10,16},{0,0,0,T^3,0,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,T^3,0,0,0,0,7*T^3,1,0,T^3,0,T^3,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,3,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,4,10},{0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,0,5*T^2,0,0,1,1,2,3,2,9,15},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,0,1,0,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,3,9},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,924)$ |
3 |
25 |
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9: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 3 & 2 & 3 & 1 & 3 & 2 & 1 & 1 & 0 & 2 & 3 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 1 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {1, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (25): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{0, 1, 2, 3}, {2, 4, 5, 7}, {4, 5, 6, 7}, {0, 1, 3, 8}, {6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,4,5},{0,2,5},{3,4,5},{1,2,4},{0,3,5}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{1,1,0},{1,0,0},{0,1,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{3,4,1},{2,4,1},{3,3,1},{1,4,1},{2,3,1},{3,2,1},{3,3,0},{2,2,1},{3,1,1},{1,3,1},{3,2,0},{2,3,0},{1,2,1},{1,3,0},{0,3,1},{2,2,0},{3,1,0},{2,1,1},{1,1,1},{0,2,1},{2,1,0},{1,2,0},{0,1,1},{0,2,0},{2,0,0},{1,1,0},{0,1,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,6,10,6,4,21,10,21,9,13,46,27,36,31,16,36,81,81,57,67,146,117,91,127,227,207,377},{0,1,0,3,3,0,0,6,T^3,10,0,4,21,13,21,9,0,10,36,46,16,31,81,67,25,57,127,91,207},{0,0,1,0,3,3,1,10,6,6,4,3,21,6,10,13,9,21,46,36,31,27,81,46,57,67,117,127,227},{0,0,0,1,0,T^3,0,0,7*T^3,3,0,0,6,4,10,0,T^3,T^3,10,21,0,9,36,31,T^3,16,57,25,91},{0,0,0,0,1,0,0,3,0,3,0,1,10,3,6,4,0,6,21,21,9,13,46,27,16,31,67,57,127},{0,0,0,T^3,0,1,0,3,3,0,1,0,6,0,T^3,3,4,10,21,10,13,6,36,10,31,27,46,67,117},{0,0,0,0,0,0,1,0,0,0,3,3,0,6,0,10,6,0,0,0,21,21,0,36,36,46,81,81,146},{0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,1,0,3,10,6,4,3,21,6,9,13,27,31,67},{0,T^3,0,7*T^3,0,0,0,0,1,T^3,0,0,0,T^3,7*T^3,0,1,3,6,T^3,3,0,10,T^3,13,6,10,27,46},{0,0,0,0,0,0,0,0,T^3,1,0,0,3,1,3,0,0,0,6,10,0,4,21,13,0,9,31,16,57},{0,0,0,T^3,0,0,0,0,0,0,1,0,0,0,T^3,3,3,0,0,0,10,6,0,10,21,21,36,46,81},{0,0,0,0,0,0,0,0,T^3,0,0,1,0,3,0,3,0,0,0,0,6,10,0,21,10,21,46,36,81},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,0,1,10,3,0,4,13,9,31},{0,0,0,0,0,T^3,0,0,7*T^3,0,0,0,0,1,0,0,T^3,T^3,0,0,0,3,0,10,T^3,6,21,10,36},{0,0,0,0,0,T^3,0,0,7*T^3,0,0,0,0,0,1,0,T^3,T^3,0,3,0,0,6,4,T^3,0,9,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,0,6,6,10,21,21,46},{0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,7*T^3,0,1,0,0,T^3,3,0,0,T^3,10,6,10,21,36},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,1,3,0,1,0,6,0,4,3,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,1,3,4,13},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,0,4,0,9},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,0,3,3,6,10,21},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,10,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4},{0,0,0,0,0,T^3,0,0,7*T^3,0,0,0,0,0,0,0,T^3,T^3,0,0,0,0,0,1,T^3,0,3,0,6},{0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,7*T^3,0,0,0,0,T^3,0,0,0,T^3,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,10},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,929)$ |
3 |
25 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 5 & 4 & 5 & 3 & 5 & 4 & 2 & 3 & 4 & 3 & 2 & 4 & 3 & 2 & 3 & 2 & 3 & 1 & 1 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 4 & 3 & 2 & 3 & 3 & 1 & 2 & 3 & 2 & 2 & 1 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-2, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (25): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{0, 1}, {0, 4, 5, 7}, {4, 5, 6, 7}, {1, 2, 3, 8}, {2, 3, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,1},{1,2,2}},{{3,4,5},{0,2,5},{2,3,5},{1,3,4},{0,4,5},{0,1,4}},{1,1,1})
Cox degrees: {{1,2,1},{1,0,0},{0,0,1},{0,0,1},{0,1,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,5,4},{1,4,4},{1,5,3},{1,3,4},{1,5,2},{1,4,3},{1,2,4},{1,3,3},{1,4,2},{0,3,3},{1,2,3},{1,4,1},{1,3,2},{0,2,3},{0,3,2},{1,2,2},{1,3,1},{1,1,3},{0,1,3},{0,2,2},{1,1,2},{1,2,1},{0,3,1},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,6,10,10,21,21,22,36,36,46,39,49,81,81,55,61,91,126,146,87,147,231,167,217,267,277,417,452,692},{0,1,0,3,0,3,6,10,6,10,21,10,21,22,21,46,36,36,39,49,81,81,36,91,146,87,147,136,167,277,267,452},{0,0,1,0,3,3,T^3,6,10,6,10,21,21,10,22,36,46,15+T^3,15,39,55,81,49,61,126,91,88,167,147,217,277,417},{0,0,0,1,T^3,0,3,3,0,3,10,T^3,6,10,6,21,10,21,22,21,46,36,10,49,81,36,91,55,87,167,136,267},{0,0,0,T^3,1,0,7*T^3,0,3,0,T^3,10,6,0,6,10,21,7*T^3,T^3,10,15+T^3,36,22,15,55,39,21+T^3,91,61,88,147,217},{0,0,0,0,0,1,0,3,3,3,6,6,10,6,10,21,21,10,10,22,36,46,21,39,81,49,61,87,91,147,167,277},{0,0,T^3,0,7*T^3,0,1,0,T^3,0,3,7*T^3,0,3,0,6,T^3,10,10,6,21,10,T^3,21,36,10,49,15+T^3,36,87,55,136},{0,0,0,0,0,0,0,1,0,1,3,0,3,3,3,10,6,6,6,10,21,21,6,22,46,21,39,36,49,91,87,167},{0,0,0,0,0,0,T^3,0,1,0,0,3,3,0,3,6,10,T^3,0,6,10,21,10,10,36,22,15,49,39,61,91,147},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,0,6,10,0,0,6,21,0,21,36,36,46,81,81,146},{0,0,0,0,T^3,0,0,0,0,0,1,T^3,0,1,0,3,0,3,3,3,10,6,0,10,21,6,22,10,21,49,36,87},{0,0,0,T^3,0,0,7*T^3,0,0,0,T^3,1,0,0,0,0,3,7*T^3,T^3,0,T^3,6,3,0,10,6,T^3,22,10,15,39,61},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,0,0,3,6,10,3,6,21,10,10,21,22,39,49,91},{0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,1,0,0,0,0,3,3,0,0,0,10,0,6,21,10,21,46,36,81},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,T^3,0,3,0,0,3,6,0,10,10,21,21,36,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,0,3,10,3,6,6,10,22,21,49},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,T^3,0,0,0,3,1,0,6,3,0,10,6,10,22,39},{T^3,0,4*T^3,0,13*T^3,0,0,0,T^3,T^3,0,7*T^3,0,0,3*T^3,0,T^3,1,1,0,3,0,7*T^3,3,6,0,10,T^3,6,21,10,36},{0,0,T^3,0,7*T^3,0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,1,0,0,0,T^3,3,0,0,10,T^3,6,21,10,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,6,6,10,21,21,46},{0,0,T^3,0,4*T^3,0,0,0,0,0,0,T^3,0,0,T^3,0,0,0,0,0,1,0,3*T^3,1,3,0,3,0,3,10,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,3,6,10,22},{0,0,0,T^3,0,0,7*T^3,0,0,0,T^3,0,0,0,0,0,0,7*T^3,T^3,0,T^3,0,1,0,0,3,T^3,10,6,10,21,36},{0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,10,6,21},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,0,1,3,3,10},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,3,3,6,10,21},{0,0,T^3,0,7*T^3,0,0,0,T^3,0,0,7*T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,1,T^3,0,3,0,6},{0,0,0,T^3,0,0,7*T^3,0,0,0,T^3,0,0,0,0,0,0,7*T^3,T^3,0,T^3,0,0,0,0,0,T^3,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,10},{0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,931)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -1 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 3 & 4 & 2 & 3 & 1 & 2 & 4 & 0 & 2 & 3 & -1 & 1 & 3 & 1 & 0 & 2 & 0 & 2 & 1 & -1 & 3 & 1 & 0 & -1 & 2 & 0 & 1 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -1}, {1, 1, 1, -1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{1,2,5},{1,2,3},{0,2,3},{0,2,5},{0,4,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,-1},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (29): {{1,3,3},{1,2,4},{1,3,2},{1,2,3},{1,3,1},{1,2,2},{1,1,4},{1,3,0},{0,2,2},{1,1,3},{1,3,-1},{1,2,1},{0,1,3},{0,2,1},{1,2,0},{1,1,2},{0,2,0},{0,1,2},{1,1,1},{1,2,-1},{0,0,3},{0,1,1},{1,1,0},{0,2,-1},{0,0,2},{0,1,0},{0,0,1},{0,1,-1},{0,0,0}}
Ext matrix: {{1,2,4,9,10,24,14,20,25,39,35,50,41,54,90,84,100,93,155,147,133,179,258,167,263,308,463,489,749},{0,1,0,4,0,10,9,0,10,24,0,20,25,20,35,50,35,54,90,56,93,100,147,56,179,167,308,259,489},{0,0,1,2,4,9,3,10,9,14,20,24,14,25,50,39,54,41,84,90,57,93,155,100,133,179,263,308,463},{0,0,0,1,0,4,2,0,4,9,0,10,9,10,20,24,20,25,50,35,41,54,90,35,93,100,179,167,308},{0,0,0,0,1,2,0,4,2,3,10,9,3,9,24,14,25,14,39,50,19,41,84,54,57,93,133,179,263},{0,0,0,0,0,1,0,0,1,2,0,4,2,4,10,9,10,9,24,20,14,25,50,20,41,54,93,100,179},{0,0,0,0,0,0,1,0,0,4,0,0,4,0,0,10,0,10,20,0,25,20,35,0,54,35,100,56,167},{0,T^3,0,0,0,0,T^3,1,0,0,4,2,T^3,2,9,3,9,3,14,24,4+T^3,14,39,25,19,41,57,93,133},{0,0,0,0,0,0,0,0,1,0,0,0,2,4,0,0,10,9,0,0,14,24,0,20,39,50,84,90,155},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,0,4,10,0,9,10,20,0,25,20,54,35,100},{T^3,6*T^3,0,T^3,0,0,6*T^3,0,T^3,T^3,1,0,7*T^3,0,2,0,2,T^3,3,9,7*T^3,3,14,9,4+T^3,14,19,41,57},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,2,4,2,9,10,3,9,24,10,14,25,41,54,93},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,9,10,0,0,24,20,50,35,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,0,3,9,0,10,14,24,39,50,84},{0,T^3,0,0,0,0,T^3,0,0,0,0,0,T^3,0,1,0,1,0,2,4,T^3,2,9,4,3,9,14,25,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,2,4,10,0,9,10,25,20,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,4,3,9,14,24,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,0,9,10,24,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,2,4,9,10,25},{0,4*T^3,0,T^3,0,0,6*T^3,0,0,T^3,0,0,5*T^3,0,0,0,0,T^3,0,1,7*T^3,0,2,1,T^3,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,9,10,24},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,1,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,939)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 4 & 3 & 3 & 2 & 2 & 2 & 1 & 3 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{2,3,4},{3,4,5},{0,3,5},{1,4,5},{0,1,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,2,5},{1,1,5},{1,2,4},{1,1,4},{1,2,3},{0,2,4},{1,0,4},{0,1,4},{0,2,3},{1,1,3},{1,2,2},{1,1,2},{0,2,2},{1,2,1},{1,0,3},{0,1,3},{0,0,3},{0,1,2},{1,0,2},{1,1,1},{0,2,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,9,10,5,14,11,14,24,20,50,30,35,39,33,53,74,84,90,55,123,155,140,239,237,413},{0,1,0,4,0,0,9,5,0,10,0,20,0,0,24,14,33,30,50,35,0,74,90,55,140,91,237},{0,0,1,2,4,1,3,2,5,9,10,24,14,20,14,11,17,33,39,50,30,53,84,74,123,140,239},{0,0,0,1,0,0,2,1,0,4,0,10,0,0,9,5,11,14,24,20,0,33,50,30,74,55,140},{0,0,0,0,1,0,0,0,1,2,4,9,5,10,3,2,3,11,14,24,14,17,39,33,53,74,123},{0,0,0,0,0,1,0,2,4,0,0,0,10,0,0,9,14,24,0,0,20,39,0,50,84,90,155},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,5,0,10,0,0,14,20,0,30,0,55},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,9,10,0,0,0,24,0,20,50,35,90},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,2,3,9,0,0,10,14,0,24,39,50,84},{0,0,0,0,0,0,0,0,0,1,0,4,0,0,2,1,2,5,9,10,0,11,24,14,33,30,74},{0,T^3,0,0,0,0,T^3,T^3,0,0,1,2,1,4,0,0,T^3,2,3,9,5,3,14,11,17,33,53},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,2,4,0,2,9,5,11,14,33},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,4,3,0,9,14,24,39},{T^3,6*T^3,0,T^3,0,T^3,6*T^3,7*T^3,0,0,0,0,0,1,T^3,T^3,7*T^3,0,0,2,1,T^3,3,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,0,0,5,10,0,14,0,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,0,0,0,9,0,10,24,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,4,9,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,5,0,14},{0,T^3,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,0,T^3,0,0,1,0,0,2,1,2,5,11},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,1,0,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,941)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 4 & 2 & 3 & 3 & 4 & 3 & 2 & 1 & 2 & 2 & 3 & 1 & 3 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{3,4,5},{0,1,4},{0,2,5},{0,4,5},{1,3,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,-1,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,2,4},{1,1,4},{1,2,3},{1,0,4},{0,2,4},{1,2,2},{1,1,3},{0,2,3},{0,1,4},{1,0,3},{1,1,2},{1,2,1},{1,0,2},{0,2,2},{0,1,3},{1,1,1},{0,0,3},{0,1,2},{1,0,1},{1,1,0},{0,2,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,3,3,10,9,13,5,14,24,20,39,34,23,50,33,63,84,90,70,93,155,134,203,245,379},{0,1,0,2,1,0,4,4,3,9,10,0,24,10,13,20,23,34,50,35,20,63,90,70,134,125,245},{0,0,1,0,0,4,2,3,0,3,9,10,14,13,5,24,7,23,39,50,34,33,84,63,93,134,203},{0,0,0,1,0,0,0,0,1,4,0,0,10,0,4,0,13,10,20,0,0,34,35,20,70,35,125},{0,0,0,0,1,0,0,4,2,0,0,0,0,10,9,0,14,24,0,0,20,39,0,50,84,90,155},{0,0,0,T^3,0,1,0,0,T^3,0,2,4,3,3,0,9,T^3,5,14,24,13,7,39,23,33,63,93},{0,0,0,0,0,0,1,1,0,2,4,0,9,4,3,10,5,13,24,20,10,23,50,34,63,70,134},{0,0,0,0,0,0,0,1,0,0,0,0,0,4,2,0,3,9,0,0,10,14,0,24,39,50,84},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,9,10,0,0,0,24,0,20,50,35,90},{0,0,0,0,0,0,0,0,0,1,0,0,4,0,1,0,3,4,10,0,0,13,20,10,34,20,70},{0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,4,0,3,9,10,4,5,24,13,23,34,63},{0,T^3,0,6*T^3,T^3,0,0,0,7*T^3,T^3,0,1,0,0,T^3,2,7*T^3,0,3,9,3,T^3,14,5,7,23,33},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,0,0,3,10,4,13,10,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,4,3,0,9,14,24,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,0,0,0,9,0,10,24,20,50},{0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,1,T^3,0,2,4,1,0,9,3,5,13,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,4,9,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,3,4,13},{0,T^3,0,6*T^3,T^3,0,0,0,7*T^3,T^3,0,0,0,0,T^3,0,7*T^3,0,0,1,0,T^3,2,0,0,3,5},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,1,0,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,942)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 1 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 2 & 0 & 0 & 1 & 0 \\ 1 & 2 & 1 & 1 & 2 & 0 & 2 & 1 & 1 & 1 & 0 & 0 & 2 & 2 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 4 & 4 & 3 & 2 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {3, 5, 6, 7}, {0, 1, 2, 8}, {0, 1, 4, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{3,4,5},{0,1,4},{3,5,6},{0,4,5},{0,2,5},{1,3,4},{2,5,6}},{2,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,1},{1,0,0},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,4},{1,2,4},{1,1,4},{2,1,3},{1,2,3},{2,0,3},{0,2,4},{0,1,4},{1,1,3},{2,1,2},{1,0,3},{2,0,2},{1,2,2},{0,2,3},{0,1,3},{1,1,2},{2,1,1},{2,0,1},{0,2,2},{0,0,3},{1,0,2},{1,1,1},{0,1,2},{0,0,2},{1,0,1},{2,0,0},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,3,4,4,7,3,6,13,10,18,22,10,13,27,34,20,50,34,34,55,70,73,103,124,95,154,233,235,444},{0,1,1,1,4,1,3,3,7,4,7,7,10,13,18,22,10,22,34,18,28,50,55,64,74,50,124,161,155,329},{0,0,1,0,0,1,1,3,4,0,7,4,0,4,13,10,0,10,10,18,22,20,34,55,50,20,70,124,95,235},{0,0,0,1,1,1,0,0,3,4,3,7,4,3,6,13,10,22,13,6,18,34,27,34,55,50,73,103,124,233},{0,0,0,0,1,0,0,0,1,1,1,1,4,3,3,7,4,7,13,3,7,22,18,18,28,22,55,64,74,161},{0,0,0,0,0,1,0,0,1,0,3,4,0,1,3,4,0,10,4,6,13,10,13,27,34,20,34,73,70,154},{0,0,0,0,0,0,1,1,1,0,1,1,0,4,7,4,0,4,10,7,7,10,22,28,22,10,50,74,50,155},{0,0,0,0,0,0,0,1,0,0,1,0,0,0,4,0,0,0,0,7,4,0,10,22,10,0,20,50,20,95},{0,0,0,0,0,0,0,0,1,0,1,1,0,1,3,4,0,4,4,3,7,10,13,18,22,10,34,55,50,124},{0,0,0,0,0,0,0,T^3,0,1,0,1,1,0,0,3,4,7,3,T^3,3,13,6,6,18,22,27,34,55,103},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,3,4,0,4,13,10,0,10,34,20,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,0,3,4,3,6,13,10,13,27,34,73},{0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,1,1,1,3,T^3,1,7,3,3,7,7,18,18,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,4,1,1,4,7,7,7,4,22,28,22,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,4,7,4,0,10,22,10,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,4,3,3,7,4,13,18,22,55},{0,0,T^3,0,0,0,T^3,7*T^3,0,0,T^3,0,0,0,T^3,0,1,1,0,7*T^3,0,3,0,T^3,3,7,6,6,18,34},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,T^3,0,1,0,0,3,4,3,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,4,0,4,13,10,34},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,1,1,3,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,4,7,4,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,4,13},{0,0,T^3,0,0,0,T^3,7*T^3,0,0,T^3,0,0,0,T^3,0,0,0,0,7*T^3,0,0,0,T^3,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,943)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 2 & 2 & 0 & 0 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 2 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (28): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3}, {2, 4, 5, 7}, {4, 5, 6, 7}, {0, 1, 3, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,4,5},{0,3,5},{1,2,4},{0,2,5},{3,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,1,0},{1,0,0},{0,1,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{2,4,2},{1,4,2},{2,4,1},{2,3,2},{1,3,2},{2,3,1},{1,4,1},{2,2,2},{0,3,2},{1,3,1},{1,2,2},{2,2,1},{2,3,0},{2,1,2},{0,2,2},{0,3,1},{1,1,2},{1,3,0},{2,2,0},{1,2,1},{2,1,1},{0,2,1},{1,1,1},{2,1,0},{1,2,0},{0,1,2},{0,1,1},{0,2,0},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,7,7,4,6,11,16,15,15,11,10,25,25,26,25,25,37,26,61,67,45,61,45,115,100,115,106,187,187,196,328},{0,1,0,0,3,0,2,0,7,7,6,0,0,T^3,15,16,10,11,0,15,0,37,26,0,25,26,67,61,45,40,106,71,115,187},{0,0,1,0,0,3,2,0,0,7,0,6,7,T^3,0,11,0,16,15,15,10,25,26,26,37,0,45,61,67,40,71,106,115,187},{0,0,0,1,2,2,0,3,3,4,7,7,3,6,11,6,15,6,11,16,15,25,37,25,25,25,61,39,61,67,115,115,100,196},{0,0,0,0,1,0,0,0,2,2,3,0,0,0,7,4,6,3,0,7,0,16,15,0,11,15,37,25,25,26,67,45,61,115},{0,0,0,0,0,1,0,0,0,2,0,3,2,0,0,3,0,4,7,7,6,11,15,15,16,0,25,25,37,26,45,67,61,115},{0,0,0,0,0,0,1,T^3,0,3,0,0,0,7*T^3,0,7,T^3,7,0,6,T^3,15,10,0,15,0,26,37,26,15+T^3,40,40,67,106},{0,0,0,0,0,0,0,1,0,0,2,2,0,3,3,0,7,0,3,4,7,6,16,11,6,11,25,9,25,37,61,61,39,100},{0,0,0,0,0,0,0,0,1,0,0,0,0,T^3,3,2,0,0,0,0,0,7,0,0,0,6,15,11,0,0,26,0,25,45},{0,0,0,0,0,0,0,0,0,1,0,0,0,T^3,0,2,0,2,0,3,0,7,6,0,7,0,15,16,15,10,26,26,37,67},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,0,0,2,0,4,7,0,3,7,16,6,11,15,37,25,25,61},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,2,3,3,7,7,4,0,11,6,16,15,25,37,25,61},{0,0,0,0,0,0,0,0,0,0,0,0,1,T^3,0,0,0,2,3,0,0,0,0,6,7,0,0,11,15,0,0,26,25,45},{0,2*T^3,2*T^3,0,0,0,6*T^3,0,2*T^3,0,0,0,2*T^3,1,0,3*T^3,2,3*T^3,0,0,2,0,4,3,0,3,6,0,6,16,25,25,9,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,3,7,3,0,0,15,0,11,25},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,7*T^3,0,1,T^3,0,0,0,T^3,3,0,0,0,0,6,7,0,T^3,10,0,15,26},{0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,T^3,0,0,0,1,2*T^3,0,0,0,0,2,0,0,2,4,0,3,7,16,11,6,25},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,7*T^3,0,0,T^3,1,0,0,T^3,0,0,0,3,0,0,7,6,T^3,0,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,2,0,0,3,7,0,0,15,11,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,2,0,7,4,7,6,15,15,16,37},{0,T^3,0,0,0,0,2*T^3,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,1,0,2,2,0,0,3,0,4,7,11,16,6,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,0,0,3,2,0,0,6,0,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,3,7,7,4,16},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,7,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,0,0,6,7,15},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,2,0,0,0,7,0,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,2,7},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,7*T^3,0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,1,0,T^3,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,7},{0,T^3,T^3,0,0,0,4*T^3,0,T^3,0,0,0,T^3,0,0,2*T^3,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,4},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,947)$ |
3 |
28 |
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9: $\begin{pmatrix}1 & -1 & -1 & 0 & 0 & -1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}-1 & 0 & -1 & -2 & 0 & -1 & 0 & -1 & -2 & -1 & 1 & -2 & -1 & 1 & 0 & 0 & -1 & 0 & -2 & 1 & 1 & -2 & 0 & -1 & -1 & -2 & 0 & 1 & -1 & 0 & -1 & 1 & -1 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 1 & 1 & 0 & 2 & 3 & 2 & 1 & 2 & 1 & 3 & 0 & 1 & 2 & 3 & 0 & 2 & 2 & 1 & 0 & 3 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 0 & 1 & 0 \\ 3 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, 0, 0, 1, 1, 1}, {0, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{3,5,6},{3,4,6},{2,5,6},{1,3,4},{0,2,5},{0,3,5},{0,1,3}},{2,1,3})
Cox degrees: {{1,-1,0},{-1,0,1},{-1,0,1},{0,1,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (35): {{-1,3,3},{0,3,2},{-1,2,3},{-2,3,3},{0,2,2},{-1,1,3},{0,1,2},{-1,0,3},{-2,2,3},{-1,3,2},{1,2,1},{-2,1,3},{-1,2,2},{1,1,1},{0,3,1},{0,0,2},{-1,1,2},{0,2,1},{-2,3,2},{1,0,1},{1,2,0},{-2,2,2},{0,1,1},{-1,0,2},{-1,3,1},{-2,1,2},{0,0,1},{1,1,0},{-1,2,1},{0,2,0},{-1,1,1},{1,0,0},{-1,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,4,7,6,15,10,9,10,11,16,25,25,16,26,47,43,28,45,61,57,85,76,49,97,142,125,106,158,188,215,295,290,467},{0,1,0,0,3,0,6,T^3,0,4,7,0,9,15,10,10,16,25,10,26,43,19,47,25,28,31,76,85,57,106,97,142,148,188,295},{0,0,1,1,2,3,7,6,4,2,3,9,10,11,3,15,25,16,10,25,22,28,43,47,16,57,85,61,49,70,106,125,188,158,290},{0,0,0,1,0,0,0,0,3,2,0,6,7,0,3,0,15,11,10,0,15,25,25,26,16,47,45,35,43,61,85,65,142,125,215},{0,0,0,0,1,0,3,0,0,1,2,0,4,7,2,6,9,10,4,15,16,10,25,16,10,19,47,43,28,49,57,85,97,106,188},{0,0,0,0,0,1,2,3,1,0,0,4,2,3,0,7,10,3,2,11,4,10,16,25,3,28,43,22,16,22,49,61,106,70,158},{0,0,0,0,0,0,1,0,0,0,0,0,1,2,0,3,4,2,1,7,3,4,10,9,2,10,25,16,10,16,28,43,57,49,106},{0,2*T^3,0,0,0,0,0,1,0,0,2*T^3,1,0,0,3*T^3,2,2,0,0,3,3*T^3,2,3,10,0,10,16,4,3,4,16,22,49,22,70},{0,0,0,0,0,0,0,0,1,0,0,3,2,0,0,0,7,3,2,0,4,10,11,15,3,25,25,15,16,22,43,35,85,61,125},{0,0,0,0,0,0,0,T^3,0,1,0,0,3,0,2,0,6,7,4,0,11,9,15,10,10,16,26,25,25,43,47,45,76,85,142},{0,0,0,T^2,0,0,0,T^3,3*T^2,0,1,6*T^2,0,3,1,0,0,4,T^2,6,10,3*T^2,9,0,4,6*T^2,16,25,10,28,19,47,31,57,97},{0,T^3,0,0,0,0,0,0,0,0,T^3,1,0,0,2*T^3,0,2,0,0,0,2*T^3,2,3,7,0,10,11,4,3,4,16,15,43,22,61},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,1,0,3,4,7,6,2,9,15,11,10,16,25,25,47,43,85},{0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,1,0,0,0,1,0,3,2,T^2,4,0,1,3*T^2,9,10,4,10,10,25,19,28,57},{0,0,0,0,0,T^3,0,7*T^3,0,0,0,T^3,0,0,1,T^3,0,3,0,0,7,0,6,T^3,4,0,10,15,9,25,16,26,25,47,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,0,1,2,4,0,4,10,3,2,3,10,16,28,16,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,2,3,0,4,7,3,2,3,10,11,25,16,43},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,0,1,0,6,7,4,10,9,15,16,25,47},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,2,6,0,0,7,11,15,0,26,25,45},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,0,1,0,0,T^2,4,2,1,2,4,10,10,10,28},{0,0,0,T^2,0,T^3,0,7*T^3,3*T^2,0,0,6*T^2+T^3,0,0,0,T^3,0,0,T^2,0,1,3*T^2,0,T^3,0,6*T^2,0,3,0,4,0,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,2,3,7,0,15,11,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,1,2,4,7,9,10,25},{0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,2*T^3,0,0,1,0,1,2,0,0,0,2,3,10,3,16},{0,0,0,0,0,T^3,0,7*T^3,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,0,T^3,1,0,0,0,3,7,6,0,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,1,0,0,0,0,2,0,7,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,4,2,10},{0,0,0,0,0,0,0,T^3,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,1,0,3,0,4,9},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,6,7,15},{0,0,0,0,0,T^3,0,7*T^3,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,948)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & -1 & -1 & 0 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}-2 & -2 & -1 & -2 & 0 & -1 & -2 & -2 & -1 & 0 & -1 & -1 & 0 & -2 & -1 & 0 & -2 & -2 & 0 & -1 & 0 & -1 & -2 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & 0 \\ 3 & 2 & 3 & 1 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 3 & 3 & 0 & 1 & 1 & 2 & 0 & 3 & 2 & 1 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, -1, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{2,4,5},{2,3,5},{0,1,4},{1,4,5},{0,2,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{-1,0,1},{0,1,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{-2,3,4},{-2,2,4},{-1,3,3},{-2,1,4},{0,3,2},{-1,2,3},{-2,3,3},{-2,2,3},{-1,3,2},{0,2,2},{-1,1,3},{-1,2,2},{0,3,1},{-2,3,2},{-1,0,3},{0,1,2},{-2,1,3},{-2,2,2},{0,0,2},{-1,3,1},{0,2,1},{-1,1,2},{-2,1,2},{0,1,1},{-1,2,1},{-1,0,2},{0,0,1},{0,2,0},{-1,1,1},{-1,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,2,6,3,7,4,13,7,11,15,25,10,10,26,25,27,34,45,16,37,55,73,85,58,97,155,82,130,233,190,350},{0,1,0,3,0,2,0,4,0,3,7,7,0,0,15,11,13,10,25,0,10,25,34,37,16,55,85,22,58,130,82,190},{0,0,1,0,2,3,1,3,4,7,6,13,7,4,10,15,6,13,26,10,25,27,27,55,34,46,97,58,73,127,130,233},{0,0,0,1,2*T^3,0,0,0,0,0,2,0,3*T^3,0,7,3,4,0,11,0,0,7,10,10,0,25,37,0,16,58,22,82},{0,0,0,T^3,1,0,0,0,1,3,0,3,4,1,T^3,6,0,3,10,4,13,6,6,27,13,10,46,34,27,46,73,127},{0,0,0,0,0,1,0,1,0,2,3,4,0,0,6,7,3,4,15,0,7,13,13,25,10,27,55,16,34,73,58,130},{0,0,0,0,0,0,1,3,2,0,0,7,3,4,0,0,6,13,0,7,11,15,27,25,25,26,45,37,55,97,85,155},{0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,3,4,0,0,3,7,13,11,7,15,25,10,25,55,37,85},{0,0,0,T^3,0,0,0,0,1,0,0,3,2,1,T^3,0,0,3,0,4,7,6,6,15,13,10,26,25,27,46,55,97},{0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,3,0,1,6,0,4,3,3,13,4,6,27,10,13,27,34,73},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,1,0,7,0,0,4,4,7,0,13,25,0,10,34,16,58},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,2,3,3,7,4,6,15,7,13,27,25,55},{0,T^3,0,7*T^3,0,0,0,0,0,0,T^3,0,1,0,7*T^3,0,T^3,0,T^3,1,3,0,0,6,3,T^3,10,13,6,10,27,46},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,T^3,0,0,3,0,2,0,0,6,0,7,0,0,11,15,26,25,45},{0,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,1,0,0,0,2,0,0,0,0,0,0,4,7,0,0,10,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,1,1,4,0,3,13,0,4,13,10,34},{0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,0,0,0,0,2,4,3,0,7,11,0,7,25,10,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,2,0,0,3,7,15,11,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,4,0,0,4,0,10},{0,T^3,0,7*T^3,0,0,0,0,0,0,T^3,0,0,0,7*T^3,0,T^3,0,T^3,1,0,0,0,0,3,T^3,0,7,6,10,15,26},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,3,1,0,6,4,3,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,3,7,0,4,13,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,7,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,4,13},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,7,15},{0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,4,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,T^3,0,7*T^3,0,0,0,0,0,0,T^3,0,0,0,7*T^3,0,T^3,0,T^3,0,0,0,0,0,0,T^3,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,949)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 4 & 3 & 1 & 2 & 4 & 3 & 1 & 2 & 3 & 1 & 0 & 2 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{3,4,5},{0,2,5},{0,1,4},{1,3,4},{0,4,5}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{2,1,4},{2,0,4},{2,1,3},{1,1,4},{2,0,3},{2,1,2},{1,0,4},{1,1,3},{2,1,1},{2,0,2},{0,1,4},{1,0,3},{2,0,1},{1,1,2},{0,1,3},{1,1,1},{2,0,0},{1,0,2},{0,1,2},{0,0,3},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,3,5,10,3,13,20,14,6,15,30,34,27,70,55,43,73,30,94,87,175,154,193,364},{0,1,0,1,4,0,3,4,0,10,3,13,20,10,13,20,35,34,34,27,70,73,125,70,154,280},{0,0,1,0,1,4,0,3,10,5,0,3,14,13,6,34,30,15,27,6,43,30,94,73,87,193},{0,0,0,1,0,0,1,4,0,0,3,5,0,10,13,20,0,14,34,15,30,43,55,70,94,175},{0,0,0,0,1,0,0,1,0,4,0,3,10,4,3,10,20,13,13,6,34,27,70,34,73,154},{0,0,0,0,0,1,T^3,0,4,1,T^3,0,5,3,0,13,14,3,6,T^3,15,6,43,27,30,87},{0,0,0,0,0,0,1,0,0,0,1,4,0,0,4,0,0,10,10,13,20,34,35,20,70,125},{0,0,0,0,0,0,0,1,0,0,0,1,0,4,3,10,0,5,13,3,14,15,30,34,43,94},{0,T^3,0,T^3,0,0,7*T^3,0,1,0,7*T^3,T^3,1,0,T^3,3,5,0,0,7*T^3,3,T^3,15,6,6,30},{0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,4,10,3,3,0,13,6,34,13,27,73},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,10,5,0,14,0,20,30,55},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,4,3,10,13,20,10,34,70},{0,0,0,0,0,0,T^3,0,0,0,T^3,0,1,0,0,1,4,0,0,T^3,3,0,13,3,6,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,3,0,5,3,14,13,15,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,5,0,10,14,30},{0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,1,0,0,0,T^3,1,0,5,3,3,15},{0,T^3,0,T^3,0,0,7*T^3,0,0,0,7*T^3,T^3,0,0,T^3,0,1,0,0,7*T^3,0,T^3,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,3,10,4,13,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,950)$ |
3 |
25 |
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9: $\begin{pmatrix}0 & 0 & -1 & 0 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}-1 & 0 & -1 & -1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & -1 & -1 & 0 & 0 & -1 & -1 & 0 & -1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 1 & 2 & 3 & 2 & 3 & 1 & 3 & 2 & 1 & 0 & 1 & 3 & 2 & 1 & 2 & 0 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 0 \\ 4 & 3 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, -1, -1, -1}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 1, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{2,4,5},{2,3,5},{1,4,5},{0,2,4},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{0,1,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{-1,3,4},{0,3,3},{-1,2,4},{-1,1,4},{0,2,3},{-1,3,3},{-1,2,3},{0,3,2},{0,1,3},{-1,3,2},{0,2,2},{-1,1,3},{0,0,3},{0,1,2},{0,3,1},{-1,2,2},{-1,1,2},{0,2,1},{0,0,2},{-1,3,1},{-1,2,1},{0,1,1},{-1,1,1},{0,2,0},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,1,3,6,4,4,13,4,9,10,16,27,16,37,10,34,73,40,67,20,70,94,154,80,173,190,354},{0,1,0,0,3,1,3,4,6,4,13,6,10,27,10,13,27,34,46,10,34,73,73,70,127,154,273},{0,0,1,3,1,0,4,0,4,0,4,13,9,16,0,10,34,10,37,0,20,40,70,20,94,80,190},{0,0,0,1,0,0,0,0,1,0,0,4,4,4,0,0,10,0,16,0,0,10,20,0,40,20,80},{0,0,0,0,1,0,1,0,3,0,4,3,6,13,0,4,13,10,27,0,10,34,34,20,73,70,154},{0,0,0,0,0,1,3,1,0,4,4,6,0,9,4,13,27,16,16,10,34,37,73,40,67,94,173},{0,0,0,0,0,0,1,0,0,0,1,3,0,4,0,4,13,4,9,0,10,16,34,10,37,40,94},{0,0,0,T^3,0,0,0,1,0,1,3,0,T^3,6,4,3,6,13,10,4,13,27,27,34,46,73,127},{0,0,0,0,0,0,0,0,1,0,0,1,3,4,0,0,4,0,13,0,0,10,10,0,34,20,70},{0,0,0,T^3,0,0,0,0,0,1,0,0,T^3,0,1,3,6,4,0,4,13,9,27,16,16,37,67},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,4,6,0,4,13,13,10,27,34,73},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,0,4,0,0,4,10,0,16,10,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,0,0,4,4,0,13,10,34},{0,0,T^3,7*T^3,0,0,0,0,T^3,0,0,T^3,7*T^3,0,1,0,0,3,T^3,1,3,6,6,13,10,27,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,4,4,13,4,9,16,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,0,4,4,16},{0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,1,3,3,4,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,10},{0,0,T^3,7*T^3,0,0,0,0,T^3,0,0,T^3,7*T^3,0,0,0,0,0,T^3,1,3,0,6,4,0,9,16},{0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,3,1,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4},{0,0,T^3,7*T^3,0,0,0,0,T^3,0,0,T^3,7*T^3,0,0,0,0,0,T^3,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,972)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
37: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 6 & 5 & 4 & 5 & 3 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 4 & 2 & 4 & 3 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 5 & 3 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}, {0, 0, 1, 1, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 1, 7}, {2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,2,2}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{1,2,2},{1,2,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (37): {{2,6,6},{2,5,6},{2,6,5},{2,4,6},{2,6,4},{2,5,5},{2,4,5},{2,5,4},{2,3,5},{2,5,3},{2,4,4},{1,4,4},{2,4,3},{2,3,4},{1,3,4},{2,3,3},{1,4,3},{1,2,4},{1,4,2},{1,3,3},{1,2,3},{1,3,2},{1,1,3},{1,3,1},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,6,9,18,18,30,30,36,38,60,60,66,100,66,102,102,118,186,186,270,270,297,300,435,435,444,641,444,618,618,668,942,942,1342},{0,1,0,3,0,3,9,6,18,10,18,18,30,36,38,60,30,66,45,66,118,102,186,146,186,186,270,297,300,435,270,444,370,444,668,618,942},{0,0,1,0,3,3,6,9,10,18,18,18,36,30,30,60,38,45,66,66,102,118,146,186,186,186,297,270,270,435,300,370,444,444,618,668,942},{0,0,0,1,0,0,3,0,9,0,6,6,10,18,18,30,10,38,15,30,66,45,118,63,102,102,146,186,186,270,146,300,198,270,444,370,618},{0,0,0,0,1,0,0,3,0,9,6,6,18,10,10,30,18,15,38,30,45,66,63,118,102,102,186,146,146,270,186,198,300,270,370,444,618},{0,0,0,0,0,1,3,3,6,6,9,9,18,18,18,36,18,30,30,38,66,66,102,102,118,118,186,186,186,297,186,270,270,300,444,444,668},{0,0,0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,10,18,38,30,66,45,66,66,102,118,118,186,102,186,146,186,300,270,444},{0,0,0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,18,18,30,38,45,66,66,66,118,102,102,186,118,146,186,186,270,300,444},{0,0,T^2,0,3*T^2,0,0,0,1,0,0,0,0,3,3,6,2*T^2,9,6*T^2,6,18,10,38,15,30,30,45,66,66,102,45+3*T^2,118,63+9*T^2,102,186,146,270},{0,T^2,0,3*T^2,0,0,0,0,0,1,0,0,3,0,2*T^2,6,3,6*T^2,9,6,10,18,15,38,30,30,66,45,45+3*T^2,102,66,63+9*T^2,118,102,146,186,270},{0,0,0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,9,18,18,30,30,38,38,66,66,66,118,66,102,102,118,186,186,300},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,30,30,36,38,60,60,66,100,66,102,102,118,186,186,297},{0,0,0,T^2,0,0,0,0,0,0,0,0,1,0,0,3,1,2*T^2,3,3,6,9,10,18,18,18,38,30,30,66,38,45+3*T^2,66,66,102,118,186},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,1,3,0,3,2*T^2,3,9,6,18,10,18,18,30,38,38,66,30,66,45+3*T^2,66,118,102,186},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18,10,18,18,30,36,38,60,30,66,45,66,118,102,186},{T^4,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,1,0,0,0,1,3,3,6,6,9,9+3*T^4,18,18,18,38,18,30,30,38,66,66,118},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,10,18,18,18,36,30,30,60,38,45,66,66,102,118,186},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,9,0,6,6,10,18,18,30,10,38,15,30,66,45,102},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,9,6,6,18,10,10,30,18,15,38,30,45,66,102},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,6,6,9,9,18,18,18,36,18,30,30,38,66,66,118},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,10,18,38,30,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,18,18,30,38,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,3*T^2,0,0,0,1,0,0,0,0,3,3,6,2*T^2,9,6*T^2,6,18,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,1,0,0,3,0,2*T^2,6,3,6*T^2,9,6,10,18,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,9,18,18,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,0,0,3,1,2*T^2,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,1,3,0,3,2*T^2,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,1,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1039)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
37: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 3 & 3 & 1 & 3 & 2 & 2 & 3 & 2 & 1 & 1 & 2 & 1 & 3 & 0 & 1 & 3 & 2 & 2 & 0 & 2 & 1 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 2 & 0 & 1 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 4 & 5 & 3 & 4 & 4 & 3 & 3 & 4 & 4 & 3 & 3 & 2 & 4 & 3 & 1 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 1, -1, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {2, 3, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,2},{1,1,2}},{{1,2,4},{0,3,4},{0,1,4},{2,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,0,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (37): {{2,3,6},{2,2,6},{2,3,5},{2,1,6},{2,2,5},{2,3,4},{1,3,4},{2,1,5},{2,3,3},{2,2,4},{1,2,4},{1,3,3},{2,2,3},{2,1,4},{1,1,4},{1,2,3},{2,1,3},{1,3,2},{1,0,4},{1,1,3},{1,3,1},{1,2,2},{0,2,2},{1,0,3},{1,2,1},{1,1,2},{0,1,2},{0,2,1},{1,1,1},{1,0,2},{0,0,2},{0,1,1},{1,0,1},{0,2,0},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,9,6,7,18,10,18,22,13,30,36,45,42,60,21,76,87,31,69,73,148,103,144,154,115,216,246,265,246,370,168,427,363,634},{0,1,0,3,3,0,0,9,0,6,7,0,10,18,22,13,30,0,45,42,0,21,22,87,31,69,73,34,103,144,154,115,216,49,246,168,363},{0,0,1,0,3,3,3,6,6,9,9,7,18,18,18,22,36,13,30,45,21,42,42,76,69,87,87,73,144,148,148,154,246,115,265,246,427},{0,0,0,1,0,0,T^2,3,0,0,0,3*T^2,0,6,7,0,10,6*T^2,22,13,10*T^2,0,T^2,42,0,21,22,3*T^2,31,69,73,34,103,6*T^2,115,49,168},{0,0,0,0,1,0,0,3,0,3,3,0,6,9,9,7,18,0,18,22,0,13,13,45,21,42,42,22,69,87,87,73,144,34,154,115,246},{0,0,0,0,0,1,1,0,3,3,3,3,9,6,6,9,18,7,10,18,13,22,22,30,42,45,45,42,87,76,76,87,148,73,148,154,265},{0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,9,0,6,10,18,10,18,22,30,30,36,45,42,60,60,76,87,100,69,148,144,246},{0,0,0,0,0,0,0,1,0,0,0,T^2,0,3,3,0,6,3*T^2,9,7,6*T^2,0,0,22,0,13,13,T^2,21,42,42,22,69,3*T^2,73,34,115},{T^2,3*T^2,0,6*T^2,0,0,T^2,0,1,0,4*T^2,1,3,0,9*T^2,3,6,3,16*T^2,6,7,9,9+4*T^2,10,22,18,18+10*T^2,22,45,30,30+19*T^2,45,76,42,76,87,148},{0,0,0,0,0,0,0,0,0,1,1,0,3,3,3,3,9,0,6,9,0,7,7,18,13,22,22,13,42,45,45,42,87,22,87,73,154},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,9,0,6,7,18,10,18,22,13,30,36,45,42,60,21,87,69,144},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,6,9,9,10,18,18,18,22,36,30,30,45,60,42,76,87,148},{0,T^2,0,3*T^2,0,0,0,0,0,0,T^2,0,1,0,4*T^2,1,3,0,9*T^2,3,0,3,3+T^2,6,7,9,9+4*T^2,7,22,18,18+10*T^2,22,45,13,45,42,87},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,T^2,3,3,3*T^2,0,0,9,0,7,7,0,13,22,22,13,42,T^2,42,22,73},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,0,9,0,6,7,0,10,18,22,13,30,0,42,21,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,3,6,6,9,9,7,18,18,18,22,36,13,45,42,87},{0,0,0,T^2,0,0,T^4,0,0,0,0,0,0,0,T^2,0,1,0,4*T^2,1,T^2,0,T^4,3,0,3,3+T^2,0,7,9,9+4*T^2,7,22,0,22,13,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,3,0,9,6,6,9,18,10,10,18,30,22,30,45,76},{0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,6*T^2,1,0,10*T^2,0,T^2,3,0,0,0,3*T^2,0,6,7,0,10,6*T^2,13,0,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,3,0,6,9,9,7,18,0,22,13,42},{0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,10*T^2,0,1,0,4*T^2,0,3,0,9*T^2,3,6,0,16*T^2,6,10,9,10,18,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,3,3,3,9,6,6,9,18,7,18,22,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,9,0,6,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,6*T^2,0,0,1,0,0,0,T^2,0,3,3,0,6,3*T^2,7,0,13},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,T^2,0,1,0,4*T^2,1,3,0,9*T^2,3,6,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,3,3,3,9,0,9,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,T^2,0,1,0,4*T^2,1,3,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,1,1,0,3,T^2,3,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,9},{0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,T^4,0,0,0,0,0,0,0,T^2,0,1,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1059)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & -2 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
40: $\begin{pmatrix}1 & 2 & 1 & 2 & 0 & 0 & -1 & 1 & 2 & 2 & 1 & 0 & -1 & 2 & 1 & -1 & 0 & 1 & 2 & 0 & -1 & 0 & -1 & 1 & 2 & 2 & -1 & 1 & 0 & 1 & 2 & 0 & -1 & 1 & 2 & 0 & -1 & 1 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 5 & 4 & 6 & 5 & 6 & 4 & 3 & 4 & 3 & 4 & 5 & 3 & 4 & 4 & 3 & 3 & 2 & 4 & 3 & 3 & 4 & 2 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, -2, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-2,1,2}},{{0,2,3},{1,3,4},{0,1,3},{2,3,4}},{2,3,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-2,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (40): {{1,2,6},{2,2,5},{1,2,5},{2,2,4},{0,2,6},{0,2,5},{-1,2,6},{1,2,4},{2,2,3},{2,1,4},{1,2,3},{0,2,4},{-1,2,5},{2,1,3},{1,1,4},{-1,2,4},{0,2,3},{1,1,3},{2,1,2},{0,1,4},{-1,2,3},{0,1,3},{-1,1,4},{1,1,2},{2,1,1},{2,0,2},{-1,1,3},{1,1,1},{0,1,2},{1,0,2},{2,0,1},{0,1,1},{-1,1,2},{1,0,1},{2,0,0},{0,0,2},{-1,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,0,3,0,3,9,6,6,0,3,10,18,18,9,13,36,30,31,18,31,60,69,57,57,30,31,123,91,123,79,69,193,216,157,123,157,336,265,295,483},{0,1,3,3,0,6,0,9,6,3,18,18,10,13,9,30,36,31,31,18,60,57,30,69,57,31,91,123,123,69,79,216,193,157,157,123,336,295,265,483},{0,0,1,0,0,3,0,3,0,0,6,9,6,3,3,18,18,13,9,9,36,31,18,31,18,9,57,57,69,31,31,123,123,79,69,69,216,157,157,295},{0,0,0,1,0,0,0,3,3,1,9,6,0,3,3,10,18,9,13,6,30,18,10,31,31,13,30,69,57,31,31,123,91,69,79,57,193,157,123,265},{0,0,0,0,1,3,3,0,0,1,0,6,9,3,3,18,10,9,6,13,30,31,31,18,10,13,69,30,57,31,31,91,123,69,57,79,193,123,157,265},{0,0,0,0,0,1,0,0,0,0,0,3,3,1,0,9,6,3,3,3,18,13,9,9,6,3,31,18,31,9,13,57,69,31,31,31,123,69,79,157},{0,3*T^2,0,6*T^2,0,0,1,0,10*T^2,7*T^2,0,0,3,13*T^2,1,6,0,3,21*T^2,3,10,9,13,6,31*T^2,3+22*T^2,31,10,18,13,9+34*T^2,30,57,31,18+49*T^2,31,91,57,69,123},{0,0,0,0,0,0,0,1,0,0,3,3,0,0,1,6,9,3,3,3,18,9,6,13,9,3,18,31,31,13,9,69,57,31,31,31,123,79,69,157},{3*T^2,0,0,0,6*T^2,0,10*T^2,0,1,7*T^2,3,0,0,1,13*T^2,0,6,3,3,21*T^2,10,6,31*T^2,9,13,3+22*T^2,10,31,18,9+34*T^2,13,57,30,31,31,18+49*T^2,91,69,57,123},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,9,6,6,0,18,10,18,10,13,30,30,36,31,31,60,60,69,57,57,100,123,123,216},{T^2,0,0,0,3*T^2,0,6*T^2,0,0,3*T^2,1,0,0,0,7*T^2,0,3,1,0,13*T^2,6,3,21*T^2,3,3,13*T^2,6,13,9,3+22*T^2,3,31,18,13,9,9+34*T^2,57,31,31,69},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,1,1,9,3,3,3,3,1,9,9,13,3,3,31,31,9,13,13,69,31,31,79},{0,T^2,0,3*T^2,0,0,0,0,6*T^2,3*T^2,0,0,1,7*T^2,0,3,0,1,13*T^2,0,6,3,3,3,21*T^2,13*T^2,13,6,9,3,3+22*T^2,18,31,13,9+34*T^2,9,57,31,31,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,0,9,6,3,10,18,18,9,13,36,30,31,31,18,60,69,57,123},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,0,9,6,6,0,3,18,10,18,13,9,30,36,31,18,31,60,57,69,123},{0,0,0,T^2,0,0,0,0,3*T^2,T^2,0,0,0,3*T^2,0,1,0,0,7*T^2,0,3,0,1,1,13*T^2,7*T^2,3,3,3,1,13*T^2,9,13,3,3+22*T^2,3,31,13,9,31},{0,0,0,0,T^2,0,3*T^2,0,0,T^2,0,0,0,0,3*T^2,0,1,0,0,7*T^2,3,1,13*T^2,0,1,7*T^2,3,3,3,13*T^2,1,13,9,3,3,3+22*T^2,31,9,13,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,0,6,6,9,3,3,18,18,13,9,9,36,31,31,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,1,0,9,6,3,3,18,10,9,13,6,30,31,18,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,0,0,1,9,0,6,3,3,10,18,9,6,13,30,18,31,57},{0,0,0,0,0,0,T^2,0,T^2,T^4,0,0,0,T^2,T^2,0,0,0,3*T^2,3*T^2,1,0,7*T^2,0,7*T^2,6*T^2+T^4,1,1,0,7*T^2,7*T^2,3,3,1,13*T^2,13*T^2,13,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,3,0,1,6,9,3,3,3,18,9,13,31},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,1,0,10*T^2,7*T^2,3,0,0,1,13*T^2,0,6,3,21*T^2,3,10,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,1,0,9,6,3,3,3,18,13,9,31},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,10*T^2,0,1,7*T^2,0,3,0,13*T^2,1,6,0,3,3,21*T^2,10,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,9,6,6,0,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,6*T^2,3*T^2,1,0,0,0,7*T^2,0,3,1,13*T^2,0,6,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,6*T^2,0,0,3*T^2,0,1,0,7*T^2,0,3,0,1,0,13*T^2,6,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,1,1,9,3,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,0,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,T^2,0,0,0,3*T^2,0,1,0,0,0,7*T^2,3,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,T^2,0,0,0,0,3*T^2,0,1,0,7*T^2,0,3,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,T^4,0,0,0,T^2,T^2,0,0,0,3*T^2,3*T^2,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1470)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 2 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}3 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5, 6}, {2, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{1,1,2},{1,1,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{3,4,8},{3,3,8},{3,4,7},{3,3,7},{3,4,6},{3,3,6},{3,4,5},{2,3,6},{3,3,5},{2,2,6},{2,3,5},{2,2,5},{2,3,4},{2,2,4},{2,3,3},{1,2,4},{2,2,3},{1,1,4},{1,2,3},{1,1,3},{1,2,2},{1,1,2},{1,2,1},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,12,10,15,20,24,29,48,48,81,72,87,123,126,141,210,210,319,294,329,453,448,483,672,672,951},{0,1,0,3,0,6,0,6,10,15,10,29,15,48,21,48,72,87,72,141,101,210,135,210,294,329,294,483,393,672},{0,0,1,2,3,6,6,6,12,9,15,24,29,48,48,48,81,67,87,126,141,210,210,210,319,279,329,448,483,672},{0,0,0,1,0,3,0,3,6,6,6,15,10,29,15,29,48,48,48,87,72,141,101,141,210,210,210,329,294,483},{0,0,0,0,1,2,3,2,6,3,6,9,15,24,29,24,48,33,48,67,87,126,141,126,210,165,210,279,329,448},{0,0,0,0,0,1,0,1,3,2,3,6,6,15,10,15,29,24,29,48,48,87,72,87,141,126,141,210,210,329},{T^2,2*T^2,0,0,0,0,1,3*T^2,2,6*T^2,2,3,6,9,15,9+6*T^2,24,12+12*T^2,24,33,48,67,87,67+10*T^2,126,86+20*T^2,126,165,210,279},{0,0,0,0,0,0,0,1,0,2,3,6,6,12,10,15,20,24,29,48,48,81,72,87,123,126,141,210,210,319},{0,T^2,0,0,0,0,0,0,1,3*T^2,1,2,3,6,6,6,15,9+6*T^2,15,24,29,48,48,48,87,67+10*T^2,87,126,141,210},{0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,6,10,15,10,29,15,48,21,48,72,87,72,141,101,210},{0,0,0,0,0,0,0,0,0,0,1,2,3,6,6,6,12,9,15,24,29,48,48,48,81,67,87,126,141,210},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,6,15,10,29,15,29,48,48,48,87,72,141},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,2,6,3,6,9,15,24,29,24,48,33,48,67,87,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,6,6,15,10,15,29,24,29,48,48,87},{0,0,0,0,0,0,0,T^2,0,2*T^2,0,0,0,0,1,3*T^2,2,6*T^2,2,3,6,9,15,9+6*T^2,24,12+12*T^2,24,33,48,67},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12,10,15,20,24,29,48,48,81},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,2,3,6,6,6,15,9+6*T^2,15,24,29,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,6,10,15,10,29,15,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6,6,6,12,9,15,24,29,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,6,15,10,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,2,6,3,6,9,15,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,6,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,2*T^2,0,0,0,0,1,3*T^2,2,6*T^2,2,3,6,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1845)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 0 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 2 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 8 & 7 & 8 & 6 & 7 & 5 & 6 & 6 & 5 & 6 & 5 & 4 & 5 & 4 & 3 & 4 & 3 & 3 & 4 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 5}, {3, 4, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{0,1,3},{1,3,4},{2,3,4}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{0,1,2},{-1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,8},{1,3,7},{0,3,8},{1,3,6},{0,3,7},{1,3,5},{1,2,6},{0,3,6},{1,2,5},{0,2,6},{0,3,5},{1,2,4},{0,2,5},{1,1,4},{1,2,3},{0,2,4},{1,1,3},{0,2,3},{0,1,4},{1,1,2},{0,1,3},{1,1,1},{1,0,2},{0,1,2},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,2,6,6,10,10,12,22,19,20,39,41,49,61,72,91,112,88,148,160,220,168,257,280,287,379,427,469,706},{0,1,0,3,2,6,3,6,10,6,12,22,19,22,39,41,49,72,41,91,88,148,91,160,168,160,257,280,287,469},{0,0,1,0,3,0,1,6,3,10,10,6,22,10,10,39,22,61,49,39,91,61,49,148,91,168,220,148,280,427},{0,0,0,1,0,3,1,2,3,2,6,10,6,10,22,19,22,41,19,49,41,91,49,88,91,88,160,168,160,287},{0,0,0,0,1,0,0,3,1,3,6,3,10,3,6,22,10,39,22,22,49,39,22,91,49,91,148,91,168,280},{T^2,0,2*T^2,0,0,1,4*T^2,0,1,7*T^2,2,3,2,3+10*T^2,10,6,10,19,6+16*T^2,22,19,49,22+20*T^2,41,49,41+30*T^2,88,91,88,160},{0,0,0,0,0,0,1,0,3,2,0,6,6,10,10,12,22,20,19,39,41,61,49,72,91,88,112,148,160,257},{0,0,0,0,0,0,0,1,0,1,3,1,3,1,3,10,3,22,10,10,22,22,10,49,22,49,91,49,91,168},{0,0,0,0,0,0,0,0,1,0,0,3,2,3,6,6,10,12,6,22,19,39,22,41,49,41,72,91,88,160},{0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,6,3,10,10,6,22,10,10,39,22,49,61,39,91,148},{0,0,T^2,0,0,0,T^2,0,0,4*T^2,1,0,1,4*T^2,1,3,1,10,3+10*T^2,3,10,10,3+10*T^2,22,10,22+20*T^2,49,22,49,91},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,6,2,10,6,22,10,19,22,19,41,49,41,88},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,6,3,3,10,6,3,22,10,22,39,22,49,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,2,6,6,10,10,12,22,19,20,39,41,72},{0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,4*T^2,1,0,1,2,7*T^2,3,2,10,3+10*T^2,6,10,6+16*T^2,19,22,19,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,3,1,10,3,10,22,10,22,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,6,3,6,10,6,12,22,19,41},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,1,4*T^2,0,1,1,4*T^2,3,1,3+10*T^2,10,3,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,6,3,10,10,6,22,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,3,2,6,10,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,6,3,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,1,4*T^2,0,1,7*T^2,2,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,4*T^2,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1849)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 4 & 4 & 0 & 2 & 0 & 1\end{pmatrix}$
43: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 6 & 6 & 6 & 5 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 14 & 13 & 12 & 12 & 11 & 11 & 10 & 10 & 9 & 10 & 9 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 8 & 7 & 6 & 6 & 5 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 0, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,2,4}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,2},{1,2,4},{1,2,4},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (43): {{2,6,14},{2,6,13},{2,6,12},{2,5,12},{2,6,11},{2,5,11},{2,5,10},{2,4,10},{2,5,9},{1,4,10},{2,4,9},{1,4,9},{2,4,8},{2,3,8},{2,4,7},{1,4,8},{1,4,7},{2,3,7},{1,3,8},{1,3,7},{2,3,6},{1,3,6},{2,3,5},{1,2,6},{1,3,5},{0,2,6},{1,2,5},{0,2,5},{1,2,4},{1,1,4},{1,2,3},{0,2,4},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,8,10,16,27,30,41,32,50,56,76,80,108,88,128,120,96,152,170,224,230,235,312,238,345,354,482,496,646,500,676,688,520,736,921,1002,1195,1028,1318,1396,1840},{0,1,3,3,6,8,16,16,27,16,30,32,50,50,76,56,88,80,56,96,120,152,170,152,224,152,235,238,345,345,482,354,500,496,354,520,688,736,921,736,1002,1028,1396},{0,0,1,1,3,3,8,8,16,8,16,16,30,30,50,32,56,50,32,56,80,96,120,96,152,96,152,152,235,235,345,238,354,345,238,354,496,520,688,520,736,736,1028},{0,0,0,1,0,3,6,8,10,8,16,16,27,30,41,27,41,50,32,56,76,88,108,96,128,96,152,152,224,235,312,224,312,345,238,354,482,500,646,520,676,736,1002},{T^2,0,0,2*T^2,1,1,3,3+3*T^2,8,3+5*T^2,8,8,16,16+4*T^2,30,16,32,30,16+8*T^2,32,50,56,80,56+11*T^2,96,56+14*T^2,96,96,152,152+14*T^2,235,152,238,235,152+20*T^2,238,345,354,496,354+26*T^2,520,520,736},{0,0,0,0,0,1,3,3,6,3,8,8,16,16,27,16,27,30,16,32,50,56,76,56,88,56,96,96,152,152,224,152,224,235,152,238,345,354,482,354,500,520,736},{0,0,0,0,0,0,1,1,3,1,3,3,8,8,16,8,16,16,8,16,30,32,50,32,56,32,56,56,96,96,152,96,152,152,96,152,235,238,345,238,354,354,520},{0,0,0,0,0,0,0,1,0,1,3,3,6,8,10,6,10,16,8,16,27,27,41,32,41,32,56,56,88,96,128,88,128,152,96,152,224,224,312,238,312,354,500},{0,0,0,T^2,0,0,0,2*T^2,1,2*T^2,1,1,3,3+3*T^2,8,3,8,8,3+5*T^2,8,16,16,30,16+8*T^2,32,16+8*T^2,32,32,56,56+11*T^2,96,56,96,96,56+14*T^2,96,152,152,235,152+20*T^2,238,238,354},{0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,6,10,0,8,16,0,27,0,30,41,32,50,56,76,80,108,88,128,120,96,152,170,224,230,235,312,345,482},{0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,8,3,8,16,16,27,16,27,16,32,32,56,56,88,56,88,96,56,96,152,152,224,152,224,238,354},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,0,3,8,0,16,0,16,27,16,30,32,50,50,76,56,88,80,56,96,120,152,170,152,224,235,345},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,1,3,8,8,16,8,16,8,16,16,32,32,56,32,56,56,32,56,96,96,152,96,152,152,238},{0,0,T^2,0,3*T^2,0,0,0,0,0,0,0,0,1,0,2*T^2,6*T^2,3,1,3,6,6,10,8,10,8,16,16,27,32,41,27+3*T^2,41+9*T^2,56,32,56,88,88,128,96,128,152,224},{0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,2*T^2,1,0,1,1,2*T^2,1,3,3,8,3+5*T^2,8,3+5*T^2,8,8,16,16+8*T^2,32,16,32,32,16+8*T^2,32,56,56,96,56+14*T^2,96,96,152},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,3,0,8,0,8,16,8,16,16,30,30,50,32,56,50,32,56,80,96,120,96,152,152,235},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3+3*T^2,8,3+5*T^2,8,8,16,16+4*T^2,30,16,32,30,16+8*T^2,32,50,56,80,56+11*T^2,96,96,152},{T^4,0,0,0,T^2,0,0,0,0,2*T^4,0,0,0,0,0,0,2*T^2,1,0,1,3,3,6,3,6,3+3*T^4,8,8,16,16,27,16,27+3*T^2,32,16,32,56,56,88,56,88,96,152},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,8,10,8,16,16,27,30,41,27,41,50,32,56,76,88,108,96,128,152,224},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,3,8,8,16,16,27,16,27,30,16,32,50,56,76,56,88,96,152},{3*T^4,T^4,0,0,0,0,0,0,0,6*T^4,0,2*T^4,0,0,0,0,0,0,0,0,1,1,3,1,3,1+9*T^4,3,3+3*T^4,8,8,16,8,16,16,8,16,32,32,56,32,56,56,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,3,8,8,16,8,16,16,8,16,30,32,50,32,56,56,96},{6*T^4,3*T^4,T^4,0,0,0,0,0,0,12*T^4,0,6*T^4,0,T^2,0,2*T^4,0,0,T^2,0,0,0,1,2*T^2,1,2*T^2+18*T^4,1,1+9*T^4,3,3+5*T^2,8,3+3*T^4,8,8,3+5*T^2,8,16,16,32,16+8*T^2,32,32,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,8,10,6,10,16,8,16,27,27,41,32,41,56,88},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,1,2*T^2,1,1,3,3+3*T^2,8,3,8,8,3+5*T^2,8,16,16,30,16+8*T^2,32,32,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,6,10,0,8,16,0,27,0,30,41,50,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,8,3,8,16,16,27,16,27,32,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,0,3,8,0,16,0,16,27,30,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,1,3,8,8,16,8,16,16,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,3*T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2*T^2,6*T^2,3,1,3,6,6,10,8,10,16,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,2*T^2,1,0,1,1,2*T^2,1,3,3,8,3+5*T^2,8,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,3,0,8,0,8,16,16,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3+3*T^2,8,8,16},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,2*T^2,1,0,1,3,3,6,3,6,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,8,10,16,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,8,16},{0,0,0,0,0,0,0,0,0,3*T^4,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,6*T^4,0,2*T^4,0,0,0,0,0,0,0,0,1,1,3,1,3,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,8},{0,0,0,0,0,0,0,0,0,6*T^4,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,12*T^4,0,6*T^4,0,T^2,0,2*T^4,0,0,T^2,0,0,0,1,2*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1863)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 0 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 2 & 0 & 1 & 0 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 8 & 8 & 7 & 6 & 7 & 6 & 6 & 5 & 5 & 5 & 6 & 4 & 5 & 6 & 4 & 4 & 3 & 5 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 4 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, -1, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{0,1,4},{1,3,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,2},{1,0,0},{1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (38): {{2,3,8},{1,3,8},{2,3,7},{2,3,6},{1,3,7},{1,3,6},{2,2,6},{2,3,5},{1,3,5},{2,2,5},{1,2,6},{2,2,4},{1,2,5},{0,2,6},{1,2,4},{2,1,4},{2,2,3},{0,2,5},{1,1,4},{0,2,4},{2,1,3},{1,2,3},{0,2,3},{1,1,3},{2,1,2},{0,1,4},{1,1,2},{0,1,3},{2,1,1},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,12,8,10,20,16,17,27,35,26,60,30,41,54,68,93,50,92,143,116,76,107,179,185,108,288,190,257,416,308,290,476,416,689},{0,1,0,0,3,6,0,0,10,0,8,0,16,17,27,0,0,35,30,60,0,41,92,50,0,68,76,116,0,179,80,108,257,190,120,290,170,416},{0,0,1,3,2,6,3,6,12,8,6,16,17,9,35,16,27,26,35,54,30,60,93,68,50,54,116,107,76,185,116,179,288,185,190,308,290,476},{0,0,0,1,0,2,1,3,6,3,2,8,6,3,17,8,16,9,17,26,16,35,54,35,30,26,68,54,50,107,68,116,185,107,116,185,190,308},{0,0,0,0,1,3,0,0,6,0,3,0,8,6,16,0,0,17,16,35,0,27,60,30,0,35,50,68,0,116,50,76,179,116,80,190,120,290},{0,0,0,0,0,1,0,0,3,0,1,0,3,2,8,0,0,6,8,17,0,16,35,16,0,17,30,35,0,68,30,50,116,68,50,116,80,190},{0,0,0,0,0,0,1,0,0,3,2,6,6,3,12,8,10,9,17,18,16,20,30,35,27,26,60,54,41,93,68,92,143,107,116,185,179,288},{T^2,2*T^2,0,0,0,0,2*T^2,1,2,1,5*T^2,3,2,8*T^2,6,3+3*T^2,8,3,6+8*T^2,9,8,17,26,17,16,9+14*T^2,35,26,30,54,35+11*T^2,68,107,54+20*T^2,68,107,116,185},{0,T^2,0,0,0,0,0,0,1,0,2*T^2,0,1,5*T^2,3,0,0,2,3+3*T^2,6,0,8,17,8,0,6+8*T^2,16,17,0,35,16+4*T^2,30,68,35+11*T^2,30,68,50,116},{0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,3,6,3,6,9,8,12,18,17,16,9,35,26,27,54,35,60,93,54,68,107,116,185},{0,0,0,0,0,0,0,0,0,0,1,0,3,2,6,0,0,6,8,12,0,10,20,16,0,17,27,35,0,60,30,41,92,68,50,116,76,179},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,3,0,2,3,3,6,9,6,8,3,17,9,16,26,17,35,54,26,35,54,68,107},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,2,3,6,0,6,12,8,0,6,16,17,0,35,16,27,60,35,30,68,50,116},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,0,0,10,0,0,8,0,16,0,27,0,0,41,30,0,50,0,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,0,3,6,3,0,2,8,6,0,17,8,16,35,17,16,35,30,68},{0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,1,0,0,2,T^2,3,0,3*T^2,6,6,3,12,9,10,18,17,20,30,26,35,54,60,93},{0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,3*T^2,0,2*T^2,1,0,5*T^2,0,1,2,3,2,3,8*T^2,6,3,8,9,6+8*T^2,17,26,9+14*T^2,17,26,35,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,0,0,3,0,8,0,16,0,0,27,16,0,30,0,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,2,6,6,0,12,8,10,20,17,16,35,27,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,1,0,3,0,8,0,0,16,8,0,16,0,30},{0,T^4,0,0,0,0,0,0,T^2,0,0,0,0,T^4,0,0,0,0,0,0,1,0,T^2,2,3,0,6,3,6,9,6,12,18,9,17,26,35,54},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,2*T^2,0,0,1,2,1,0,5*T^2,3,2,0,6,3+3*T^2,8,17,6+8*T^2,8,17,16,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,0,0,2*T^2,0,1,0,3,0,0,8,3+3*T^2,0,8,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,0,6,3,6,12,6,8,17,16,35},{0,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,1,0,2,0,3,3,2,6,9,3,6,9,17,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,0,10,8,0,16,0,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,3,6,2,3,6,8,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,3,0,8,0,16},{0,6*T^4,0,0,3*T^4,T^4,0,0,0,0,0,0,0,6*T^4,0,T^2,0,3*T^4,2*T^2,T^4,0,0,0,0,0,3*T^2,0,0,1,0,5*T^2,2,3,8*T^2,2,3,6,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,0,8},{0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,1,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,2*T^2,1,2,5*T^2,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,2*T^2,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,T^4,0,0,0,0,0,0,T^2,0,0,0,0,T^4,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,3*T^4,0,0,T^4,0,0,0,0,0,0,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1964)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,2},{1,1,2},{1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (31): {{3,4,10},{3,4,9},{3,4,8},{3,3,8},{3,4,7},{2,3,8},{3,3,7},{2,3,7},{3,3,6},{2,3,6},{3,3,5},{2,2,6},{2,3,5},{1,2,6},{2,2,5},{1,2,5},{2,2,4},{1,2,4},{2,2,3},{1,1,4},{1,2,3},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,7,10,10,13,22,21,39,31,43,61,49,73,91,112,148,160,158,220,168,250,280,367,427,509,447,609,669,946},{0,1,3,3,6,3,7,10,13,22,21,22,39,22,43,49,73,91,112,91,148,91,158,168,250,280,367,280,427,447,669},{0,0,1,1,3,1,3,3,7,10,13,10,22,10,22,22,43,49,73,49,91,49,91,91,158,168,250,168,280,280,447},{0,0,0,1,0,1,3,3,6,6,10,10,10,10,22,22,39,39,61,49,61,49,91,91,148,148,220,168,220,280,427},{T^2,0,0,T^2,1,4*T^2,1,1,3,3,7,3+4*T^2,10,3+10*T^2,10,10,22,22,43,22+10*T^2,49,22+20*T^2,49,49,91,91,158,91+20*T^2,168,168,280},{0,0,0,0,0,1,0,3,0,6,0,7,10,10,13,22,21,39,31,43,61,49,73,91,112,148,160,158,220,250,367},{0,0,0,0,0,0,1,1,3,3,6,3,6,3,10,10,22,22,39,22,39,22,49,49,91,91,148,91,148,168,280},{0,0,0,0,0,0,0,1,0,3,0,3,6,3,7,10,13,22,21,22,39,22,43,49,73,91,112,91,148,158,250},{0,0,0,0,0,0,0,0,1,1,3,1,3,1,3,3,10,10,22,10,22,10,22,22,49,49,91,49,91,91,168},{0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,3,7,10,13,10,22,10,22,22,43,49,73,49,91,91,158},{0,0,0,T^2,0,T^2,0,0,0,0,1,4*T^2,1,4*T^2,1,1,3,3,10,3+10*T^2,10,3+10*T^2,10,10,22,22,49,22+20*T^2,49,49,91},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,6,10,10,10,10,22,22,39,39,61,49,61,91,148},{0,0,0,0,0,T^2,0,0,0,0,0,T^2,1,4*T^2,1,1,3,3,7,3+4*T^2,10,3+10*T^2,10,10,22,22,43,22+10*T^2,49,49,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,7,10,10,13,22,21,39,31,43,61,73,112},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,3,10,10,22,22,39,22,39,49,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,3,7,10,13,22,21,22,39,43,73},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,1,3,3,10,10,22,10,22,22,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,3,7,10,13,10,22,22,43},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,0,1,4*T^2,1,4*T^2,1,1,3,3,10,3+10*T^2,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,6,10,10,10,22,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,1,4*T^2,1,1,3,3,7,3+4*T^2,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,7,10,13,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,0,1,4*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,1988)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
41: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 2 & 4 & 1 & 3 & 2 & 4 & 1 & 3 & 4 & 2 & 3 & 2 & 3 & 1 & 1 & 2 & 3 & 0 & 2 & 1 & 3 & 1 & 2 & 0 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 2 & 1 & 0 & 0 & 2 & 1 & 0 \\ 6 & 6 & 6 & 5 & 6 & 5 & 5 & 4 & 5 & 4 & 3 & 4 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, -1, 1, 1, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {2, 3, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,2},{1,0,3}},{{1,2,4},{0,1,4},{2,3,5},{2,4,5},{0,3,5},{0,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,-1,1},{0,1,0},{0,1,0},{1,1,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (41): {{2,4,6},{2,3,6},{2,2,6},{2,4,5},{2,1,6},{2,3,5},{2,2,5},{2,4,4},{2,1,5},{2,3,4},{2,4,3},{2,2,4},{1,3,4},{1,2,4},{2,3,3},{2,1,4},{1,1,4},{2,2,3},{1,3,3},{1,0,4},{1,2,3},{2,1,3},{1,3,2},{1,1,3},{1,2,2},{1,0,3},{0,2,2},{1,3,1},{1,1,2},{0,1,2},{1,2,1},{1,0,2},{0,0,2},{1,1,1},{0,2,1},{0,1,1},{1,0,1},{0,0,1},{0,2,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,6,5,10,12,22,15,35,31,35,53,33,59,65,81,93,105,75,135,129,155,150,199,247,285,250,273,371,380,431,522,540,630,446,666,870,936,747,1093,1515},{0,1,3,1,6,5,12,5,22,15,15,31,15,33,35,53,59,65,37,93,75,105,80,129,150,199,150,156,247,250,273,371,380,431,276,446,630,666,477,747,1093},{0,0,1,0,3,1,5,1,12,5,5,15,5,15,15,31,33,35,15,59,37,65,37,75,80,129,80,80,150,150,156,247,250,273,156,276,431,446,283,477,747},{0,0,0,1,0,3,6,5,10,12,15,22,12,22,31,35,35,53,33,51,59,81,75,93,129,135,129,150,199,199,247,285,285,371,250,380,522,540,446,666,936},{T^2,0,0,2*T^2,1,0,1,3*T^2,5,1,1+4*T^2,5,1+2*T^2,5,5,15,15,15,5+4*T^2,33,15,35,15+6*T^2,37,37,75,37+3*T^2,37+8*T^2,80,80,80,150,150,156,80+6*T^2,156,273,276,156+9*T^2,283,477},{0,0,0,0,0,1,3,1,6,5,5,12,5,12,15,22,22,31,15,35,33,53,37,59,75,93,75,80,129,129,150,199,199,247,150,250,371,380,276,446,666},{0,0,0,0,0,0,1,0,3,1,1,5,1,5,5,12,12,15,5,22,15,31,15,33,37,59,37,37,75,75,80,129,129,150,80,150,247,250,156,276,446},{0,0,0,0,0,0,0,1,0,3,5,6,3,6,12,10,10,22,12,15,22,35,33,35,59,51,59,75,93,93,129,135,135,199,129,199,285,285,250,380,540},{0,0,0,T^2,0,0,0,2*T^2,1,0,3*T^2,1,0,1,1,5,5,5,1+2*T^2,12,5,15,5+4*T^2,15,15,33,15,15+6*T^2,37,37,37,75,75,80,37+3*T^2,80,150,150,80+6*T^2,156,276},{0,0,0,0,0,0,0,0,0,1,1,3,1,3,5,6,6,12,5,10,12,22,15,22,33,35,33,37,59,59,75,93,93,129,75,129,199,199,150,250,380},{0,T^2,3*T^2,0,6*T^2,0,0,0,0,0,1,0,0,2*T^2,3,0,6*T^2,6,3,12*T^2,6,10,12,10,22,15,22,33,35,35+3*T^2,59,51,51+9*T^2,93,59,93,135,135,129,199,285},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,3,5,1,6,5,12,5,12,15,22,15,15,33,33,37,59,59,75,37,75,129,129,80,150,250},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,0,5,10,12,0,15,22,31,35,33,35,53,59,65,81,93,105,75,129,155,199,150,247,371},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,6,5,0,5,12,15,22,15,15,31,33,35,53,59,65,37,75,105,129,80,150,247},{0,0,T^2,0,3*T^2,0,0,0,0,0,0,0,0,0,1,0,2*T^2,3,1,6*T^2,3,6,5,6,12,10,12,15,22,22,33,35,35+3*T^2,59,33,59,93,93,75,129,199},{0,0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,1,1,1,0,3,1,5,1+2*T^2,5,5,12,5,5+4*T^2,15,15,15,33,33,37,15,37,75,75,37+3*T^2,80,150},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,1,5,5,12,5,5,15,15,15,31,33,35,15,37,65,75,37,80,150},{T^4,0,0,0,T^2,0,0,0,0,0,0,0,2*T^4,0,0,0,0,1,0,2*T^2,1,3,1,3,5,6,5+3*T^4,5,12,12,15,22,22,33,15,33,59,59,37,75,129},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,5,6,12,10,12,15,22,22,31,35,35,53,33,59,81,93,75,129,199},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,1,0,0,3*T^2,1,1,5,1+2*T^2,1+4*T^2,5,5,5,15,15,15,5+4*T^2,15,35,37,15+6*T^2,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,6,5,5,12,12,15,22,22,31,15,33,53,59,37,75,129},{3*T^4,T^4,0,0,0,0,0,0,0,0,T^2,0,6*T^4,2*T^4,0,0,0,0,0,0,0,1,0,1,1,3,1+9*T^4,1+2*T^2,5,5+3*T^4,5,12,12,15,5,15,33,33,15,37,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,5,6,6,12,10,10,22,12,22,35,35,33,59,93},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,1,5,5,5,12,12,15,5,15,31,33,15,37,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,3,5,6,6,12,5,12,22,22,15,33,59},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,1,0,3*T^2,1,1,1,5,5,5,1+2*T^2,5,15,15,5+4*T^2,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6,0,5,12,0,22,15,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,0,0,1,0,2*T^2,3,0,6*T^2,6,3,6,10,10,12,22,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,5,1,5,12,12,5,15,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,5,0,12,5,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,1,0,2*T^2,3,1,3,6,6,5,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,1,1,1,0,1,5,5,1+2*T^2,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,0,1,3,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,5,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,3*T^4,T^4,0,0,0,0,0,0,0,0,0,0,0,0,6*T^4,T^2,0,2*T^4,0,0,0,0,0,0,1,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2010)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
39: $\begin{pmatrix}1 & 2 & 0 & -1 & 1 & 0 & 2 & 2 & 1 & -1 & 2 & 0 & 1 & 0 & -1 & 1 & 2 & 1 & -1 & 0 & 2 & 0 & -1 & -1 & 2 & 1 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 5 & 3 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 4 & 3 & 2 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2},{-1,1,3}},{{0,2,4},{2,3,6},{4,5,6},{2,4,6},{1,3,5},{0,1,4},{1,4,5},{3,5,6}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (39): {{1,2,6},{2,2,5},{0,2,6},{-1,2,6},{1,2,5},{0,2,5},{2,2,4},{2,1,4},{1,2,4},{-1,2,5},{2,2,3},{0,2,4},{1,1,4},{0,1,4},{-1,2,4},{1,2,3},{2,1,3},{1,1,3},{-1,1,4},{0,2,3},{2,1,2},{0,1,3},{-1,2,3},{-1,1,3},{2,0,2},{1,1,2},{2,1,1},{1,0,2},{0,1,2},{-1,1,2},{1,1,1},{2,0,1},{0,0,2},{1,0,1},{0,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,3,6,5,12,5,6,15,22,15,31,19,40,53,35,21,52,69,65,55,99,105,162,59,116,120,126,204,319,226,138,223,265,373,282,442,499,792},{0,1,0,0,3,6,5,5,12,10,15,22,12,22,35,31,19,40,35,53,52,69,81,106,52,99,116,99,162,241,204,126,162,223,319,265,350,442,669},{0,0,1,3,1,5,1,1,5,12,5,15,6,19,31,15,6,21,40,35,21,52,65,99,22,55,55,59,116,204,120,61,126,138,226,141,265,282,499},{0,2*T^2,0,1,0,1,3*T^2,4*T^2,1,5,1+4*T^2,5,1,6,15,5,1+6*T^2,6,19,15,6+8*T^2,21,35,52,6+9*T^2,21,21+10*T^2,22,55,116,55,22+12*T^2,59,61,120,61+15*T^2,138,141,282},{0,0,0,0,1,3,1,1,5,6,5,12,5,12,22,15,6,19,22,31,21,40,53,69,21,52,55,52,99,162,116,59,99,126,204,138,223,265,442},{0,0,0,0,0,1,0,0,1,3,1,5,1,5,12,5,1,6,12,15,6,19,31,40,6,21,21,21,52,99,55,22,52,59,116,61,126,138,265},{0,0,0,0,0,0,1,1,3,0,5,6,3,6,10,12,5,12,10,22,19,22,35,35,19,40,52,40,69,106,99,52,69,99,162,126,162,223,350},{0,0,0,0,0,0,0,1,0,0,0,0,3,6,0,0,5,12,10,0,15,22,0,35,19,31,35,40,53,81,65,52,69,99,105,116,162,204,319},{0,0,0,0,0,0,0,0,1,0,1,3,1,3,6,5,1,5,6,12,6,12,22,22,6,19,21,19,40,69,52,21,40,52,99,59,99,126,223},{0,T^2,0,0,0,0,2*T^2,2*T^2,0,1,3*T^2,1,0,1,5,1,4*T^2,1,5,5,1+6*T^2,6,15,19,1+6*T^2,6,6+8*T^2,6,21,52,21,6+9*T^2,21,22,55,22+12*T^2,59,61,138},{T^2,0,3*T^2,6*T^2,0,0,0,T^2,0,0,1,0,4*T^2,9*T^2,0,3,1,3,16*T^2,6,5,6,10,10,5+4*T^2,12,19,12+10*T^2,22,35,40,19,22+19*T^2,40,69,52,69,99,162},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,0,1,3,5,1,5,12,12,1,6,6,6,19,40,21,6,19,21,52,22,52,59,126},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,1,5,6,0,5,12,0,22,6,15,15,19,31,53,35,21,40,52,65,55,99,116,204},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,1,5,0,12,1,5,5,6,15,31,15,6,19,21,35,21,52,55,116},{0,0,0,0,0,0,T^2,T^2,0,0,2*T^2,0,0,0,1,0,2*T^2,0,1,1,4*T^2,1,5,5,4*T^2,1,1+6*T^2,1,6,19,6,1+6*T^2,6,6,21,6+9*T^2,21,22,59},{0,0,T^2,3*T^2,0,0,0,0,0,0,0,0,T^2,4*T^2,0,1,0,1,9*T^2,3,1,3,6,6,1+T^2,5,6,5+4*T^2,12,22,19,6,12+10*T^2,19,40,21,40,52,99},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,5,6,0,10,5,12,15,12,22,35,31,19,22,40,53,52,69,99,162},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,6,1,5,5,5,12,22,15,6,12,19,31,21,40,52,99},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,1,0,3*T^2,1,0,5,4*T^2,1,1+4*T^2,1,5,15,5,1+6*T^2,6,6,15,6+8*T^2,21,21,55},{0,0,0,T^2,0,0,0,T^4,0,0,0,0,0,T^2,0,0,0,0,4*T^2,1,0,1,3,3,T^4,1,1,1+T^2,5,12,6,1,5+4*T^2,6,19,6,19,21,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,5,3,6,10,12,5,6,12,22,19,22,40,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,1,1,5,12,5,1,5,6,15,6,19,21,52},{T^4,0,0,0,0,0,0,4*T^4,0,0,T^2,0,T^4,0,0,0,T^2,0,T^2,0,2*T^2,0,1,1,2*T^2+4*T^4,0,4*T^2,T^4,1,5,1,4*T^2,1+T^2,1,6,1+6*T^2,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,1,2*T^2,0,3*T^2,0,1,5,1,4*T^2,1,1,5,1+6*T^2,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,0,5,6,12,0,15,22,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,6,5,1,3,5,12,6,12,19,40},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,3*T^2,0,0,0,0,6*T^2,0,0,0,0,0,T^2,0,1,4*T^2,0,0,3,1,9*T^2,3,6,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,5,0,5,12,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,1,1,5,1,5,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,2*T^2,0,0,1,0,2*T^2,0,0,1,4*T^2,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,T^2,0,0,1,0,4*T^2,1,3,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,12},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^4,0,0,0,0,0,0,0,T^2,0,1,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2144)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, -1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{0,1,4},{2,3,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,8},{0,3,8},{1,3,7},{0,3,7},{1,3,6},{0,3,6},{1,2,6},{0,2,6},{1,3,5},{0,3,5},{1,2,5},{0,2,5},{1,2,4},{0,2,4},{1,1,4},{0,1,4},{1,2,3},{1,1,3},{0,2,3},{0,1,3},{1,1,2},{0,1,2},{1,0,2},{0,0,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,7,10,16,13,22,20,30,32,51,65,98,71,110,116,140,167,209,249,358,259,378,408,567,448,637,727,1006},{0,1,1,4,4,10,4,13,10,20,13,32,32,65,32,71,65,71,116,140,140,249,140,259,249,408,259,448,448,727},{0,0,1,2,4,7,4,7,10,16,13,22,32,51,32,51,65,71,98,110,140,209,140,209,249,358,259,378,448,637},{0,0,0,1,1,4,1,4,4,10,4,13,13,32,13,32,32,32,65,71,71,140,71,140,140,249,140,259,259,448},{0,0,0,0,1,2,1,2,4,7,4,7,13,22,13,22,32,32,51,51,71,110,71,110,140,209,140,209,259,378},{0,0,0,0,0,1,0,1,1,4,1,4,4,13,4,13,13,13,32,32,32,71,32,71,71,140,71,140,140,259},{0,0,0,0,0,0,1,2,0,0,4,7,10,16,13,22,20,32,30,51,65,98,71,110,116,167,140,209,249,358},{0,0,0,0,0,0,0,1,0,0,1,4,4,10,4,13,10,13,20,32,32,65,32,71,65,116,71,140,140,249},{0,T^2,0,0,0,0,0,3*T^2,1,2,1,2,4,7,4,7+6*T^2,13,13,22,22,32,51,32,51+10*T^2,71,110,71,110,140,209},{T^3,0,0,0,0,0,3*T^3,0,0,1,0,1,1,4,1+6*T^3,4,4,4,13,13,13,32,13+10*T^3,32,32,71,32,71,71,140},{0,0,0,0,0,0,0,0,0,0,1,2,4,7,4,7,10,13,16,22,32,51,32,51,65,98,71,110,140,209},{0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,4,4,4,10,13,13,32,13,32,32,65,32,71,71,140},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,4,4,7,7,13,22,13,22,32,51,32,51,71,110},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,4,4,4,13,4,13,13,32,13,32,32,71},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,4,0,7,10,16,13,22,20,30,32,51,65,98},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,4,13,10,20,13,32,32,65},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,1,1,2,2,4,7,4,7+6*T^2,13,22,13,22,32,51},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,7,4,7,10,16,13,22,32,51},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,1,1,1,4,1+6*T^3,4,4,13,4,13,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,4,4,10,4,13,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,4,7,4,7,13,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,4,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,1,2,1,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,3*T^3,0,0,1,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2276)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & -1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}4 & 3 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 3 & 1 & 2 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 0, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (23): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}}
Primitive collections: {{1, 2, 3, 4, 6}, {5, 7}, {2, 3, 4, 6, 7}, {0, 1, 8}, {0, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,2},{-1,1,2}},{{0,3,4},{0,1,2},{3,4,5},{0,1,4},{1,4,5},{0,2,3}},{4,1,2})
Cox degrees: {{0,0,1},{1,-1,-1},{1,0,0},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{4,0,2},{3,1,3},{4,0,1},{3,1,2},{3,0,2},{4,0,0},{2,1,3},{3,1,1},{3,0,1},{2,1,2},{2,0,2},{3,0,0},{1,1,3},{2,1,1},{2,0,1},{1,1,2},{1,0,2},{2,0,0},{0,1,3},{1,1,1},{1,0,1},{0,1,2},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,3,3,7,6,7,6,18,18,28,34,28,34,64,64,84,115,84,115,175,175,210,301,301,406,672},{0,1,1,3,3,3,7,6,10,18,18,22,28,34,44,64,64,85,84,115,135,175,175,241,301,336,567},{0,0,1,1,1,3,1,3,7,7,7,18,7,18,28,28,28,64,28,64,84,84,84,175,175,210,406},{0,0,0,1,1,1,1,3,3,7,7,10,7,18,18,28,28,44,28,64,64,84,84,135,175,175,336},{0,0,0,0,1,0,1,0,3,3,7,6,7,6,18,18,28,34,28,34,64,64,84,115,115,175,301},{0,0,0,0,0,1,0,1,1,1,1,7,1,7,7,7,7,28,7,28,28,28,28,84,84,84,210},{0,0,0,0,0,0,1,0,1,3,3,3,7,6,10,18,18,22,28,34,44,64,64,85,115,135,241},{T^2,0,0,0,4*T^2,0,0,1,1,1,1+10*T^2,3,1,7,7,7,7+20*T^2,18,7,28,28,28,28+35*T^2,64,84,84,175},{0,0,0,0,0,0,0,0,1,1,1,3,1,3,7,7,7,18,7,18,28,28,28,64,64,84,175},{0,0,0,0,0,0,0,0,0,1,1,1,1,3,3,7,7,10,7,18,18,28,28,44,64,64,135},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,7,6,7,6,18,18,28,34,34,64,115},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,7,1,7,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,3,7,6,10,18,18,22,34,44,85},{0,0,0,0,T^2,0,0,0,0,0,4*T^2,0,0,1,1,1,1+10*T^2,3,1,7,7,7,7+20*T^2,18,28,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,1,3,7,7,7,18,18,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,3,3,7,7,10,18,18,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,7,6,6,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,3,6,10,22},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,4*T^2,0,0,1,1,1,1+10*T^2,3,7,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,4*T^2,0,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2282)$ |
3 |
27 |
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9: $\begin{pmatrix}-1 & -1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}1 & 2 & 0 & -1 & 1 & 0 & 2 & 1 & -1 & 1 & 2 & 0 & 2 & 0 & -1 & 1 & -1 & 0 & 1 & 0 & 2 & -1 & 1 & 0 & 2 & 1 & -1 & 1 & 2 & 0 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 6 & 5 & 5 & 4 & 4 & 5 & 4 & 3 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {-1, -1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{1,3,4},{0,1,4},{2,3,4}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (38): {{1,2,6},{2,2,5},{0,2,6},{-1,2,6},{1,2,5},{0,2,5},{2,2,4},{1,2,4},{-1,2,5},{1,1,4},{2,2,3},{0,2,4},{2,1,3},{0,1,4},{-1,2,4},{1,2,3},{-1,1,4},{0,2,3},{1,1,3},{0,1,3},{2,1,2},{-1,1,3},{1,1,2},{0,1,2},{2,1,1},{1,0,2},{-1,1,2},{1,1,1},{2,0,1},{0,0,2},{1,0,1},{-1,0,2},{0,1,1},{2,0,0},{0,0,1},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,6,7,15,11,25,26,27,35,45,39,51,71,65,83,105,79,135,107,207,190,300,245,193,437,396,251,309,417,455,588,525,633,899,817,1185},{0,1,0,0,3,6,7,15,10,15,25,26,27,26,40,45,40,71,51,83,79,123,135,207,190,135,295,300,193,207,309,295,437,417,455,631,633,899},{0,0,1,3,2,7,3,11,15,11,15,25,15,27,45,35,51,65,39,79,51,135,107,190,135,107,300,245,135,193,251,309,396,309,417,633,525,817},{0,T^2,0,1,0,2,T^2,3,7,3,4+T^2,11,4+3*T^2,11,25,15,27,35,15,39,19+3*T^2,79,51,107,63+3*T^2,51,190,135,63+6*T^2,107,135,193,245,163+6*T^2,251,417,309,525},{0,0,0,0,1,3,2,7,6,7,11,15,11,15,26,25,26,45,27,51,39,83,79,135,107,79,207,190,107,135,193,207,300,251,309,455,417,633},{0,0,0,0,0,1,0,2,3,2,3,7,3,7,15,11,15,25,11,27,15,51,39,79,51,39,135,107,51,79,107,135,190,135,193,309,251,417},{0,0,0,0,0,0,1,3,0,3,7,6,7,6,10,15,10,26,15,26,27,40,51,83,79,51,123,135,79,83,135,123,207,193,207,295,309,455},{0,0,0,0,0,0,0,1,0,1,2,3,2,3,6,7,6,15,7,15,11,26,27,51,39,27,83,79,39,51,79,83,135,107,135,207,193,309},{0,T^2,0,0,0,0,T^2,0,1,0,T^2,2,3*T^2,2,7,3,7,11,3,11,4+3*T^2,27,15,39,19+3*T^2,15,79,51,19+6*T^2,39,51,79,107,63+6*T^2,107,193,135,251},{0,0,0,0,0,0,0,0,0,1,0,0,2,3,0,0,6,0,7,15,11,26,25,45,35,27,71,65,39,51,79,83,105,107,135,207,190,300},{0,0,T^2,3*T^2,0,0,0,0,0,0,1,0,1,2*T^2,0,3,6*T^2,6,3,6,7,10,15,26,27,15,40,51,27,26+3*T^2,51,40+9*T^2,83,79,83,123,135,207},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,7,2,7,3,15,11,27,15,11,51,39,15,27,39,51,79,51,79,135,107,193},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,6,7,10,15,26,25,15,40,45,27,26,51,40,71,79,83,123,135,207},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,2,7,3,15,11,25,15,11,45,35,15,27,39,51,65,51,79,135,107,190},{0,0,0,0,0,0,T^2,0,0,0,T^2,0,T^2,0,1,0,1,2,0,2,3*T^2,7,3,11,4+3*T^2,3,27,15,4+3*T^2,11,15,27,39,19+6*T^2,39,79,51,107},{0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,1,2*T^2,3,1,3,2,6,7,15,11,7,26,27,11,15,27,26+3*T^2,51,39,51,83,79,135},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,1,0,0,2,T^2,7,3,11,4+T^2,3,25,15,4+3*T^2,11,15,27,35,19+3*T^2,39,79,51,107},{T^4,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,1,0,1,0,3,2,7,3,2+3*T^4,15,11,3,7,11,15,27,15,27,51,39,79},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,6,7,15,11,7,26,25,11,15,27,26,45,39,51,83,79,135},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,7,3,2,15,11,3,7,11,15,25,15,27,51,39,79},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6,7,3,10,15,7,6,15,10,26,27,26,40,51,83},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,T^2,1,0,2,T^2,0,7,3,3*T^2,2,3,7,11,4+3*T^2,11,27,15,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,1,6,7,2,3,7,6,15,11,15,26,27,51},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,0,1,2,3,7,3,7,15,11,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,1,0,0,3,1,2*T^2,3,6*T^2,6,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,7,6,0,11,15,26,25,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,1,0,T^2,0,0,1,2,3*T^2,2,7,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2*T^2,3,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,3,7,15,11,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,T^2,2,7,3,11},{0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2307)$ |
3 |
27 |
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9: $\begin{pmatrix}1 & 1 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ -1 & -1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & -1 & 2 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
37: $\begin{pmatrix}3 & 2 & 4 & 1 & 3 & 4 & 2 & 2 & 3 & 1 & 3 & 2 & 1 & 0 & 2 & 3 & 1 & 1 & 0 & 2 & 0 & 1 & 2 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & -1 & 0 & -1 & 1 & 0 \\ 0 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 0 & 2 & -1 & 1 & 1 & 2 & 0 & -1 & 1 & 0 & 2 & 0 & 1 & 1 & -1 & 0 & 2 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & 1 & -1 & 0 \\ 2 & 3 & 0 & 4 & 1 & -1 & 2 & 2 & 0 & 3 & 0 & 1 & 3 & 4 & 1 & -1 & 2 & 2 & 3 & 0 & 3 & 1 & 0 & 1 & 4 & 2 & -1 & 2 & 3 & 0 & 0 & 1 & 3 & 1 & 2 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 1, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 3, 4, 6}, {2, 5, 7}, {3, 4, 6, 7}, {0, 1, 8}, {2, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,2},{-1,1,2}},{{0,3,4},{3,4,5},{0,2,3},{0,1,2},{1,4,5},{0,1,4}},{4,1,2})
Cox degrees: {{1,-1,-1},{1,-1,-1},{-1,1,2},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (37): {{3,0,2},{2,1,3},{4,-1,0},{1,2,4},{3,0,1},{4,-1,-1},{2,1,2},{2,0,2},{3,0,0},{1,2,3},{3,-1,0},{2,1,1},{1,1,3},{0,2,4},{2,0,1},{3,-1,-1},{1,1,2},{1,0,2},{0,2,3},{2,0,0},{0,1,3},{1,1,1},{2,-1,0},{1,0,1},{-1,2,4},{0,1,2},{2,-1,-1},{0,0,2},{-1,2,3},{1,0,0},{1,-1,0},{0,1,1},{-1,1,3},{0,0,1},{-1,1,2},{1,-1,-1},{0,0,0}}
Ext matrix: {{1,2,2,3,5,8,8,11,14,11,20,20,17,23,35,54,50,56,65,82,77,110,94,140,98,186,208,196,232,289,309,370,252,420,531,603,789},{0,1,0,2,2,3,5,5,8,8,8,14,11,17,20,29,35,35,50,54,56,82,54,94,77,140,133,140,186,208,208,289,196,309,420,427,603},{0,0,1,3*T^2,2,5,3,3,8,4+3*T^2,11,11,4,5+6*T^2,17,35,23,23,29+6*T^2,50,29,65,56,77,35+10*T^2,98,140,98,119+10*T^2,186,196,232,119,252,308,420,531},{0,0,0,1,0,0,2,2,3,5,3,8,5,11,8,11,20,20,35,29,35,54,29,54,56,94,73,94,140,133,133,208,140,208,309,277,427},{0,0,0,0,1,2,2,2,5,3,5,8,3,4,11,20,17,17,23,35,23,50,35,56,29,77,94,77,98,140,140,186,98,196,252,309,420},{0,0,0,3*T^2,0,1,0,0,2,3*T^2,2,3,0,6*T^2,3,11,4,4,5+6*T^2,17,5,23,17,23,6+10*T^2,29,56,29,35+10*T^2,77,77,98,35,98,119,196,252},{0,0,0,0,0,0,1,1,2,2,2,5,2,3,5,8,11,11,17,20,17,35,20,35,23,56,54,56,77,94,94,140,77,140,196,208,309},{0,0,0,0,0,0,0,1,0,0,2,0,2,3,5,8,8,11,11,14,17,20,20,35,23,50,54,56,65,82,94,110,77,140,186,208,289},{0,0,0,0,0,0,0,0,1,0,1,2,0,0,2,5,3,3,4,11,4,17,11,17,5,23,35,23,29,56,56,77,29,77,98,140,196},{T^2,0,2*T^2,0,0,0,0,3*T^2,0,1,6*T^2,2,1,2,2,3,5,5+6*T^2,11,8,11,20,8+12*T^2,20,17,35,29,35+10*T^2,56,54,54+20*T^2,94,56,94,140,133,208},{0,0,0,T^2,0,0,0,0,0,T^2,1,0,0,3*T^2,2,5,3,3,4+3*T^2,8,4,11,11,17,5+6*T^2,23,35,23,29+6*T^2,50,56,65,29,77,98,140,186},{0,0,T^2,0,0,0,0,0,0,0,3*T^2,1,0,0,1,2,2,2,3,5,3,11,5+6*T^2,11,4,17,20,17,23,35,35+10*T^2,56,23,56,77,94,140},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,3,5,5,8,8,11,14,8,20,17,35,29,35,50,54,54,82,56,94,140,133,208},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,5,3,5,8,3,8,11,20,11,20,35,29,29,54,35,54,94,73,133},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,2,3,5,3,8,5,11,4,17,20,17,23,35,35,50,23,56,77,94,140},{0,0,0,T^2,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,0,3*T^2,2,0,3,2,3,6*T^2,4,11,4,5+6*T^2,17,17,23,5,23,29,56,77},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,5,2,5,3,11,8,11,17,20,20,35,17,35,56,54,94},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,5,3,8,8,11,11,14,20,20,17,35,50,54,82},{0,0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,0,0,3*T^2,1,0,1,2,6*T^2,2,2,5,3,5+6*T^2,11,8,8+12*T^2,20,11,20,35,29,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,0,3,5,3,4,11,11,17,4,17,23,35,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,5,3,5,8,8,8,14,11,20,35,29,54},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,3*T^2,1,0,2,2,2,3,5,5+6*T^2,11,3,11,17,20,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,0,0,1,2,3*T^2,3,5,3,4+3*T^2,8,11,11,4,17,23,35,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,2,3,5,5,8,3,11,17,20,35},{0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,2,5,3,3,8,5,8,20,11,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,5,2,5,11,8,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,1,0,3*T^2,2,2,3,0,3,4,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,5,8,8,14},{0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,3*T^2,1,0,6*T^2,2,1,2,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,2,3,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,1,0,0,2,3,5,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,1,0,1,2,2,5},{0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,5},{0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2308)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 2 & 3 & 4 & 1 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 5 & 4 & 3 & 4 & 3 & 2 & 4 & 3 & 2 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}, {0, 0, 1, 1, 1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 1, 7}, {2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,2,2}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,2,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,4,5},{1,3,5},{1,4,4},{1,2,5},{1,3,4},{1,4,3},{1,2,4},{1,3,3},{1,4,2},{1,1,4},{1,2,3},{1,3,2},{0,2,3},{1,1,3},{1,3,1},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,24,30,20,40,60,60,61,100,105,120,103,124,210,200,156,212,350,220,324,356,380,585,620,960},{0,1,0,3,4,0,12,10,0,24,30,20,30,60,35,60,61,60,105,120,103,124,210,105,212,168,220,380,356,620},{0,0,1,0,3,4,6,12,10,10,24,30,24,40,60,60,40,61,120,100,60,103,200,124,156,220,212,324,380,585},{0,0,0,1,0,0,4,0,0,12,10,0,10,30,0,20,30,20,35,60,61,60,105,35,124,56,105,220,168,356},{0,0,0,0,1,0,3,4,0,6,12,10,12,24,20,30,24,30,60,60,40,61,120,60,103,105,124,212,220,380},{0,0,0,0,0,1,0,3,4,0,6,12,6,10,30,24,10,24,60,40,15,40,100,61,60,124,103,156,212,324},{0,0,0,0,0,0,1,0,0,3,4,0,4,12,0,10,12,10,20,30,24,30,60,20,61,35,60,124,105,220},{0,0,0,0,0,0,0,1,0,0,3,4,3,6,10,12,6,12,30,24,10,24,60,30,40,60,61,103,124,212},{0,0,0,0,0,0,0,0,1,0,0,3,0,0,12,6,0,6,24,10,0,10,40,24,15,61,40,60,103,156},{0,0,T^2,0,0,4*T^2,0,0,10*T^2,1,0,0,0,4,0,0,4,T^2,0,10,12,10,20,4*T^2,30,10*T^2,20,60,35,105},{0,0,0,0,0,0,0,0,0,0,1,0,1,3,0,4,3,4,10,12,6,12,30,10,24,20,30,61,60,124},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,3,0,3,12,6,0,6,24,12,10,30,24,40,61,103},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,6,12,0,10,24,20,30,60,60,120},{0,0,0,0,0,T^2,0,0,4*T^2,0,0,0,0,1,0,0,1,0,0,4,3,4,10,T^2,12,4*T^2,10,30,20,60},{0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,0,1,0,T^3,0,3,0,3*T^3,0,6,3,0,12,6,10,24,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,3,0,3,12,4,6,10,12,24,30,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,12,24,30,60},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^3,0,3,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,3,T^2,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,12,10,30},{T^5,0,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2311)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 2 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 5 & 3 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 1, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {2, 3, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,1,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,4,6},{2,3,6},{2,4,5},{2,2,6},{2,3,5},{2,4,4},{2,2,5},{2,4,3},{2,3,4},{1,3,4},{2,3,3},{2,2,4},{1,2,4},{2,2,3},{1,3,3},{1,1,4},{1,2,3},{1,3,2},{1,1,3},{1,3,1},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,9,6,18,10,18,20,30,36,42,60,36,72,78,57,136,83,126,129,186,222,231,330,195,363,276,357,569,514,828},{0,1,0,3,3,0,9,0,6,6,10,18,20,30,10,42,36,15,78,21,57,57,83,126,129,186,83,231,114,195,357,276,514},{0,0,1,0,3,3,6,6,9,9,18,18,18,36,20,30,42,36,72,57,78,78,126,136,136,222,129,210,195,231,363,357,569},{0,0,0,1,0,0,3,0,0,0,0,6,6,10,0,20,10,0,36,0,15,15,21,57,57,83,21,129,28,83,195,114,276},{0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,20,10,42,15,36,36,57,78,78,126,57,136,83,129,231,195,357},{0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,18,20,30,36,42,42,78,72,72,136,78,110,129,136,210,231,363},{0,0,0,0,0,0,1,0,0,0,0,3,3,6,0,9,6,0,20,0,10,10,15,36,36,57,15,78,21,57,129,83,195},{T^2,3*T^2,0,6*T^2,0,0,0,1,0,2*T^2,3,0,6*T^2,6,3,12*T^2,6,9,10,20,18,18+3*T^2,42,30,30+9*T^2,72,42,45+18*T^2,78,72,110,136,210},{0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,9,6,18,10,20,20,36,42,42,78,36,72,57,78,136,129,231},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,9,6,18,10,18,20,30,36,42,60,36,72,57,78,136,126,222},{0,T^2,0,3*T^2,0,0,0,0,0,0,1,0,2*T^2,3,1,6*T^2,3,3,6,6,9,9,20,18,18+3*T^2,42,20,30+9*T^2,36,42,72,78,136},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,3,3,0,9,0,6,6,10,20,20,36,10,42,15,36,78,57,129},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,9,0,6,6,10,18,20,30,10,42,15,36,78,57,126},{0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3,3,6,9,9,20,6,18+3*T^2,10,20,42,36,78},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,6,9,9,18,18,18,36,20,30,36,42,72,78,136},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,0,0,6,6,10,0,20,0,10,36,15,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,10,20,42,36,78},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,20,18,30,42,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,6,0,9,0,6,20,10,36},{0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,6*T^2,0,0,0,1,0,2*T^2,3,0,6*T^2,6,3,12*T^2,9,6,10,18,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,9,18,20,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,1,0,2*T^2,3,1,6*T^2,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,3,0,3,9,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,2*T^2,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2314)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 0 & 0 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 6 & 3 & 4 & 4 & 3 & 5 & 3 & 4 & 2 & 4 & 3 & 4 & 3 & 2 & 1 & 2 & 1 & 3 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{0,1,3},{1,3,4},{2,3,4}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,2,6},{2,2,5},{1,2,6},{2,2,4},{1,2,5},{0,2,6},{2,2,3},{2,1,4},{1,2,4},{2,1,3},{0,2,5},{1,2,3},{1,1,4},{2,1,2},{0,2,4},{1,1,3},{0,1,4},{0,2,3},{2,0,2},{2,1,1},{1,1,2},{2,0,1},{0,1,3},{1,1,1},{1,0,2},{0,1,2},{2,0,0},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,3,6,9,6,10,10,18,22,18,30,27,39,36,57,52,60,49,61,99,91,108,153,118,186,148,210,217,286,333,379,594},{0,1,0,3,3,0,6,3,9,10,6,18,9,22,18,27,18,36,22,39,57,49,52,99,57,108,91,118,108,186,210,217,379},{0,0,1,0,3,3,0,1,6,3,9,10,10,6,18,22,27,30,10,10,39,22,57,61,49,99,39,91,118,153,148,210,333},{0,0,0,1,0,0,3,1,3,3,0,9,3,10,6,9,6,18,10,22,27,22,18,57,27,52,49,57,52,108,118,108,217},{0,0,0,0,1,0,0,0,3,1,3,6,3,3,9,10,9,18,3,6,22,10,27,39,22,57,22,49,57,99,91,118,210},{0,0,0,0,0,1,0,0,0,0,3,0,1,0,6,3,10,10,1,0,6,3,22,10,10,39,6,22,49,61,39,91,148},{T^2,0,3*T^2,0,0,6*T^2,1,4*T^2,0,1,0,3,9*T^2,3,0,3,16*T^2,6,3+10*T^2,10,9,10,6,27,9+19*T^2,18,22,27,18+31*T^2,52,57,52,108},{0,0,0,0,0,0,0,1,0,3,0,0,3,6,0,9,6,0,10,10,18,22,18,30,27,36,39,57,52,60,99,108,186},{0,0,0,0,0,0,0,0,1,0,0,3,1,1,3,3,3,9,1,3,10,3,9,22,10,27,10,22,27,57,49,57,118},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,0,3,6,9,10,6,18,9,18,22,27,18,36,57,52,108},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,3,6,0,0,3,1,10,6,3,22,3,10,22,39,22,49,91},{0,0,T^2,0,0,3*T^2,0,T^2,0,0,0,1,4*T^2,0,0,1,9*T^2,3,4*T^2,1,3,1,3,10,3+10*T^2,9,3,10,9+19*T^2,27,22,27,57},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,1,0,6,3,9,10,10,18,6,22,27,30,39,57,99},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,3,3,0,9,3,6,10,9,6,18,27,18,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,0,0,1,0,3,3,1,10,1,3,10,22,10,22,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,1,3,6,3,9,3,10,9,18,22,27,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,1,6,0,3,10,10,6,22,39},{0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,0,0,4*T^2,1,T^2,0,0,0,1,1,4*T^2,3,0,1,3+10*T^2,10,3,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,3,0,6,9,6,0,18,18,36},{0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,6*T^2,0,4*T^2,1,0,1,0,3,9*T^2,0,3,3,16*T^2,6,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,1,3,3,9,10,9,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,0,0,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,6,3,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,T^2,0,0,0,0,1,4*T^2,0,0,1,9*T^2,3,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,T^2,0,0,0,4*T^2,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2315)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & 4 & 0 & 2 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 12 & 11 & 10 & 10 & 9 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,2,4}},{{2,3,4},{1,3,4},{0,2,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,2},{0,1,2},{1,2,4},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (35): {{1,5,12},{1,5,11},{1,5,10},{1,4,10},{1,5,9},{1,4,9},{1,4,8},{1,3,8},{1,4,7},{0,3,8},{1,3,7},{0,3,7},{1,3,6},{1,2,6},{1,3,5},{0,3,6},{0,2,6},{0,3,5},{1,2,5},{1,2,4},{0,2,5},{0,2,4},{1,1,4},{1,2,3},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,9,10,19,33,39,51,40,69,72,109,119,159,115,128,169,189,279,208,312,294,389,440,434,333,503,609,718,819,749,978,1071,1469},{0,1,3,3,6,9,19,19,33,19,39,40,69,69,109,72,72,115,119,189,128,208,189,279,312,294,208,333,434,503,609,503,718,749,1071},{0,0,1,1,3,3,9,9,19,9,19,19,39,39,69,40,40,72,69,119,72,128,119,189,208,189,128,208,294,333,434,333,503,503,749},{0,0,0,1,0,3,6,9,10,9,19,19,33,39,51,33,40,51,69,109,72,115,119,159,169,189,128,208,279,312,389,333,440,503,718},{T^2,0,0,3*T^2,1,1,3,3+6*T^2,9,3+7*T^2,9,9,19,19+10*T^2,39,19,19+13*T^2,40,39,69,40,72,69+15*T^2,119,128,119,72+21*T^2,128,189,208,294,208+31*T^2,333,333,503},{0,0,0,0,0,1,3,3,6,3,9,9,19,19,33,19,19,33,39,69,40,72,69,109,115,119,72,128,189,208,279,208,312,333,503},{0,0,0,0,0,0,1,1,3,1,3,3,9,9,19,9,9,19,19,39,19,40,39,69,72,69,40,72,119,128,189,128,208,208,333},{0,0,0,0,0,0,0,1,0,1,3,3,6,9,10,6,9,10,19,33,19,33,39,51,51,69,40,72,109,115,159,128,169,208,312},{0,0,0,T^2,0,0,0,3*T^2,1,3*T^2,1,1,3,3+6*T^2,9,3,3+7*T^2,9,9,19,9,19,19+10*T^2,39,40,39,19+13*T^2,40,69,72,119,72+21*T^2,128,128,208},{0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,6,9,10,0,0,19,33,0,0,51,0,39,69,0,109,0,119,159,189,279},{0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,3,6,9,19,9,19,19,33,33,39,19,40,69,72,109,72,115,128,208},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,6,0,0,9,19,0,0,33,0,19,39,0,69,0,69,109,119,189},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,1,3,3,9,3,9,9,19,19,19,9,19,39,40,69,40,72,72,128},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,6,3,6,9,10,10,19,9,19,33,33,51,40,51,72,115},{0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,3*T^2,1,0,3*T^2,1,1,3,1,3,3+6*T^2,9,9,9,3+7*T^2,9,19,19,39,19+13*T^2,40,40,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,0,3,9,0,0,19,0,9,19,0,39,0,39,69,69,119},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,0,0,10,0,9,19,0,33,0,39,51,69,109},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,1,0,0,1,3,0,0,9,0,3+6*T^2,9,0,19,0,19+10*T^2,39,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,3,6,6,9,3,9,19,19,33,19,33,40,72},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,3,3,1,3,9,9,19,9,19,19,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,0,3,9,0,19,0,19,33,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,0,9,0,9,19,19,39},{0,0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,3*T^3,0,0,0,0,1,0,0,3,1,3,6,6,10,9,10,19,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,0,0,0,0,3*T^2,1,1,1,3*T^2,1,3,3,9,3+7*T^2,9,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,3*T^2,1,0,3,0,3+6*T^2,9,9,19},{T^5,0,0,0,T^3,0,0,0,0,T^5,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,1,3,3,6,3,6,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,9,10,19,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,9,19},{3*T^5,T^5,0,0,0,0,0,0,0,3*T^5,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,9},{6*T^5,3*T^5,T^5,0,0,0,0,0,0,6*T^5,0,3*T^5,0,0,0,T^5,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,1,3*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2329)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 2 & 0 & 2 & 2 & 2 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{1,3,4},{0,2,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,2},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (31): {{1,4,10},{1,4,9},{1,4,8},{1,3,8},{1,4,7},{0,3,8},{1,3,7},{0,3,7},{1,3,6},{1,2,6},{1,3,5},{0,3,6},{0,2,6},{0,3,5},{1,2,5},{1,2,4},{0,2,5},{0,2,4},{1,1,4},{1,2,3},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,9,10,10,19,22,33,39,51,39,48,61,69,109,88,142,119,159,210,189,158,258,279,388,389,413,548,623,888},{0,1,3,3,6,3,9,10,19,19,33,22,22,39,39,69,48,88,69,109,142,119,88,158,189,258,279,258,388,413,623},{0,0,1,1,3,1,3,3,9,9,19,10,10,22,19,39,22,48,39,69,88,69,48,88,119,158,189,158,258,258,413},{0,0,0,1,0,1,3,3,6,9,10,6,10,10,19,33,22,39,39,51,61,69,48,88,109,142,159,158,210,258,388},{T^2,0,0,3*T^2,1,4*T^2,1,1,3,3+6*T^2,9,3,3+9*T^2,10,9,19,10,22,19+10*T^2,39,48,39,22+16*T^2,48,69,88,119,88+25*T^2,158,158,258},{0,0,0,0,0,1,0,3,0,0,0,6,9,10,0,0,19,33,0,0,51,0,39,69,0,109,0,119,159,189,279},{0,0,0,0,0,0,1,1,3,3,6,3,3,6,9,19,10,22,19,33,39,39,22,48,69,88,109,88,142,158,258},{0,0,0,0,0,0,0,1,0,0,0,3,3,6,0,0,9,19,0,0,33,0,19,39,0,69,0,69,109,119,189},{0,0,0,0,0,0,0,0,1,1,3,1,1,3,3,9,3,10,9,19,22,19,10,22,39,48,69,48,88,88,158},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,6,3,6,9,10,10,19,10,22,33,39,51,48,61,88,142},{0,0,0,T^2,0,T^2,0,0,0,3*T^2,1,0,4*T^2,1,1,3,1,3,3+6*T^2,9,10,9,3+9*T^2,10,19,22,39,22+16*T^2,48,48,88},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,0,3,9,0,0,19,0,9,19,0,39,0,39,69,69,119},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,0,0,10,0,9,19,0,33,0,39,51,69,109},{0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,1,0,0,1,3,0,0,9,0,3+6*T^2,9,0,19,0,19+10*T^2,39,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,3,6,6,9,3,10,19,22,33,22,39,48,88},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,3,3,1,3,9,10,19,10,22,22,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,0,3,9,0,19,0,19,33,39,69},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,0,9,0,9,19,19,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,6,6,10,10,10,22,39},{0,0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,0,0,0,0,3*T^2,1,1,1,4*T^2,1,3,3,9,3+9*T^2,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,3*T^2,1,0,3,0,3+6*T^2,9,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,3,6,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,9,10,19,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,1,4*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2330)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 2 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 5 & 6 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 4 & 3 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,3,8},{0,3,8},{1,3,7},{0,3,7},{1,3,6},{0,3,6},{1,3,5},{1,2,6},{0,3,5},{1,2,5},{0,2,6},{0,2,5},{1,2,4},{0,2,4},{1,1,4},{1,2,3},{1,1,3},{0,2,3},{0,1,4},{0,1,3},{1,1,2},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,12,10,9,20,19,18,38,33,66,39,51,69,102,78,138,109,218,119,159,318,238,189,378,279,558},{0,1,0,3,0,6,0,0,10,0,9,19,0,33,0,0,0,51,39,69,0,109,0,0,159,119,0,189,0,279},{0,0,1,2,3,6,6,3,12,9,6,18,19,38,19,33,39,66,38,78,69,138,69,109,218,138,119,238,189,378},{0,0,0,1,0,3,0,0,6,0,3,9,0,19,0,0,0,33,19,39,0,69,0,0,109,69,0,119,0,189},{0,0,0,0,1,2,3,1,6,3,2,6,9,18,9,19,19,38,18,38,39,78,39,69,138,78,69,138,119,238},{0,0,0,0,0,1,0,0,3,0,1,3,0,9,0,0,0,19,9,19,0,39,0,0,69,39,0,69,0,119},{T^2,2*T^2,0,0,0,0,1,3*T^2,2,1,6*T^2,2,3,6,3+6*T^2,9,9,18,6+12*T^2,18,19,38,19+10*T^2,39,78,38+20*T^2,39,78,69,138},{0,0,0,0,0,0,0,1,0,3,2,6,6,12,9,10,19,20,18,38,33,66,39,51,102,78,69,138,109,218},{0,T^2,0,0,0,0,0,0,1,0,3*T^2,1,0,3,0,0,0,9,3+6*T^2,9,0,19,0,0,39,19+10*T^2,0,39,0,69},{0,0,0,0,0,0,0,0,0,1,0,2,3,6,3,6,9,12,6,18,19,38,19,33,66,38,39,78,69,138},{0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,0,0,10,9,19,0,33,0,0,51,39,0,69,0,109},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,6,3,9,0,19,0,0,33,19,0,39,0,69},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,3,3,6,2,6,9,18,9,19,38,18,19,38,39,78},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,3,0,9,0,0,19,9,0,19,0,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,2,6,6,12,9,10,20,18,19,38,33,66},{0,0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,3*T^2,1,1,2,6*T^2,2,3,6,3+6*T^2,9,18,6+12*T^2,9,18,19,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,3,6,12,6,9,18,19,38},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,0,3,0,0,9,3+6*T^2,0,9,0,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,0,10,9,0,19,0,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,3,0,9,0,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,3,6,2,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,3*T^2,1,2,6*T^2,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,3*T^2,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2331)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 8 & 8 & 7 & 8 & 7 & 7 & 6 & 5 & 6 & 6 & 6 & 5 & 5 & 5 & 6 & 4 & 5 & 3 & 4 & 3 & 4 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{1,3,4},{0,1,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,2},{1,1,2},{1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (35): {{2,4,10},{2,4,9},{2,4,8},{2,3,8},{2,4,7},{1,3,8},{2,3,7},{1,3,7},{2,3,6},{2,3,5},{2,2,6},{1,3,6},{1,2,6},{1,3,5},{2,2,5},{1,2,5},{0,2,6},{2,2,4},{0,2,5},{2,2,3},{1,2,4},{1,2,3},{1,1,4},{0,2,4},{0,2,3},{1,1,3},{0,1,4},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,8,10,10,16,22,27,41,30,39,46,61,50,82,49,76,91,108,130,190,140,148,220,220,164,268,322,403,446,425,569,635,898},{0,1,3,3,6,3,8,10,16,27,16,22,22,39,30,46,22,50,49,76,82,130,82,91,148,140,91,164,220,268,322,268,403,425,635},{0,0,1,1,3,1,3,3,8,16,8,10,10,22,16,22,10,30,22,50,46,82,46,49,91,82,49,91,140,164,220,164,268,268,425},{0,0,0,1,0,1,3,3,6,10,8,6,10,10,16,22,10,27,22,41,39,61,46,39,61,82,49,91,130,148,190,164,220,268,403},{T^2,0,0,2*T^2,1,4*T^2,1,1,3,8,3+3*T^2,3,3+7*T^2,10,8,10,3+10*T^2,16,10,30,22,46,22+10*T^2,22,49,46,22+16*T^2,49,82,91,140,91+22*T^2,164,164,268},{0,0,0,0,0,1,0,3,0,0,0,6,8,10,0,16,10,0,22,0,27,41,30,39,61,50,46,82,76,130,108,140,190,220,322},{0,0,0,0,0,0,1,1,3,6,3,3,3,6,8,10,3,16,10,27,22,39,22,22,39,46,22,49,82,91,130,91,148,164,268},{0,0,0,0,0,0,0,1,0,0,0,3,3,6,0,8,3,0,10,0,16,27,16,22,39,30,22,46,50,82,76,82,130,140,220},{0,0,0,0,0,0,0,0,1,3,1,1,1,3,3,3,1,8,3,16,10,22,10,10,22,22,10,22,46,49,82,49,91,91,164},{0,0,0,T^2,0,T^2,0,0,0,1,2*T^2,0,4*T^2,1,1,1,4*T^2,3,1,8,3,10,3+7*T^2,3,10,10,3+10*T^2,10,22,22,46,22+16*T^2,49,49,91},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,1,6,3,10,6,10,10,6,10,22,10,22,39,39,61,49,61,91,148},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,3,1,0,3,0,8,16,8,10,22,16,10,22,30,46,50,46,82,82,140},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,0,6,10,8,6,10,16,10,22,27,39,41,46,61,82,130},{0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,1,0,1,4*T^2,0,1,0,3,8,3+3*T^2,3,10,8,3+7*T^2,10,16,22,30,22+10*T^2,46,46,82},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,1,6,3,6,3,3,6,10,3,10,22,22,39,22,39,49,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,6,3,3,6,8,3,10,16,22,27,22,39,46,82},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,0,6,10,0,8,16,0,27,0,30,41,50,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,3,1,1,3,3,1,3,10,10,22,10,22,22,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6,0,3,8,0,16,0,16,27,30,50},{0,0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,T^2,0,0,1,0,1,4*T^2,0,1,1,4*T^2,1,3,3,10,3+10*T^2,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,1,3,3,1,3,8,10,16,10,22,22,46},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,0,1,2*T^2,0,1,1,4*T^2,1,3,3,8,3+7*T^2,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,6,6,10,10,10,22,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,3,0,8,0,8,16,16,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3+3*T^2,8,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,3,6,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,8,10,16,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,1,4*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2332)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 2 & 4 & 1 & 3 & 0 & 2 & 4 & 1 & 3 & 0 & 2 & 4 & 3 & 2 & 3 & 1 & 2 & 3 & 0 & 1 & 0 & 2 & 1 & 1 & 3 & 0 & 0 & 2 & 1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, -1, 1, 1, 1, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {2, 3, 4, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,2},{1,0,3}},{{1,2,4},{0,1,4},{2,3,5},{2,4,5},{0,3,5},{0,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,-1,1},{0,1,0},{0,1,0},{0,1,0},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,4,4},{1,3,4},{1,2,4},{1,4,3},{1,1,4},{1,3,3},{1,0,4},{1,2,3},{1,4,2},{1,1,3},{1,3,2},{1,0,3},{1,2,2},{1,4,1},{0,3,2},{0,2,2},{1,3,1},{1,1,2},{1,2,1},{0,3,1},{1,0,2},{0,1,2},{0,0,2},{0,2,1},{1,1,1},{0,1,1},{0,3,0},{1,0,1},{0,0,1},{0,2,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,4,10,6,20,18,35,40,21,75,52,126,105,56,53,109,121,186,226,127,301,196,321,244,381,421,267,596,671,483,801,1242},{0,1,4,1,10,6,20,18,6,40,21,75,52,21,21,53,56,105,121,57,186,109,196,127,226,244,132,381,421,267,483,801},{0,0,1,0,4,1,10,6,1,18,6,40,21,6,6,21,21,52,56,21,105,53,109,57,121,127,57,226,244,132,267,483},{0,0,0,1,0,4,0,10,6,20,18,35,40,21,18,40,52,75,105,53,126,75,126,109,186,196,127,301,321,244,421,671},{0,0,0,0,1,0,4,1,0,6,1,18,6,1,1,6,6,21,21,6,52,21,53,21,56,57,21,121,127,57,132,267},{0,0,0,0,0,1,0,4,1,10,6,20,18,6,6,18,21,40,52,21,75,40,75,53,105,109,57,186,196,127,244,421},{T^3,0,0,2*T^3,0,0,1,0,3*T^3,1,0,6,1,4*T^3,T^3,1,1,6,6,1+2*T^3,21,6,21,6,21,21,6+3*T^3,56,57,21,57,132},{0,0,0,0,0,0,0,1,0,4,1,10,6,1,1,6,6,18,21,6,40,18,40,21,52,53,21,105,109,57,127,244},{0,0,0,0,0,0,0,0,1,0,4,0,10,6,4,10,18,20,40,18,35,20,35,40,75,75,53,126,126,109,196,321},{0,0,0,0,0,0,0,0,0,1,0,4,1,0,0,1,1,6,6,1,18,6,18,6,21,21,6,52,53,21,57,127},{0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,6,10,18,6,20,10,20,18,40,40,21,75,75,53,109,196},{0,0,0,T^3,0,0,0,0,2*T^3,0,0,1,0,3*T^3,0,0,0,1,1,T^3,6,1,6,1,6,6,1+2*T^3,21,21,6,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,6,1,10,4,10,6,18,18,6,40,40,21,53,109},{0,T^2,4*T^2,0,10*T^2,0,20*T^2,0,0,0,0,0,0,1,0,T^2,4,0,10,4,0,4*T^2,10*T^2,10,20,20,18,35,35,40,75,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,6,0,10,20,18,0,40,21,0,75,52,105,186},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,10,6,0,18,6,0,40,21,52,105},{0,0,T^2,0,4*T^2,0,10*T^2,0,0,0,0,0,0,0,0,0,1,0,4,1,0,T^2,4*T^2,4,10,10,6,20,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,1,4,1,6,6,1,18,18,6,21,53},{0,0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,T^2,1,4,4,1,10,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,6,0,20,18,40,75},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,0,0,1,0,1,0,1,1,T^3,6,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,6,1,0,18,6,21,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,10,6,18,40},{T^5,0,0,0,0,0,T^2,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,1,1,0,4,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,T^3,4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2334)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}3 & 2 & 1 & 0 & 3 & 2 & -1 & 1 & 3 & 0 & 3 & -1 & 2 & 1 & 2 & 1 & 0 & 3 & -1 & 0 & 2 & 3 & 2 & -1 & 1 & 1 & 0 & 3 & -1 & 0 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -2, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,2}},{{0,2,4},{0,1,4},{1,3,4},{2,3,4}},{1,1,3})
Cox degrees: {{0,0,1},{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (34): {{3,1,4},{2,1,4},{1,1,4},{0,1,4},{3,1,3},{2,1,3},{-1,1,4},{1,1,3},{3,1,2},{0,1,3},{3,0,2},{-1,1,3},{2,1,2},{1,1,2},{2,0,2},{1,0,2},{0,1,2},{3,1,1},{-1,1,2},{0,0,2},{2,1,1},{3,0,1},{2,0,1},{-1,0,2},{1,1,1},{1,0,1},{0,1,1},{3,0,0},{-1,1,1},{0,0,1},{-1,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,10,20,12,28,35,55,58,96,59,154,108,184,112,194,292,188,438,312,308,200,336,473,478,533,708,541,1008,804,1162,836,1242,1780},{0,1,4,10,4,12,20,28,28,55,28,96,58,108,59,112,184,108,292,194,188,112,200,312,308,336,478,336,708,533,804,541,836,1242},{0,0,1,4,1,4,10,12,12,28,12,55,28,58,28,59,108,58,184,112,108,59,112,194,188,200,308,200,478,336,533,336,541,836},{0,0,0,1,0,1,4,4,4,12,4,28,12,28,12,28,58,28,108,59,58,28,59,112,108,112,188,112,308,200,336,200,336,541},{0,0,0,0,1,4,0,10,12,20,12,35,28,55,28,55,96,58,154,96,108,59,112,154,184,194,292,200,438,312,473,336,533,804},{0,0,0,0,0,1,0,4,4,10,4,20,12,28,12,28,55,28,96,55,58,28,59,96,108,112,184,112,292,194,312,200,336,533},{T^3,0,0,0,2*T^3,0,1,1,1+3*T^3,4,1+4*T^3,12,4,12,4,12,28,12+4*T^3,58,28,28,12+6*T^3,28,59,58,59,108,59+8*T^3,188,112,200,112,200,336},{0,0,0,0,0,0,0,1,1,4,1,10,4,12,4,12,28,12,55,28,28,12,28,55,58,59,108,59,184,112,194,112,200,336},{0,0,0,0,0,0,0,0,1,0,1,0,4,10,4,10,20,12,35,20,28,12,28,35,55,55,96,59,154,96,154,112,194,312},{0,0,0,0,0,0,0,0,0,1,0,4,1,4,1,4,12,4,28,12,12,4,12,28,28,28,58,28,108,59,112,59,112,200},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,0,0,20,0,12,28,35,0,55,0,58,0,96,154,108,184,292},{0,0,0,0,T^3,0,0,0,2*T^3,0,2*T^3,1,0,1,0,1,4,1+3*T^3,12,4,4,1+4*T^3,4,12,12,12,28,12+6*T^3,58,28,59,28,59,112},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,12,4,12,20,28,28,55,28,96,55,96,59,112,194},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,1,4,10,12,12,28,12,55,28,55,28,59,112},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,10,0,4,12,20,0,28,0,28,0,55,96,58,108,184},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,1,4,10,0,12,0,12,0,28,55,28,58,108},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,0,1,4,4,4,12,4,28,12,28,12,28,59},{0,0,T^2,4*T^2,0,0,10*T^2,0,0,0,0,0,0,0,0,T^2,0,1,0,4*T^2,4,1,4,10*T^2,10,10,20,12,35,20,35,28,55,96},{0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,2*T^3,1,0,0,2*T^3,0,1,1,1,4,1+4*T^3,12,4,12,4,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,0,4,0,12,28,12,28,58},{0,0,0,T^2,0,0,4*T^2,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,1,4*T^2,4,4,10,4,20,10,20,12,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,12,0,20,35,28,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,20,12,28,55},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,2*T^3,0,1,0,1,0,1+3*T^3,0,4,12,4,12,28},{T^5,0,0,0,0,0,T^2,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,1,4,1,10,4,10,4,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,10,4,12,28},{4*T^5,T^5,0,0,0,0,0,0,0,0,4*T^5,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,4,1,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,20},{10*T^5,4*T^5,T^5,0,0,0,0,0,0,0,10*T^5,0,0,0,4*T^5,T^5,0,T^3,0,0,0,T^3,0,0,0,0,0,2*T^3,1,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2335)$ |
3 |
24 |
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9: $\begin{pmatrix}-1 & -1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}2 & 3 & 1 & 0 & 2 & -1 & 3 & 1 & 2 & 0 & 3 & 1 & -1 & 2 & 0 & 2 & 3 & 1 & -1 & 0 & 1 & 2 & 3 & -1 & 1 & 0 & 0 & 2 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 4 & 3 & 4 & 2 & 3 & 2 & 3 & 1 & 2 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {-1, -1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{0,1,4},{2,3,4},{1,3,4}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (31): {{2,1,4},{3,1,3},{1,1,4},{0,1,4},{2,1,3},{-1,1,4},{3,1,2},{1,1,3},{2,1,2},{0,1,3},{3,1,1},{1,1,2},{-1,1,3},{2,0,2},{0,1,2},{2,1,1},{3,0,1},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{3,0,0},{-1,0,2},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,10,9,20,14,24,39,50,54,84,90,40,155,119,56,88,258,165,224,128,168,278,248,379,429,333,684,588,954},{0,1,0,0,4,0,9,10,24,20,39,50,35,24,90,84,40,50,147,90,155,88,128,147,165,258,278,248,434,429,684},{0,0,1,4,2,10,3,9,14,24,19,39,50,14,84,54,19,40,155,88,119,56,72,165,128,224,248,168,429,333,588},{0,0,0,1,0,4,0,2,3,9,4,14,24,3,39,19,4,14,84,40,54,19,24,88,56,119,128,72,248,168,333},{0,0,0,0,1,0,2,4,9,10,14,24,20,9,50,39,14,24,90,50,84,40,56,90,88,155,165,128,278,248,429},{0,T^3,0,0,0,1,T^3,0,0,2,T^3,3,9,0,14,4,2*T^3,3,39,14,19,4,5+2*T^3,40,19,54,56,24,128,72,168},{0,0,0,0,0,0,1,0,4,0,9,10,0,4,20,24,9,10,35,20,50,24,40,35,50,90,90,88,147,165,278},{0,0,0,0,0,0,0,1,2,4,3,9,10,2,24,14,3,9,50,24,39,14,19,50,40,84,88,56,165,128,248},{0,0,0,0,0,0,0,0,1,0,2,4,0,1,10,9,2,4,20,10,24,9,14,20,24,50,50,40,90,88,165},{0,0,0,0,0,0,0,0,0,1,0,2,4,0,9,3,0,2,24,9,14,3,4,24,14,39,40,19,88,56,128},{0,0,T^2,4*T^2,0,10*T^2,0,0,0,0,1,0,0,0,0,4,1,T^2,0,4*T^2,10,4,9,10*T^2,10,20,20,24,35,50,90},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,1,10,4,9,2,3,10,9,24,24,14,50,40,88},{0,T^3,0,0,0,0,T^3,0,0,0,T^3,0,1,0,2,0,2*T^3,0,9,2,3,0,2*T^3,9,3,14,14,4,40,19,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,10,0,9,14,20,24,0,50,39,90,84,155},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,2,0,0,4,2,9,9,3,24,14,40},{0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,1,0,0,0,T^2,4,1,2,4*T^2,4,10,10,9,20,24,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,9,0,10,0,20,24,35,50,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,3,10,9,0,24,14,50,39,84},{0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,T^3,0,1,0,0,0,2*T^3,1,0,2,2,0,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,0,9,3,24,14,39},{0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,T^2,1,4,4,2,10,9,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,4,0,10,9,20,24,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,1,0,0,2,0,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,10,9,24},{T^5,0,0,0,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2336)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 1 & 2 & 4 & 3 & 3 & 1 & 3 & 2 & 2 & 3 & 2 & 1 & 1 & 2 & 1 & 3 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 4 & 3 & 1 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 1, 1, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {2, 3, 4, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{0,1,0},{0,1,0},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,4,4},{1,3,4},{1,4,3},{1,2,4},{1,3,3},{1,4,2},{1,1,4},{1,2,3},{1,4,1},{1,3,2},{0,3,2},{1,1,3},{1,3,1},{1,2,2},{0,2,2},{0,3,1},{1,2,1},{1,1,2},{0,1,2},{0,2,1},{1,1,1},{0,3,0},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,4,3,10,12,6,20,30,10,24,25,60,40,60,64,43,100,120,130,112,200,66,230,174,230,410,360,645},{0,1,0,4,3,0,10,12,0,6,6,30,10,24,25,10,40,60,64,43,100,15,130,66,112,230,174,360},{0,0,1,0,4,3,0,10,6,12,12,20,24,30,30,25,60,60,60,64,120,43,105,112,130,230,230,410},{0,0,0,1,0,0,4,3,0,0,0,12,0,6,6,0,10,24,25,10,40,0,64,15,43,112,66,174},{0,0,0,0,1,0,0,4,0,3,3,10,6,12,12,6,24,30,30,25,60,10,60,43,64,130,112,230},{0,0,0,0,0,1,0,0,3,4,4,0,12,10,10,12,30,20,20,30,60,25,35,64,60,105,130,230},{0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,6,6,0,10,0,25,0,10,43,15,66},{0,0,0,0,0,0,0,1,0,0,0,4,0,3,3,0,6,12,12,6,24,0,30,10,25,64,43,112},{T^2,4*T^2,0,10*T^2,0,0,20*T^2,0,1,0,T^2,0,4,0,4*T^2,4,10,0,10*T^2,10,20,12,20*T^2,30,20,35,60,105},{0,0,0,0,0,0,0,0,0,1,1,0,3,4,4,3,12,10,10,12,30,6,20,25,30,60,64,130},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,3,0,0,10,12,0,6,20,24,30,60,60,120},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,0,6,0,12,0,6,25,10,43},{0,T^2,0,4*T^2,0,0,10*T^2,0,0,0,0,0,1,0,T^2,1,4,0,4*T^2,4,10,3,10*T^2,12,10,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,4,4,3,12,0,10,6,12,30,25,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,3,0,0,10,6,12,30,24,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,0,12,10,20,30,60},{0,0,0,T^2,0,0,4*T^2,0,0,0,0,0,0,0,0,0,1,0,T^2,1,4,0,4*T^2,3,4,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,0,4,0,3,12,6,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,10,12,30},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,T^2,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2341)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 2 & 3 & 1 & 0 & 2 & 1 & 3 & 0 & 3 & 2 & 3 & 1 & 2 & 1 & 2 & 3 & 0 & 0 & 2 & 1 & 0 & 3 & 1 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{0,1,4},{2,3,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,1,4},{2,1,4},{3,1,3},{1,1,4},{0,1,4},{2,1,3},{1,1,3},{3,1,2},{0,1,3},{3,0,2},{2,1,2},{3,1,1},{1,1,2},{2,0,2},{1,0,2},{2,1,1},{3,0,1},{0,1,2},{0,0,2},{2,0,1},{1,1,1},{0,1,1},{3,0,0},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,6,10,20,18,40,21,75,22,52,56,105,56,115,121,62,186,206,139,226,381,147,266,456,298,536,882},{0,1,1,4,10,6,18,6,40,6,21,21,52,22,56,56,22,105,115,62,121,226,62,139,266,147,298,536},{0,0,1,0,0,4,10,6,20,6,18,21,40,18,40,52,22,75,75,56,105,186,62,115,206,139,266,456},{0,0,0,1,4,1,6,1,18,1,6,6,21,6,22,21,6,52,56,22,56,121,22,62,139,62,147,298},{0,0,0,0,1,0,1,0,6,0,1,1,6,1,6,6,1,21,22,6,21,56,6,22,62,22,62,147},{0,0,0,0,0,1,4,1,10,1,6,6,18,6,18,21,6,40,40,22,52,105,22,56,115,62,139,266},{0,0,0,0,0,0,1,0,4,0,1,1,6,1,6,6,1,18,18,6,21,52,6,22,56,22,62,139},{0,0,0,0,0,0,0,1,0,1,4,6,10,4,10,18,6,20,20,18,40,75,22,40,75,56,115,206},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,6,6,1,6,21,1,6,22,6,22,62},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,6,0,20,18,0,0,21,40,75,52,105,186},{0,0,0,0,0,0,0,0,0,0,1,1,4,1,4,6,1,10,10,6,18,40,6,18,40,22,56,115},{0,T^2,0,4*T^2,10*T^2,0,0,0,0,0,0,1,0,T^2,4*T^2,4,1,0,10*T^2,4,10,20,6,10,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,4,4,1,6,18,1,6,18,6,22,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,0,10,6,0,0,6,18,40,21,52,105},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,0,1,6,18,6,21,52},{0,0,0,T^2,4*T^2,0,0,0,0,0,0,0,0,0,T^2,1,0,0,4*T^2,1,4,10,1,4,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,6,10,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,6,0,1,6,1,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,10,6,18,40},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,4,0,1,4,1,6,18},{T^5,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2342)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -2 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 1 & 3 & 0 & 2 & -1 & -2 & 1 & 3 & 0 & -1 & 2 & 3 & 1 & -2 & 2 & 3 & 0 & 1 & 0 & 2 & 3 & -1 & -1 & -2 & 1 & 2 & 1 & 0 & 3 & 0 & -1 & 2 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, -2, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,2},{-1,1,2}},{{0,2,4},{0,1,4},{2,3,5},{2,4,5},{1,3,5},{1,4,5}},{1,1,3})
Cox degrees: {{0,0,1},{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,1,4},{1,1,4},{3,1,3},{0,1,4},{2,1,3},{-1,1,4},{-2,1,4},{1,1,3},{3,1,2},{0,1,3},{-1,1,3},{2,1,2},{3,0,2},{1,1,2},{-2,1,3},{2,0,2},{3,1,1},{0,1,2},{1,0,2},{0,0,2},{2,1,1},{3,0,1},{-1,1,2},{-1,0,2},{-2,1,2},{1,1,1},{2,0,1},{1,0,1},{0,1,1},{3,0,0},{0,0,1},{-1,1,1},{2,0,0},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,4,10,12,20,35,28,28,55,96,58,29,108,154,62,108,184,118,204,188,120,292,327,438,308,216,363,478,366,574,708,591,862,912,1350},{0,1,1,4,4,10,20,12,12,28,55,28,12,58,96,29,58,108,62,118,108,62,184,204,292,188,120,216,308,216,363,478,366,574,591,912},{0,0,1,0,4,0,0,10,12,20,35,28,12,55,56,28,58,96,55,96,108,62,154,154,232,184,118,204,292,216,327,438,363,494,574,862},{0,0,0,1,1,4,10,4,4,12,28,12,4,28,55,12,28,58,29,62,58,29,108,118,184,108,62,120,188,120,216,308,216,363,366,591},{0,0,0,0,1,0,0,4,4,10,20,12,4,28,35,12,28,55,28,55,58,29,96,96,154,108,62,118,184,120,204,292,216,327,363,574},{0,0,2*T^3,0,0,1,4,1,1+3*T^3,4,12,4,1+3*T^3,12,28,4,12+4*T^3,28,12,29,28,12+4*T^3,58,62,108,58,29,62,108,62+5*T^3,120,188,120,216,216,366},{T^3,0,8*T^3,0,2*T^3,0,1,0,12*T^3,1,4,1+3*T^3,13*T^3,4,12,1+3*T^3,4+16*T^3,12,4,12,12+4*T^3,4+18*T^3,28,29,58,28,12+4*T^3,29,58,29+23*T^3,62,108,62+5*T^3,120,120,216},{0,0,0,0,0,0,0,1,1,4,10,4,1,12,20,4,12,28,12,28,28,12,55,55,96,58,29,62,108,62,118,184,120,204,216,363},{0,0,0,0,0,0,0,0,1,0,0,4,1,10,0,4,12,20,10,20,28,12,35,35,56,55,28,55,96,62,96,154,118,154,204,327},{0,0,0,0,0,0,0,0,0,1,4,1,0,4,10,1,4,12,4,12,12,4,28,28,55,28,12,29,58,29,62,108,62,118,120,216},{0,0,T^3,0,0,0,0,0,2*T^3,0,1,0,2*T^3,1,4,0,1+3*T^3,4,1,4,4,1+3*T^3,12,12,28,12,4,12,28,12+4*T^3,29,58,29,62,62,120},{0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,4,10,4,10,12,4,20,20,35,28,12,28,55,29,55,96,62,96,118,204},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,12,0,35,0,0,28,55,0,58,96,0,108,154,184,292},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,4,4,1,10,10,20,12,4,12,28,12,28,55,29,55,62,118},{0,0,4*T^3,0,T^3,0,0,0,8*T^3,0,0,2*T^3,8*T^3,0,1,2*T^3,12*T^3,1,0,1,1+3*T^3,13*T^3,4,4,12,4,1+3*T^3,4,12,4+18*T^3,12,28,12+4*T^3,29,29,62},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,4,0,20,0,0,12,28,0,28,55,0,58,96,108,184},{0,T^2,0,4*T^2,0,10*T^2,20*T^2,0,0,0,0,0,0,0,0,T^2,1,0,4*T^2,10*T^2,4,1,0,20*T^2,0,10,4,10,20,12,20,35,28,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,4,4,10,4,1,4,12,4,12,28,12,28,29,62},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,0,10,0,0,4,12,0,12,28,0,28,55,58,108},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,1,4,0,4,12,0,12,28,28,58},{0,0,0,T^2,0,4*T^2,10*T^2,0,0,0,0,0,0,0,0,0,0,0,T^2,4*T^2,1,0,0,10*T^2,0,4,1,4,10,4,10,20,12,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,10,0,12,20,0,28,35,55,96},{0,0,0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,2*T^3,1,1,4,1,0,1,4,1+3*T^3,4,12,4,12,12,29},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,1,0,0,0,1,0,1+3*T^3,4,0,4,12,12,28},{0,0,0,0,0,0,0,0,4*T^3,0,0,T^3,4*T^3,0,0,T^3,8*T^3,0,0,0,2*T^3,8*T^3,0,0,1,0,2*T^3,0,1,13*T^3,1,4,1+3*T^3,4,4,12},{0,0,0,0,0,T^2,4*T^2,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,4*T^2,0,1,0,1,4,1,4,10,4,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,10,0,12,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,4,10,12,28},{T^5,0,0,0,0,0,T^2,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,1,4,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,12},{4*T^5,T^5,0,0,0,0,0,0,0,0,0,0,4*T^5,0,0,T^5,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,1,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2343)$ |
3 |
24 |
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9: $\begin{pmatrix}-1 & -1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}1 & 2 & 0 & -1 & 3 & 1 & 0 & -2 & 2 & 1 & -1 & 2 & 3 & 0 & -2 & 2 & 3 & 1 & 0 & 2 & -1 & 1 & 3 & -1 & 1 & 0 & 2 & 0 & 1 & -1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 4 & 2 & 3 & 3 & 4 & 2 & 2 & 3 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {-1, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2}},{{0,2,4},{1,4,5},{2,3,5},{0,1,4},{2,4,5},{1,3,5}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (31): {{1,1,4},{2,1,3},{0,1,4},{-1,1,4},{3,1,2},{1,1,3},{0,1,3},{-2,1,4},{2,1,2},{1,1,2},{-1,1,3},{2,0,2},{3,1,1},{0,1,2},{-2,1,3},{2,1,1},{3,0,1},{1,0,2},{0,0,2},{2,0,1},{-1,1,2},{1,1,1},{3,0,0},{-1,0,2},{1,0,1},{0,1,1},{2,0,0},{0,0,1},{1,0,0},{-1,0,1},{0,0,0}}
Ext matrix: {{1,2,4,10,3,9,24,20,14,39,50,15,19,84,90,54,21,43,94,63,155,119,83,175,143,224,193,274,378,469,659},{0,1,0,0,2,4,10,0,9,24,20,9,14,50,35,39,15,24,50,43,90,84,63,90,94,155,143,175,274,293,469},{0,0,1,4,0,2,9,10,3,14,24,3,4,39,50,19,4,15,43,21,84,54,27,94,63,119,83,143,193,274,378},{0,0,0,1,T^3,0,2,4,0,3,9,0,T^3,14,24,4,T^3,3,15,4,39,19,5+T^3,43,21,54,27,63,83,143,193},{0,0,0,0,1,0,0,0,4,10,0,4,9,20,0,24,9,10,20,24,35,50,43,35,50,90,94,90,175,147,293},{0,0,0,0,0,1,4,0,2,9,10,2,3,24,20,14,3,9,24,15,50,39,21,50,43,84,63,94,143,175,274},{0,0,0,0,0,0,1,0,0,2,4,0,0,9,10,3,0,2,9,3,24,14,4,24,15,39,21,43,63,94,143},{0,T^3,0,0,6*T^3,0,0,1,T^3,0,2,T^3,6*T^3,3,9,T^3,7*T^3,0,3,T^3,14,4,7*T^3,15,4,19,5+T^3,21,27,63,83},{0,0,0,0,0,0,0,0,1,4,0,1,2,10,0,9,2,4,10,9,20,24,15,20,24,50,43,50,94,90,175},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,2,0,1,4,2,10,9,3,10,9,24,15,24,43,50,94},{0,0,0,0,T^3,0,0,0,0,0,1,0,T^3,2,4,0,T^3,0,2,0,9,3,T^3,9,3,14,4,15,21,43,63},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,4,10,9,0,0,14,20,24,0,39,50,84,90,155},{T^2,0,4*T^2,10*T^2,0,0,0,20*T^2,0,0,0,T^2,1,0,0,4,1,4*T^2,10*T^2,4,0,10,9,20*T^2,10,20,24,20,50,35,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,4,2,0,4,2,9,3,9,15,24,43},{0,T^3,0,0,6*T^3,0,0,0,T^3,0,0,T^3,6*T^3,0,1,T^3,7*T^3,0,0,T^3,2,0,7*T^3,2,0,3,T^3,3,4,15,21},{0,0,T^2,4*T^2,0,0,0,10*T^2,0,0,0,0,0,0,0,1,0,T^2,4*T^2,1,0,4,2,10*T^2,4,10,9,10,24,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,9,0,10,0,24,20,50,35,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,0,0,3,10,9,0,14,24,39,50,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,2,0,3,9,14,24,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,0,9,10,24,20,50},{0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,1,0,T^3,1,0,2,0,2,3,9,15},{0,0,0,T^2,0,0,0,4*T^2,0,0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,4*T^2,1,4,2,4,9,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,1,0,0,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,9,10,24},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2344)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 0 & 3 & 3 & 0 & 1 & 2 & 3 & 2 & 0 & 3 & 1 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 4 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,1,4},{2,1,4},{3,1,3},{1,1,4},{2,1,3},{3,1,2},{2,1,2},{1,1,3},{0,1,4},{3,1,1},{3,0,2},{0,1,3},{1,1,2},{2,1,1},{3,0,1},{2,0,2},{0,1,2},{3,0,0},{1,1,1},{2,0,1},{1,0,2},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,3,10,12,6,24,30,20,10,7,60,60,40,13,28,120,21,100,52,70,140,200,84,130,260,210,420},{0,1,0,4,3,0,6,12,10,0,0,30,24,10,0,7,60,0,40,13,28,70,100,21,52,130,84,210},{0,0,1,0,4,3,12,10,0,6,3,20,30,24,7,12,60,13,60,28,30,60,120,52,70,140,130,260},{0,0,0,1,0,0,0,3,4,0,0,12,6,0,0,0,24,0,10,0,7,28,40,0,13,52,21,84},{0,0,0,0,1,0,3,4,0,0,0,10,12,6,0,3,30,0,24,7,12,30,60,13,28,70,52,130},{0,0,0,0,0,1,4,0,0,3,1,0,10,12,3,4,20,7,30,12,10,20,60,28,30,60,70,140},{0,0,0,0,0,0,1,0,0,0,0,0,4,3,0,1,10,0,12,3,4,10,30,7,12,30,28,70},{0,0,0,0,0,0,0,1,0,0,0,4,3,0,0,0,12,0,6,0,3,12,24,0,7,28,13,52},{0,0,0,0,0,0,0,0,1,0,0,3,0,0,0,0,6,0,0,0,0,7,10,0,0,13,0,21},{T^2,4*T^2,0,10*T^2,0,0,0,0,20*T^2,1,T^2,0,0,4,1,4*T^2,0,3,10,4,10*T^2,20*T^2,20,12,10,20,30,60},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,6,0,12,10,20,0,24,30,60,60,120},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,3,6,0,0,7,0,13},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,0,1,4,12,0,3,12,7,28},{0,T^2,0,4*T^2,0,0,0,0,10*T^2,0,0,0,0,1,0,T^2,0,0,4,1,4*T^2,10*T^2,10,3,4,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,0,0,0,12,10,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,10,0,6,12,30,24,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,0,0,3,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,0,10,20},{0,0,0,T^2,0,0,0,0,4*T^2,0,0,0,0,0,0,0,0,0,1,0,T^2,4*T^2,4,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,3,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2345)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 3 & 1 & 0 & 2 & -1 & 3 & 1 & 3 & 0 & 2 & 1 & 2 & -1 & 3 & 0 & 3 & 2 & 1 & -1 & 0 & 1 & 2 & 3 & 1 & 0 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 4 & 3 & 4 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2}},{{0,2,4},{2,3,5},{0,1,4},{2,4,5},{1,3,5},{1,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,4},{3,1,3},{1,1,4},{0,1,4},{2,1,3},{-1,1,4},{3,1,2},{1,1,3},{3,0,2},{0,1,3},{2,1,2},{1,1,2},{2,0,2},{-1,1,3},{3,1,1},{0,1,2},{3,0,1},{2,1,1},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{3,0,0},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,4,10,6,20,6,18,7,40,21,52,25,75,21,105,27,56,62,186,125,121,74,77,161,226,301,178,351,617},{0,1,0,0,4,0,6,10,6,20,18,40,18,35,21,75,25,52,40,126,75,105,62,74,125,186,221,161,301,507},{0,0,1,4,1,10,1,6,1,18,6,21,7,40,6,52,7,21,25,105,62,56,27,27,74,121,161,77,178,351},{0,0,0,1,0,4,0,1,0,6,1,6,1,18,1,21,1,6,7,52,25,21,7,7,27,56,74,27,77,178},{0,0,0,0,1,0,1,4,1,10,6,18,6,20,6,40,7,21,18,75,40,52,25,27,62,105,125,74,161,301},{0,2*T^3,0,0,0,1,3*T^3,0,3*T^3,1,0,1,0,6,4*T^3,6,4*T^3,1,1,21,7,6,1,1+5*T^3,7,21,27,7,27,77},{0,0,0,0,0,0,1,0,1,0,4,10,4,0,6,20,6,18,10,35,20,40,18,25,40,75,75,62,125,221},{0,0,0,0,0,0,0,1,0,4,1,6,1,10,1,18,1,6,6,40,18,21,7,7,25,52,62,27,74,161},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,6,0,10,0,20,0,18,21,40,0,75,52,105,186},{0,0,0,0,0,0,0,0,0,1,0,1,0,4,0,6,0,1,1,18,6,6,1,1,7,21,25,7,27,74},{0,0,0,0,0,0,0,0,0,0,1,4,1,0,1,10,1,6,4,20,10,18,6,7,18,40,40,25,62,125},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,1,1,10,4,6,1,1,6,18,18,7,25,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,0,10,0,6,6,18,0,40,21,52,105},{0,T^3,0,0,0,0,2*T^3,0,2*T^3,0,0,0,0,1,3*T^3,1,3*T^3,0,0,6,1,1,0,4*T^3,1,6,7,1,7,27},{T^2,0,4*T^2,10*T^2,0,20*T^2,0,0,T^2,0,0,0,4*T^2,0,1,0,1,4,10*T^2,0,20*T^2,10,4,6,10,20,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,1,0,0,1,6,6,1,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,6,10,0,20,18,40,75},{0,0,T^2,4*T^2,0,10*T^2,0,0,0,0,0,0,T^2,0,0,0,0,1,4*T^2,0,10*T^2,4,1,1,4,10,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,1,6,0,18,6,21,52},{0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,2*T^3,0,2*T^3,0,0,1,0,0,0,3*T^3,0,1,1,0,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,6,1,6,21},{0,0,0,T^2,0,4*T^2,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,4*T^2,1,0,0,1,4,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,6,18},{0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2346)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 3 & 2 & 3 & 2 & 1 & 3 & 3 & 2 & 1 & 3 & 0 & 2 & 2 & 3 & 1 & 0 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 2 & 1 & 2 & 3 & 1 & 4 & 2 & 1 & 0 & 2 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{2,3,4},{0,1,3},{1,3,4}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,1,4},{3,1,3},{2,1,4},{3,1,2},{2,1,3},{1,1,4},{3,0,2},{3,1,1},{2,1,2},{1,1,3},{3,0,1},{0,1,4},{2,0,2},{2,1,1},{3,0,0},{1,1,2},{0,1,3},{2,0,1},{1,1,1},{1,0,2},{0,1,2},{2,0,0},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,10,10,24,30,22,20,34,40,39,60,60,70,100,80,120,120,160,155,200,270,305,510},{0,1,0,3,4,0,3,6,12,10,10,0,12,24,22,30,20,34,60,30,60,70,80,60,120,160,155,305},{0,0,1,0,3,4,1,0,6,12,3,10,10,10,6,24,30,22,40,34,60,39,70,80,100,120,160,270},{0,0,0,1,0,0,1,3,4,0,3,0,4,12,10,10,0,12,30,10,20,34,30,20,60,80,60,155},{0,0,0,0,1,0,0,0,3,4,1,0,3,6,3,12,10,10,24,12,30,22,34,30,60,70,80,160},{0,0,0,0,0,1,0,0,0,3,0,4,1,0,0,6,12,3,10,10,24,6,22,34,40,39,70,120},{0,0,0,0,0,0,1,0,0,0,3,0,4,0,6,0,0,12,0,10,0,24,30,20,0,60,60,120},{T^2,0,4*T^2,0,0,10*T^2,4*T^2,1,0,0,1,20*T^2,10*T^2,4,3,0,0,4,10,20*T^2,0,12,10,35*T^2,20,30,20,60},{0,0,0,0,0,0,0,0,1,0,0,0,1,3,1,4,0,3,12,4,10,10,12,10,30,34,30,80},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,4,1,6,3,12,3,10,12,24,22,34,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,4,0,0,0,12,10,0,0,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,1,6,0,3,10,10,6,22,39},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,4,0,6,12,10,0,24,30,60},{0,0,T^2,0,0,4*T^2,T^2,0,0,0,0,10*T^2,4*T^2,1,0,0,0,1,4,10*T^2,0,3,4,20*T^2,10,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,4,1,3,4,12,10,12,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,1,3,6,3,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,10,30},{0,0,0,0,0,T^2,0,0,0,0,0,4*T^2,T^2,0,0,0,0,0,1,4*T^2,0,0,1,10*T^2,4,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,4,0,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,T^2,0,0,0,4*T^2,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2347)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & -1 & -1 & -1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}-2 & -3 & -1 & -2 & -3 & -3 & -2 & -1 & 0 & -3 & -1 & 1 & -2 & 0 & -2 & -3 & 0 & 1 & -1 & -3 & -2 & -1 & 1 & 0 & 0 & -1 & -2 & 1 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 5 & 3 & 3 & 3 & 3 & 4 & 4 & 2 & 2 & 2 & 3 & 3 & 3 & 1 & 1 & 2 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 2}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{0,1,0},{2,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{2,3,4},{1,2,4},{0,1,4},{0,3,4}},{0,3,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{-1,0,1},{-1,0,1},{2,1,0},{0,1,0},{0,0,1}}
Theta-collection (31): {{-2,1,6},{-3,1,6},{-1,1,5},{-2,1,5},{-3,1,5},{-3,1,4},{-2,1,4},{-1,1,4},{0,1,4},{-3,0,5},{-1,1,3},{1,1,3},{-2,1,3},{0,1,3},{-2,0,4},{-3,0,4},{0,1,2},{1,1,2},{-1,1,2},{-3,0,3},{-2,0,3},{-1,0,3},{1,1,1},{0,1,1},{0,0,2},{-1,0,2},{-2,0,2},{1,1,0},{-1,0,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,0,4,3,0,0,6,12,10,4,24,20,10,30,16,12,60,60,40,24,40,44,120,100,95,100,75,200,180,205,360},{0,1,0,4,3,6,12,10,0,3,30,0,24,20,12,16,60,35,60,40,44,30,105,120,60,95,100,210,205,176,368},{0,0,1,0,0,0,0,3,4,1,6,10,0,12,4,3,24,30,10,6,12,16,60,40,44,40,24,100,75,100,180},{0,0,0,1,0,0,3,4,0,0,12,0,6,10,3,4,30,20,24,12,16,12,60,60,30,44,40,120,100,95,205},{0,0,0,0,1,3,4,0,0,1,10,0,12,0,4,3,20,0,30,16,12,10,35,60,20,30,44,105,95,60,176},{4*T^2,0,10*T^2,0,0,1,0,0,20*T^2,10*T^2,0,35*T^2,4,0,20*T^2,1,0,0,10,3,4,35*T^2,0,20,56*T^2,10,12,35,30,20,60},{0,0,0,0,0,0,1,0,0,0,4,0,3,0,1,0,10,0,12,4,3,4,20,30,10,12,16,60,44,30,95},{0,0,0,0,0,0,0,1,0,0,3,0,0,4,0,1,12,10,6,3,4,3,30,24,12,16,12,60,40,44,100},{0,0,0,0,0,0,0,0,1,0,0,4,0,3,1,0,6,12,0,0,3,4,24,10,16,12,6,40,24,40,75},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,0,6,12,10,0,0,20,30,24,0,60,60,120},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,3,1,0,1,10,12,4,3,4,30,16,12,44},{0,3*T^3,0,0,6*T^3,10*T^3,0,0,0,6*T^3,0,1,0,0,0,10*T^3,0,3,0,15*T^3,0,1,6,0,4,3,0,10,6,12,24},{T^2,0,4*T^2,0,0,0,0,0,10*T^2,4*T^2,0,20*T^2,1,0,10*T^2,0,0,0,4,0,1,20*T^2,0,10,35*T^2,4,3,20,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,4,0,0,1,0,12,6,3,4,3,24,12,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,4,0,0,10,12,6,0,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,0,0,10,12,0,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,3,1,0,1,12,4,3,16},{0,T^3,0,0,3*T^3,6*T^3,0,0,0,3*T^3,0,0,0,0,0,6*T^3,0,1,0,10*T^3,0,0,3,0,0,1,0,6,3,4,12},{0,0,T^2,0,0,0,0,0,4*T^2,T^2,0,10*T^2,0,0,4*T^2,0,0,0,1,0,0,10*T^2,0,4,20*T^2,1,0,10,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,3,0,0,6,12,24},{0,0,0,0,T^3,3*T^3,0,0,0,T^3,0,0,0,0,0,3*T^3,0,0,0,6*T^3,0,0,1,0,0,0,0,3,1,0,4},{0,0,0,0,0,0,0,0,T^2,0,0,4*T^2,0,0,T^2,0,0,0,0,0,0,4*T^2,0,1,10*T^2,0,0,4,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,T^3,0,0,0,0,0,T^2,0,0,0,T^3,0,0,0,3*T^3,0,T^2,0,0,4*T^2,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2348)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 0 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 0 & 0 & 1 & 0 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 0 & 2 & 0 & 1 & 0 & 2 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, -1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{2,3,4},{1,3,4},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,2,6},{1,2,6},{0,2,6},{2,2,5},{1,2,5},{0,2,5},{2,2,4},{2,1,4},{1,2,4},{1,1,4},{2,2,3},{0,2,4},{1,2,3},{2,1,3},{0,1,4},{0,2,3},{1,1,3},{0,1,3},{2,1,2},{1,1,2},{2,0,2},{2,1,1},{1,0,2},{0,1,2},{1,1,1},{0,0,2},{2,0,1},{0,1,1},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,5,12,22,15,17,31,37,35,53,65,45,65,105,89,149,100,182,103,196,191,291,333,309,211,511,369,577,395,655,991},{0,1,3,1,5,12,5,5,15,17,15,31,35,17,37,65,45,89,45,100,45,100,103,182,196,191,103,333,211,369,211,395,655},{0,0,1,0,1,5,1,1,5,5,5,15,15,5,17,35,17,45,17,45,17,45,45,100,100,103,45,196,103,211,103,211,395},{0,0,0,1,3,6,5,5,12,12,15,22,31,17,22,53,37,65,45,89,45,100,89,149,182,149,103,291,191,309,211,369,577},{0,0,0,0,1,3,1,1,5,5,5,12,15,5,12,31,17,37,17,45,17,45,45,89,100,89,45,182,103,191,103,211,369},{0,0,0,0,0,1,0,0,1,1,1,5,5,1,5,15,5,17,5,17,5,17,17,45,45,45,17,100,45,103,45,103,211},{0,0,0,0,0,0,1,1,3,3,5,6,12,5,6,22,12,22,17,37,17,45,37,65,89,65,45,149,89,149,103,191,309},{0,0,0,0,0,0,0,1,0,3,0,0,0,5,6,0,12,22,15,31,17,35,37,53,65,65,45,105,89,149,100,182,291},{0,0,0,0,0,0,0,0,1,1,1,3,5,1,3,12,5,12,5,17,5,17,17,37,45,37,17,89,45,89,45,103,191},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,5,12,5,15,5,15,17,31,35,37,17,65,45,89,45,100,182},{0,T^2,3*T^2,0,0,0,0,0,0,2*T^2,1,0,3,1,6*T^2,6,3,6,5,12,5,17,12+3*T^2,22,37,22+9*T^2,17,65,37,65,45,89,149},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,5,1,5,1,5,1,5,5,17,17,17,5,45,17,45,17,45,103},{0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,2*T^2,3,1,3,1,5,1,5,5,12,17,12+3*T^2,5,37,17,37,17,45,89},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6,5,12,5,15,12,22,31,22,17,53,37,65,45,89,149},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,1,5,1,5,5,15,15,17,5,35,17,45,17,45,100},{T^4,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,1,0,1,0,1,3*T^4,1,1,5,5,5,1,17,5,17,5,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,5,1,5,5,12,15,12,5,31,17,37,17,45,89},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,5,5,5,1,15,5,17,5,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,5,3,6,12,6,5,22,12,22,17,37,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,5,3,1,12,5,12,5,17,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,5,0,12,22,15,31,53},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,1,2*T^2,0,3,6*T^2,1,6,3,6,5,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,5,12,5,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,5,1,5,1,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,2*T^2,0,3,1,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6,5,12,22},{0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2349)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & -1 & 2 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 3 & 1 & 2 & 1 & 3 & 1 & 2 & 1 & 3 & 0 & 2 & 1 & 2 & 0 & 2 & 0 & 1 & 0 & 2 & -1 & 1 & 0 & 1 & -1 & 1 & -1 & 0 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 \\ 1 & 0 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 2 & 1 & 1 & 0 & 1 & 0 \\ 4 & 2 & 5 & 3 & 4 & 1 & 4 & 2 & 3 & 0 & 5 & 2 & 3 & 1 & 4 & 1 & 4 & 2 & 3 & 0 & 5 & 2 & 3 & 1 & 4 & 1 & 4 & 2 & 0 & 2 & 3 & 3 & 1 & 1 & 2 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}}
Primitive collections: {{1, 3, 4, 6}, {2, 5, 7}, {3, 4, 6, 7}, {0, 1, 8}, {0, 2, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,2},{-1,1,2}},{{0,3,4},{0,1,2},{0,2,3},{0,1,4},{1,4,5},{3,4,5}},{4,1,2})
Cox degrees: {{0,0,1},{1,-1,-1},{-1,1,2},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,1,4},{3,0,2},{1,2,5},{2,1,3},{1,2,4},{3,0,1},{1,1,4},{2,1,2},{1,2,3},{3,0,0},{0,2,5},{2,0,2},{1,1,3},{2,1,1},{0,2,4},{2,0,1},{0,1,4},{1,1,2},{0,2,3},{2,0,0},{-1,2,5},{1,0,2},{0,1,3},{1,1,1},{-1,2,4},{1,0,1},{-1,1,4},{0,1,2},{1,0,0},{0,0,2},{-1,2,3},{-1,1,3},{0,1,1},{0,0,1},{-1,1,2},{0,0,0}}
Ext matrix: {{1,2,1,4,4,7,7,10,10,16,7,16,22,20,22,41,28,50,50,83,28,62,74,95,74,137,84,155,257,175,155,195,281,351,381,622},{0,1,0,1,1,4,1,4,4,10,1,7,7,10,7,22,7,22,22,50,7,28,28,50,28,74,28,74,155,84,74,84,155,195,195,381},{0,0,1,2,4,3,4,7,10,10,7,7,16,16,22,25,22,41,50,60,28,41,62,83,74,101,74,137,206,137,155,175,257,287,351,532},{0,0,0,1,1,2,1,4,4,7,1,4,7,10,7,16,7,22,22,41,7,22,28,50,28,62,28,74,137,74,74,84,155,175,195,351},{0,0,0,0,1,0,1,2,4,3,1,2,4,7,7,7,7,16,22,25,7,16,22,41,28,41,28,62,101,62,74,74,137,137,175,287},{0,0,0,0,0,1,0,1,1,4,0,1,1,4,1,7,1,7,7,22,1,7,7,22,7,28,7,28,74,28,28,28,74,84,84,195},{0,0,0,0,0,0,1,0,0,0,1,2,4,0,4,7,7,10,10,16,7,16,22,20,22,41,28,50,83,62,50,74,95,137,155,257},{0,0,0,0,0,0,0,1,1,2,0,1,1,4,1,4,1,7,7,16,1,7,7,22,7,22,7,28,62,28,28,28,74,74,84,175},{T^2,2*T^2,0,0,0,0,3*T^2,0,1,0,0,6*T^2,1,2,1,2,1+6*T^2,4,7,7,1,4+12*T^2,7,16,7,16,7+10*T^2,22,41,22+20*T^2,28,28,62,62,74,137},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,7,0,1,1,7,1,7,1,7,28,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,4,3,4,7,10,10,7,7,16,16,22,25,22,41,60,41,50,62,83,101,137,206},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,1,4,4,10,1,7,7,10,7,22,7,22,50,28,22,28,50,74,74,155},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,1,4,4,7,1,4,7,10,7,16,7,22,41,22,22,28,50,62,74,137},{0,T^2,0,0,0,0,0,0,0,0,0,3*T^2,0,1,0,1,0,1,1,4,0,1+6*T^2,1,7,1,7,1,7,22,7+10*T^2,7,7,28,28,28,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,4,3,1,2,4,7,7,7,7,16,25,16,22,22,41,41,62,101},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,0,1,1,4,1,7,1,7,22,7,7,7,22,28,28,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,4,0,4,7,7,10,16,16,10,22,20,41,50,83},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,1,1,4,1,4,1,7,16,7,7,7,22,22,28,62},{0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,3*T^2,0,1,0,0,6*T^2,1,2,1,2,1+6*T^2,4,7,4+12*T^2,7,7,16,16,22,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,7,1,1,1,7,7,7,28},{0,3*T^3,0,0,0,4*T^3,0,0,0,5*T^3,0,0,0,0,0,0,0,0,0,0,1,0,2,0,4,3,4,7,10,7,10,16,16,25,41,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,1,4,10,7,4,7,10,22,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,1,4,7,4,4,7,10,16,22,41},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,3*T^2,0,1,0,1,0,1,4,1+6*T^2,1,1,7,7,7,22},{0,2*T^3,0,0,0,3*T^3,0,0,0,4*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,2,4,4,7,7,16,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,1,1,4,7,7,22},{0,2*T^3,0,0,0,3*T^3,0,0,0,4*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,1,1,4,4,7,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10},{0,T^3,0,0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,6*T^2,1,1,2,2,4,7},{0,T^3,0,0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,1,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2350)$ |
3 |
28 |
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9: $\begin{pmatrix}1 & 1 & -1 & -1 & 1 & -1 & 1 & 0 & 0 \\ -1 & -1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ -1 & -1 & 2 & 2 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}1 & 0 & 2 & 1 & 3 & -1 & 0 & 2 & 0 & 3 & 1 & -1 & -1 & 0 & 1 & 2 & 0 & -2 & 1 & 2 & -1 & 1 & -1 & -2 & 0 & 2 & -1 & 1 & -2 & 0 & -1 & 0 & 1 & -2 & 0 & 1 & -1 & 0 \\ 1 & 2 & 0 & 1 & -1 & 3 & 2 & 0 & 1 & -1 & 1 & 3 & 2 & 2 & 0 & 0 & 1 & 3 & 1 & -1 & 2 & 0 & 1 & 3 & 1 & -1 & 2 & 0 & 2 & 0 & 1 & 1 & -1 & 2 & 0 & -1 & 1 & 0 \\ 4 & 5 & 2 & 3 & 0 & 6 & 4 & 1 & 4 & -1 & 2 & 5 & 5 & 3 & 2 & 0 & 3 & 6 & 1 & 0 & 4 & 1 & 4 & 5 & 2 & -1 & 3 & 0 & 5 & 2 & 3 & 1 & 0 & 4 & 1 & -1 & 2 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 4, 6}, {2, 3, 5, 7}, {4, 6, 7}, {0, 1, 8}, {2, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,2},{-1,1,2}},{{0,3,4},{1,4,5},{0,2,3},{0,1,4},{0,1,2},{3,4,5}},{4,1,2})
Cox degrees: {{1,-1,-1},{1,-1,-1},{-1,1,2},{-1,1,2},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (38): {{1,1,4},{0,2,5},{2,0,2},{1,1,3},{3,-1,0},{-1,3,6},{0,2,4},{2,0,1},{0,1,4},{3,-1,-1},{1,1,2},{-1,3,5},{-1,2,5},{0,2,3},{1,0,2},{2,0,0},{0,1,3},{-2,3,6},{1,1,1},{2,-1,0},{-1,2,4},{1,0,1},{-1,1,4},{-2,3,5},{0,1,2},{2,-1,-1},{-1,2,3},{1,0,0},{-2,2,5},{0,0,2},{-1,1,3},{0,1,1},{1,-1,0},{-2,2,4},{0,0,1},{1,-1,-1},{-1,1,2},{0,0,0}}
Ext matrix: {{1,2,3,7,6,3,11,15,13,26,25,15,19,35,31,45,49,25,65,57,67,95,70,85,135,157,175,230,91,144,196,305,248,248,350,554,455,737},{0,1,0,3,0,2,7,6,7,10,15,11,13,25,15,26,31,19,45,26,49,57,49,67,95,91,135,157,70,95,144,230,157,196,248,382,350,554},{0,0,1,2,3,0,3,7,3,15,11,4,4,15,13,25,19,5,35,31,25,49,25,31,67,95,85,135,31,70,91,175,144,112,196,350,248,455},{0,0,0,1,0,0,2,3,2,6,7,3,3,11,7,15,13,4,25,15,19,31,19,25,49,57,67,95,25,49,70,135,95,91,144,248,196,350},{0,0,0,0,1,2*T^3,0,2,0,7,3,2*T^3,0,4,3,11,4,3*T^3,15,13,5,19,5,6+3*T^3,25,49,31,67,6,25,31,85,70,37,91,196,112,248},{0,0,0,0,T^3,1,3,0,3,T^3,6,7,7,15,6,10,15,13,26,10,31,26,31,49,57,40,95,91,49,57,95,157,91,144,157,235,248,382},{0,0,0,0,0,0,1,0,1,0,3,2,2,7,3,6,7,3,15,6,13,15,13,19,31,26,49,57,19,31,49,95,57,70,95,157,144,248},{0,0,0,0,0,0,0,1,0,3,2,0,0,3,2,7,3,0,11,7,4,13,4,5,19,31,25,49,5,19,25,67,49,31,70,144,91,196},{0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,0,7,3,0,6,11,15,13,15,25,26,35,45,19,31,49,65,57,67,95,157,135,230},{0,0,0,0,0,2*T^3,0,0,0,1,0,2*T^3,0,0,0,2,0,3*T^3,3,2,0,3,0,3*T^3,4,13,5,19,0,4,5,25,19,6,25,70,31,91},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,3,2,0,7,3,3,7,3,4,13,15,19,31,4,13,19,49,31,25,49,95,70,144},{T^2,0,3*T^2,0,6*T^2+T^3,0,0,0,2*T^2,T^3,0,1,1,3,6*T^2,0,3,2,6,12*T^2,7,6,7+3*T^2,13,15,10,31,26,13,15+9*T^2,31,57,26+18*T^2,49,57,91,95,157},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,1,0,0,0,3,2,0,0,7,6,7,11,15,10,25,26,13,15,31,45,26,49,57,91,95,157},{0,0,T^2,0,3*T^2,0,0,0,0,0,0,0,0,1,2*T^2,0,1,0,3,6*T^2,2,3,2,3,7,6,13,15,3,7+3*T^2,13,31,15+9*T^2,19,31,57,49,95},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,3,3,7,3,4,11,15,15,25,4,13,19,35,31,25,49,95,67,135},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,2,0,0,3,7,4,13,0,3,4,19,13,5,19,49,25,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,2,3,7,6,11,15,3,7,13,25,15,19,31,57,49,95},{0,0,T^3,0,7*T^3,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,1,0,T^3,3,0,3,7,6,T^3,15,10,7,6,15,26,10,31,26,40,57,91},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2*T^2,0,1,0,0,2,3,3,7,0,2,3,13,7+3*T^2,4,13,31,19,49},{0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,1,0,2,0,2*T^3,3,7,4,11,0,3,4,15,13,5,19,49,25,67},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,0,7,6,2,3,7,15,6,13,15,26,31,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,3,7,0,2,3,11,7,4,13,31,19,49},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,3,7,0,6,11,15,26,25,45},{0,0,T^3,0,7*T^3,0,0,T^3,T^2,7*T^3,0,0,0,0,3*T^2,T^3,0,0,0,6*T^2+T^3,0,0,2*T^2,1,0,T^3,3,0,1,6*T^2,3,6,12*T^2,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,1,2,7,3,3,7,15,13,31},{0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,0,0,0,2*T^3,0,1,0,2,0,0,0,3,2,0,3,13,4,19},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,1,0,0,2*T^2,1,3,6*T^2,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,2,7,3,13},{0,0,T^3,0,7*T^3,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,T^3,0,0,1,0,3,0,0,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,3,3,7,15,11,25},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,1,2*T^2,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,0,2,7,3,11},{0,0,T^3,0,7*T^3,0,0,T^3,0,7*T^3,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2351)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 2 & 0 & 0 & 0 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 6 & 5 & 4 & 4 & 3 & 4 & 5 & 3 & 3 & 4 & 4 & 3 & 2 & 3 & 4 & 3 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,2,6},{1,2,6},{2,2,5},{0,2,6},{1,2,5},{2,2,4},{1,2,4},{2,2,3},{2,1,4},{0,2,5},{2,1,3},{1,2,3},{1,1,4},{0,2,4},{1,1,3},{2,1,2},{0,2,3},{0,1,4},{0,1,3},{1,1,2},{2,1,1},{2,0,2},{2,0,1},{1,0,2},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,6,9,6,18,10,8,18,16,30,24,36,48,27,60,48,96,81,41,30,50,90,123,162,180,246,76,150,300,228,456},{0,1,0,3,3,0,6,0,0,9,0,10,8,18,16,0,30,24,48,27,0,0,0,30,41,81,90,123,0,50,150,76,228},{0,0,1,0,3,3,9,6,3,6,8,18,9,18,24,16,36,18,48,48,27,16,30,48,81,96,96,162,50,90,180,150,300},{0,0,0,1,0,0,0,0,0,3,0,0,0,6,0,0,10,8,16,0,0,0,0,0,0,27,30,41,0,0,50,0,76},{0,0,0,0,1,0,3,0,0,3,0,6,3,9,8,0,18,9,24,16,0,0,0,16,27,48,48,81,0,30,90,50,150},{0,0,0,0,0,1,3,3,1,0,3,9,3,6,9,8,18,6,18,24,16,8,16,24,48,48,48,96,30,48,96,90,180},{0,0,0,0,0,0,1,0,0,0,0,3,1,3,3,0,9,3,9,8,0,0,0,8,16,24,24,48,0,16,48,30,90},{T^2,3*T^2,0,6*T^2,0,0,0,1,2*T^2,0,1,3,6*T^2,0,3,3,6,12*T^2,6,9,8,3+3*T^2,8,9+9*T^2,24,18,18+18*T^2,48,16,24,48,48,96},{0,0,0,0,0,0,0,0,1,0,3,0,3,0,9,6,0,6,18,18,10,8,16,24,30,36,48,60,27,48,96,81,162},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,6,3,8,0,0,0,0,0,0,16,16,27,0,0,30,0,50},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,9,6,3,8,9,18,18,18,36,16,24,48,48,96},{0,T^2,0,3*T^2,0,0,0,0,0,0,0,1,2*T^2,0,1,0,3,6*T^2,3,3,0,0,0,3+3*T^2,8,9,9+9*T^2,24,0,8,24,16,48},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,3,9,6,0,0,0,8,10,18,24,30,0,16,48,27,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,0,0,0,0,0,0,8,8,16,0,0,16,0,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,0,3,6,9,9,18,0,8,24,16,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,1,3,3,9,6,6,18,8,9,18,24,48},{0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,1,2*T^2,1,0,0,0,0,0,0,3,3+3*T^2,8,0,0,8,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,0,0,0,0,6,8,10,0,0,16,0,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,6,0,0,8,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,3,9,0,3,9,8,24},{0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,1,2*T^2,1,6*T^2,3,0,12*T^2,6,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,0,0,6,0,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,2*T^2,1,0,6*T^2,3,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,0,3,0,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,1,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2352)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 2 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}1 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & -1 & 1 & 0 & 2 & -1 & 1 & 2 & 0 & 2 & 0 & 1 & -1 & 0 & 2 & -1 & -1 & 1 & 1 & 2 & 0 & -1 & 1 & 0 & 0 & -1 & 1 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 4 & 3 & 5 & 3 & 6 & 4 & 4 & 2 & 5 & 3 & 2 & 4 & 1 & 3 & 2 & 4 & 3 & 1 & 4 & 3 & 2 & 1 & 0 & 2 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {2, 5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{0,1,3},{1,3,4},{2,3,4}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,2},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{1,2,6},{1,2,5},{0,2,6},{2,1,4},{1,2,4},{2,1,3},{0,2,5},{1,2,3},{-1,2,6},{1,1,4},{0,2,4},{2,1,2},{-1,2,5},{1,1,3},{2,0,2},{0,1,4},{2,1,1},{0,2,3},{1,1,2},{-1,2,4},{0,1,3},{2,0,1},{-1,1,4},{-1,2,3},{1,0,2},{1,1,1},{2,0,0},{0,1,2},{-1,1,3},{1,0,1},{0,1,1},{0,0,2},{-1,1,2},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,3,2,6,6,9,10,6,12,18,12,18,28,21,30,20,30,51,36,66,47,56,60,69,81,84,117,120,135,183,147,210,226,273,444},{0,1,0,0,3,2,3,6,0,3,9,6,6,12,6,9,12,18,28,18,30,21,18,36,28,51,47,66,56,69,117,66,120,135,147,273},{0,0,1,0,0,0,3,0,3,2,6,0,9,6,3,12,0,10,12,18,28,9,30,30,21,20,18,51,66,47,81,69,117,84,135,226},{0,0,0,1,0,3,0,0,0,3,0,6,0,9,12,6,10,0,18,0,18,28,10,0,30,30,51,36,30,66,60,56,60,117,120,210},{0,0,0,0,1,0,0,3,0,1,3,2,0,3,2,3,6,9,12,6,9,6,6,18,12,28,21,30,18,28,66,30,56,69,66,147},{0,0,0,0,0,1,0,0,0,0,0,3,0,3,3,0,6,0,9,0,6,12,0,0,9,18,28,18,10,30,36,18,30,66,56,120},{0,0,0,0,0,0,1,0,0,0,3,0,3,2,0,3,0,6,6,9,12,3,9,18,6,12,9,28,30,21,51,28,66,47,69,135},{T^2,0,3*T^2,2*T^2,0,0,0,1,6*T^2,6*T^2,0,0,0,1,9*T^2,12*T^2,2,3,3,0,3,2,20*T^2,6,3+18*T^2,12,6,9,6,12,30,9+30*T^2,18,28,30,66},{0,0,0,6*T^2,0,10*T^2,0,0,1,0,0,15*T^2,3,0,15*T^2,2,21*T^2,0,0,6,6,21*T^2,12,10,3,0,28*T^2,12,28,9,20,21,51,18,47,84},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,3,0,0,6,0,9,6,6,0,12,10,12,18,18,28,30,30,36,51,66,117},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,3,2,3,3,0,3,9,2,6,3,12,9,6,28,12,30,21,28,69},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,0,3,0,0,3,0,0,3,9,12,6,0,9,18,6,10,30,18,56},{0,0,0,3*T^2,0,6*T^2,0,0,0,0,0,10*T^2,1,0,10*T^2,0,15*T^2,0,0,3,2,15*T^2,3,6,0,0,21*T^2,6,12,3,12,6,28,9,21,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,3,2,0,0,3,6,6,9,6,12,18,9,18,28,30,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,0,0,3,0,6,0,0,9,0,6,0,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,3,0,2,0,0,6,9,6,10,12,18,12,28,51},{0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,6*T^2,6*T^2,1,0,0,0,0,1,10*T^2,0,12*T^2,3,3,0,0,3,6,20*T^2,0,9,6,18},{0,0,T^2,0,0,0,0,0,3*T^2,2*T^2,0,0,0,0,3*T^2,6*T^2,0,1,0,0,1,0,12*T^2,3,9*T^2,2,0,3,3,2,12,3+18*T^2,9,6,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,3,2,3,0,3,9,3,6,12,9,30},{0,0,0,T^2,0,3*T^2,0,0,0,0,0,6*T^2,0,0,6*T^2,0,10*T^2,0,0,1,0,10*T^2,1,3,0,0,15*T^2,2,3,0,6,2,12,3,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,2,6,3,9,6,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,3,0,0,0,9,6,18},{0,0,0,T^2,0,3*T^2,0,0,0,0,0,6*T^2,0,0,6*T^2,0,10*T^2,0,0,0,0,10*T^2,1,0,0,0,15*T^2,0,3,0,0,2,6,0,6,12},{0,0,0,0,0,T^2,0,0,T^2,0,0,3*T^2,0,0,3*T^2,2*T^2,6*T^2,0,0,0,0,6*T^2,6*T^2,1,3*T^2,0,10*T^2,0,1,0,2,9*T^2,3,0,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,3,0,6,9,18},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,3*T^2,0,0,0,0,0,0,6*T^2,0,6*T^2,1,0,0,0,1,3,12*T^2,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,2,3,12},{0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,3*T^2,0,6*T^2,0,0,0,0,6*T^2,0,0,0,0,10*T^2,0,1,0,0,0,3,0,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,2*T^2,0,0,0,0,0,1,6*T^2,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,3*T^2,0,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,2411)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 1 & 1 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}, {0, 0, 1, 1, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 1, 7}, {2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{1,0,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,3,3},{2,2,3},{1,3,3},{2,3,2},{1,2,3},{1,3,2},{2,2,2},{2,3,1},{2,1,3},{1,1,3},{1,2,2},{2,1,2},{2,2,1},{1,3,1},{0,2,2},{1,1,2},{2,1,1},{1,2,1},{0,1,2},{0,2,1},{1,1,1},{1,2,0},{1,0,2},{0,0,2},{0,1,1},{1,0,1},{1,1,0},{0,2,0},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,2,3,6,6,9,6,6,12,19,18,18,12,29,39,36,39,60,60,81,66,66,102,127,138,138,102,219,236,219,381},{0,1,0,0,2,0,3,0,3,6,6,9,6,0,9,19,18,12,29,18,39,20,39,60,60,81,66,30,127,138,102,219},{0,0,1,0,3,3,0,0,0,6,9,0,0,6,19,18,0,18,39,39,36,30,30,66,81,60,60,66,138,100,138,236},{0,0,0,1,0,2,3,3,0,0,6,6,9,6,9,12,18,19,18,29,39,39,20,30,60,66,81,60,102,138,127,219},{0,0,0,0,1,0,0,0,0,3,3,0,0,0,6,9,0,6,19,12,18,10,18,39,39,36,30,20,81,60,66,138},{0,0,0,0,0,1,0,0,0,0,3,0,0,3,6,6,0,9,12,19,18,18,10,20,39,30,36,39,66,60,81,138},{0,0,0,0,0,0,1,0,0,0,2,3,3,0,3,6,9,6,9,9,19,12,12,18,29,39,39,18,60,81,60,127},{0,0,0,0,T^2,0,0,1,0,3*T^2,0,0,3,2,0,0,6,6,T^2,9,12,19,0,3*T^2,18,20,39,29,30,66,60,102},{0,0,0,0,0,T^2,0,0,1,2,0,3,0,3*T^2,0,6,6,0,9,T^2,12,0,19,29,18,39,20,3*T^2,60,66,30,102},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,6,0,6,0,9,19,12,18,10,0,39,30,20,66},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,0,3,6,6,9,6,6,12,19,18,18,12,39,36,39,81},{0,0,0,0,0,0,0,0,0,0,0,1,0,T^2,0,2,3,0,3,0,6,0,6,9,9,19,12,T^2,29,39,18,60},{0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,0,0,3,2,0,3,6,6,0,T^2,9,12,19,9,18,39,29,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,6,9,0,0,12,10,18,19,20,30,39,66},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,0,6,9,0,0,6,18,0,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,0,3,6,6,9,6,0,19,18,12,39},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,1,0,0,0,2,0,0,0,3,6,6,0,9,19,9,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,3,0,0,6,6,9,6,12,18,19,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,0,0,0,9,0,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,3,6,0,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,3,0,6,9,6,19},{0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,T^2,0,0,1,0,3*T^2,0,0,3,2,0,6,6,12},{0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,0,0,T^2,0,0,1,2,0,3,0,3*T^2,6,6,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,1,0,T^2,2,3,0,6},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,0,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,3609)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5, 6}, {2, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{1,1,1}},{{1,3,4},{0,3,4},{1,2,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{1,1,1},{1,1,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,4,4},{3,3,4},{3,4,3},{2,3,4},{3,4,2},{3,3,3},{2,2,4},{3,3,2},{2,3,3},{2,2,3},{2,3,2},{1,2,3},{2,3,1},{2,2,2},{1,1,3},{2,2,1},{1,2,2},{1,1,2},{1,2,1},{0,1,2},{1,2,0},{1,1,1},{0,0,2},{1,1,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,3,6,6,5,12,11,19,24,24,42,42,37,74,57,90,105,105,168,168,153,271,203,301,336,504},{0,1,0,1,0,3,3,6,3,11,6,11,10,24,24,42,24,57,42,57,65,105,105,168,105,203,168,336},{0,0,1,0,3,2,0,6,3,5,11,6,24,19,9,42,24,37,57,42,105,90,60,168,105,153,203,301},{0,0,0,1,0,0,2,0,3,6,6,11,10,12,19,20,24,42,42,57,65,74,90,115,105,168,168,271},{0,0,0,2*T^2,1,0,4*T^2,2,0,0,3,3*T^2,11,5,6*T^2,19,6,9,24,10+4*T^2,57,37,14+8*T^2,90,42,60,105,153},{0,0,0,0,0,1,0,3,1,3,3,3,6,11,6,24,11,24,24,24,42,57,42,105,57,105,105,203},{0,0,0,0,0,0,1,0,0,3,0,3,0,6,11,10,6,24,10,24,15,42,57,65,42,105,65,168},{0,0,0,0,0,0,2*T^2,1,0,0,1,0,3,3,3*T^2,11,3,6,11,6,24,24,10+4*T^2,57,24,42,57,105},{0,0,0,0,0,0,0,0,1,2,3,3,6,6,5,12,11,19,24,24,42,42,37,74,57,90,105,168},{0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,3,11,6,11,10,24,24,42,24,57,42,105},{0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,3,5,11,6,24,19,9,42,24,37,57,90},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,6,6,11,10,12,19,20,24,42,42,74},{0,0,0,T^2,0,0,2*T^2,0,0,0,0,2*T^2,1,0,4*T^2,2,0,0,3,3*T^2,11,5,6*T^2,19,6,9,24,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,3,3,3,6,11,6,24,11,24,24,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,0,6,11,10,6,24,10,42},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,1,0,0,1,0,3,3,3*T^2,11,3,6,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,3,6,6,5,12,11,19,24,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,3,11,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,3,5,11,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,2*T^2,1,0,4*T^2,2,0,0,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,3,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,1,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,3686)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 3 & 2 & 2 & 3 & 1 & 1 & 2 & 4 & 3 & 0 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 1 & 0 & 1 & 2 & 0 & 1 & 3 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, -1, 1, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 5, 6}, {2, 4, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,0,1},{1,1,1},{2,1,1}},{{1,5,7},{6,7,8},{1,3,7},{2,3,4},{1,3,4},{0,2,8},{0,6,8},{2,3,7,8},{0,2,4},{5,6,7}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{1,0,1},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,3,4},{2,3,3},{2,2,4},{1,3,3},{2,3,2},{1,3,2},{2,2,3},{2,3,1},{1,3,1},{2,2,2},{2,1,4},{1,2,3},{1,3,0},{1,2,2},{2,1,3},{2,2,1},{0,2,2},{1,1,3},{2,1,2},{1,2,1},{0,2,1},{1,2,0},{2,1,1},{1,1,2},{0,2,0},{1,1,1},{1,0,3},{0,1,2},{0,1,1},{1,1,0},{1,0,2},{0,0,2},{1,0,1},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,5,4,6,9,12,10,16,22,15,18,25,37,31,35,43,51,53,63,78,96,81,96,124,156,115,117,202,231,201,256,313,312,421,631},{0,1,1,1,3,4,5,6,9,12,5,6,16,18,15,22,19,21,31,37,43,63,53,51,78,96,55,57,117,156,115,136,201,202,256,421},{0,0,1,0,0,0,3,0,0,6,5,4,0,9,12,10,10,18,22,16,19,25,35,37,31,63,51,43,78,96,96,117,156,124,202,312},{0,0,0,1,0,3,0,0,6,0,0,5,10,12,0,0,18,15,0,22,37,35,0,31,63,53,35,51,96,81,65,115,105,156,201,313},{0,0,0,0,1,1,1,3,4,5,1,1,9,6,5,12,6,6,15,18,19,37,31,21,43,51,21,22,57,96,55,61,115,117,136,256},{0,0,0,0,0,1,0,0,3,0,0,1,6,5,0,0,6,5,0,12,18,22,0,15,37,31,15,21,51,53,35,55,65,96,115,201},{0,0,0,0,0,0,1,0,0,3,1,1,0,4,5,6,4,6,12,9,10,16,22,18,19,37,21,19,43,63,51,57,96,78,117,202},{T^2,0,2*T^2,T^2,0,0,0,1,1,1,3*T^2,3*T^2,4,1,1,5,1+3*T^2,1+5*T^2,5,6,6,18,15,6,19,21,6+7*T^2,6+6*T^2,22,51,21,22+9*T^2,55,57,61,136},{0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,0,1,1,0,5,6,12,0,5,18,15,5,6,21,31,15,21,35,51,55,115},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,3,1,1,5,4,4,9,12,6,10,18,6,6,19,37,21,22,51,43,57,117},{0,0,0,0,0,T^2,0,0,3*T^2,0,1,0,6*T^2,0,3,0,0,4,6,0,T^2,0,10,9,3*T^2,16,18,10,19,25,37,43,63,31,78,124},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,4,5,0,6,9,10,0,12,16,22,15,18,37,35,31,51,53,63,96,156},{0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,1,0,0,0,3*T^2,3*T^2,0,1,1,5,0,1,6,5,1+4*T^2,1+5*T^2,6,15,5,6+7*T^2,15,21,21,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,3,4,6,0,5,9,12,5,6,18,22,15,21,31,37,51,96},{0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,0,1,3,0,0,0,6,4,T^2,9,6,4,10,16,18,19,37,19,43,78},{0,0,T^2,0,0,0,0,0,0,0,2*T^2,T^2,0,0,0,1,T^2,3*T^2,1,1,1,4,5,1,4,6,1+5*T^2,1+3*T^2,6,18,6,6+6*T^2,21,19,22,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,6,0,0,5,12,0,0,15,0,22,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,6,5,4,9,10,12,18,22,16,37,63},{0,0,0,T^4,0,0,0,0,0,0,0,0,T^2,0,0,0,T^4,0,1,0,0,0,3,1,0,4,1,1,4,9,6,6,18,10,19,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,1,4,5,1,1,6,12,5,6,15,18,21,51},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,1,5,0,0,5,0,12,15,31},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,2*T^2,0,0,0,1,0,0,1,1,3*T^2,3*T^2,1,5,1,1+5*T^2,5,6,6,21},{0,0,0,3*T^4,0,T^4,0,0,0,0,T^2,0,0,0,0,0,3*T^4,T^2,0,0,T^4,0,1,0,0,1,3*T^2,T^2,1,4,1,1+3*T^2,6,4,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,4,6,5,6,12,9,18,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,1,5,4,6,18},{0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,0,0,3,4,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,5,0,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,T^2,0,1,0,3*T^2,1,1,1,6},{0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,1,3,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,T^4,0,0,0,0,0,0,0,0,T^2,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,4076)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 3 & 2 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 4}, {3, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{0,1,3},{2,3,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,3,4},{1,2,4},{0,3,4},{1,3,3},{0,2,4},{1,3,2},{0,3,3},{1,2,3},{0,3,2},{1,1,3},{1,2,2},{0,2,3},{0,2,2},{0,1,3},{1,1,2},{1,2,1},{0,2,1},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,4,6,6,9,12,15,21,17,39,28,42,38,70,75,63,84,147,111,141,140,238,252,244,420},{0,1,0,0,2,0,0,3,0,9,6,6,12,17,21,10,20,39,42,38,70,75,60,84,147,141,110,244},{0,0,1,0,2,0,3,1,6,2,3,9,21,15,9,6,38,42,15,21,84,63,38,42,140,84,141,252},{0,0,0,1,0,3,2,2,6,3,9,4,17,6,15,21,39,28,21,42,75,39,84,63,111,140,147,238},{0,0,0,0,1,0,0,0,0,1,0,3,6,9,3,0,10,21,9,6,38,42,10,21,84,38,60,141},{0,3*T^2,0,0,5*T^2,1,0,0,2,6*T^2,2,0,4,9*T^2,3,9,17,6,4+10*T^2,15,28,8+14*T^2,42,21,39,63,75,111},{0,0,0,0,0,0,1,0,3,0,1,2,9,3,2,3,21,15,3,9,42,21,21,15,63,42,84,140},{0,0,0,0,0,0,0,1,0,2,3,2,6,4,9,6,12,17,15,21,39,28,38,42,75,84,70,147},{0,T^2,0,0,3*T^2,0,0,0,1,3*T^2,0,0,2,6*T^2,0,1,9,3,6*T^2,2,15,4+10*T^2,9,3,21,15,42,63},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,0,0,6,9,6,12,17,10,21,39,38,20,70},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,3,6,4,3,9,17,6,21,15,28,42,39,75},{0,0,0,0,0,0,0,0,0,0,0,1,3,2,1,0,6,9,2,3,21,15,6,9,42,21,38,84},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,0,1,9,3,3,2,15,9,21,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,6,9,0,3,21,6,10,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,3,6,4,6,9,17,21,12,39},{0,T^2,0,0,2*T^2,0,0,0,0,3*T^2,0,0,0,5*T^2,0,1,2,0,6*T^2,2,4,9*T^2,9,3,6,15,17,28},{0,0,0,0,T^2,0,0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,3*T^2,0,2,6*T^2,1,0,3,2,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,0,1,9,3,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,6,6,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,3,2,4,9,6,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,5*T^2,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,4293)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}3 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 4 & 3 & 3 & 2 & 4 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 3 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5, 6}, {4, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{1,2,3},{0,4,5},{0,2,3},{1,2,5},{0,2,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,1},{1,1,1},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{3,4,5},{3,4,4},{3,3,5},{3,4,3},{3,3,4},{3,4,2},{2,3,4},{3,3,3},{2,3,3},{3,3,2},{2,2,4},{2,3,2},{2,2,3},{2,3,1},{1,2,3},{2,2,2},{1,2,2},{2,2,1},{1,1,3},{1,2,1},{1,1,2},{1,2,0},{0,1,2},{1,1,1},{0,1,1},{1,1,0},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,4,6,9,10,12,16,25,25,31,43,58,66,64,94,112,139,133,175,221,253,231,334,364,472,420,532,643,921},{0,1,1,3,4,6,4,9,12,16,13,25,31,43,31,58,64,94,70,112,133,175,133,221,231,334,252,364,420,643},{0,0,1,0,3,0,3,6,6,10,12,10,25,15,25,43,43,66,64,66,112,94,112,175,175,253,231,253,364,532},{0,0,0,1,1,3,1,4,4,9,4,12,13,25,13,31,31,58,32,64,70,112,70,133,133,221,139,231,252,420},{0,0,0,0,1,0,1,3,3,6,4,6,12,10,12,25,25,43,31,43,64,66,64,112,112,175,133,175,231,364},{T^2,0,T^2,0,0,1,3*T^2,1,1,4,1+3*T^2,4,4,12,4+6*T^2,13,13,31,13+6*T^2,31,32,64,32+10*T^2,70,70,133,71+10*T^2,133,139,252},{0,0,0,0,0,0,1,0,3,0,4,6,9,10,12,16,25,25,31,43,58,66,64,94,112,139,133,175,221,334},{0,0,0,0,0,0,0,1,1,3,1,3,4,6,4,12,12,25,13,25,31,43,31,64,64,112,70,112,133,231},{0,0,0,0,0,0,0,0,1,0,1,3,4,6,4,9,12,16,13,25,31,43,31,58,64,94,70,112,133,221},{0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,1,3,1,4,4,12,4+6*T^2,12,13,25,13,31,31,64,32+10*T^2,64,70,133},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,10,12,10,25,15,25,43,43,66,64,66,112,175},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,4,4,9,4,12,13,25,13,31,31,58,32,64,70,133},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,4,6,12,10,12,25,25,43,31,43,64,112},{0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,1,3*T^2,1,1,4,1+3*T^2,4,4,12,4+6*T^2,13,13,31,13+6*T^2,31,32,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,6,9,10,12,16,25,25,31,43,58,94},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,4,6,4,12,12,25,13,25,31,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,4,6,4,9,12,16,13,25,31,58},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,1,3,1,4,4,12,4+6*T^2,12,13,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,10,12,10,25,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,4,4,9,4,12,13,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,4,6,12,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,1,3*T^2,1,1,4,1+3*T^2,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,6,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,3*T^2,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,4505)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 5 & 4 & 3 & 4 & 2 & 3 & 4 & 2 & 3 & 2 & 3 & 1 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{-1,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{3,4,5},{1,5,6},{0,1,6},{4,5,6},{0,4,6},{1,2,5},{2,3,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,1},{-1,1,0},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{1,3,5},{0,3,5},{1,3,4},{0,3,4},{1,3,3},{1,2,5},{1,2,4},{0,3,3},{0,2,4},{0,3,2},{1,2,3},{1,1,4},{1,2,2},{0,2,3},{0,2,2},{1,1,3},{0,2,1},{0,1,3},{1,1,2},{1,1,1},{0,1,2},{1,0,3},{0,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,3,4,6,2,9,9,10,16,21,15,38,27,53,42,88,48,84,141,105,63,187,140,161,252,294,308,510},{0,1,0,3,0,1,3,6,9,10,6,9,10,21,38,21,60,42,38,60,84,42,141,84,140,141,213,252,399},{0,0,1,1,3,0,2,4,2,9,9,3,21,10,27,15,53,16,42,84,48,21,105,63,69,140,187,161,308},{0,0,0,1,0,0,1,3,2,6,3,2,6,9,21,9,38,15,21,38,42,15,84,42,63,84,141,140,252},{0,T^2,0,0,1,3*T^2,0,1,3*T^2,4,2,6*T^2,9,2,10,3,27,3+6*T^2,15,42,16,4+10*T^2,48,21,22+10*T^2,63,105,69,161},{0,0,0,0,0,1,3,0,4,0,6,9,10,9,16,21,25,27,38,60,53,42,88,84,105,141,132,187,294},{0,0,0,0,0,0,1,0,1,0,3,2,6,4,9,9,16,10,21,38,27,15,53,42,48,84,88,105,187},{0,0,0,0,0,0,0,1,0,3,1,0,3,2,9,2,21,3,9,21,15,3,42,15,21,42,84,63,140},{0,0,0,0,0,0,0,0,1,0,0,1,0,3,6,3,10,9,6,10,21,9,38,21,42,38,60,84,141},{0,T^2,0,0,0,T^2,0,0,3*T^2,1,0,3*T^2,1,0,2,0,9,6*T^2,2,9,3,6*T^2,15,3,4+10*T^2,15,42,21,63},{0,0,0,0,0,0,0,0,0,0,1,0,3,1,4,2,9,2,9,21,10,3,27,15,16,42,53,48,105},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,9,9,16,21,27,38,25,53,88},{0,0,0,0,0,T^2,0,0,T^2,0,0,3*T^2,1,0,1,0,4,3*T^2,2,9,2,6*T^2,10,3,3+6*T^2,15,27,16,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,6,2,3,6,9,2,21,9,15,21,38,42,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,3,2,0,9,2,3,9,21,15,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,4,2,9,9,10,21,16,27,53},{0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,0,0,0,1,3*T^2,0,1,0,3*T^2,2,0,6*T^2,2,9,3,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,6,3,9,6,10,21,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,4,2,2,9,9,10,27},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,0,1,0,3*T^2,1,0,3*T^2,2,4,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,3,6,9,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,4,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,3*T^2,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,4521)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 2 & 2 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 3 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 3 & 2 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{2,3,4},{2,2,4},{1,3,4},{2,3,3},{1,3,3},{2,3,2},{2,2,3},{1,2,4},{1,3,2},{1,2,3},{2,1,3},{2,2,2},{1,2,2},{1,1,3},{0,2,3},{2,1,2},{2,2,1},{0,1,3},{0,2,2},{1,1,2},{2,1,1},{1,2,1},{0,2,1},{1,1,1},{0,1,2},{1,0,2},{0,1,1},{0,0,2},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,6,6,7,4,12,15,11,15,33,24,23,25,26,37,51,57,45,58,90,105,90,81,168,129,168,155,252,255,271,420},{0,1,0,0,0,0,3,2,0,6,7,6,12,15,9,15,10,23,18,33,26,20,30,58,51,57,90,90,90,105,168,168,140,271},{0,0,1,0,3,0,0,2,6,7,0,0,15,11,15,0,0,24,33,25,0,26,58,45,57,35,105,81,71,65,155,105,168,255},{0,0,0,1,2,3,2,0,6,4,3,7,15,6,6,11,15,9,23,24,25,33,51,57,37,33,90,51,105,81,129,155,168,252},{0,0,0,0,1,0,0,0,3,2,0,0,7,3,4,0,0,6,15,11,0,15,33,25,24,15,57,33,45,35,81,65,105,155},{0,T^2,0,0,0,1,0,3*T^2,2,0,T^2,2,4,3*T^2,0,3,7,6*T^2,6,6,11,15,23,24,9,8+3*T^2,37,12+6*T^2,57,33,51,81,90,129},{0,0,0,0,0,0,1,0,0,2,2,3,6,4,3,7,6,6,9,15,15,12,18,33,23,24,51,37,58,57,90,105,90,168},{0,0,0,0,0,0,0,1,0,3,0,0,6,7,6,0,0,15,12,15,0,10,20,26,33,25,58,57,40,45,105,71,90,168},{0,0,0,0,0,0,0,T^2,1,0,0,0,2,T^2,0,0,0,3*T^2,4,3,0,7,15,11,6,4+T^2,24,8+3*T^2,25,15,33,35,57,81},{0,0,0,0,0,0,0,0,0,1,0,0,3,2,2,0,0,4,6,7,0,6,12,15,15,11,33,24,26,25,57,45,58,105},{0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,0,2,0,3,0,3,T^2,6,6,0,3*T^2,12,9,15,18,23,20,33,51,58,30,90},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,2,3,0,3,4,7,6,9,15,6,6,23,9,33,24,37,57,51,90},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,2,0,3,6,7,4,3,15,6,15,11,24,25,33,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,0,0,0,6,6,7,12,15,10,15,33,26,20,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,0,0,0,6,0,7,0,15,11,0,0,25,0,26,45},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,0,0,2,3,0,T^2,6,3,4,9,6,12,15,23,33,18,51},{0,T^2,0,0,0,0,0,2*T^2,0,0,T^2,0,0,3*T^2,0,0,1,5*T^2,0,0,2,2,3,4,0,3*T^2,6,6*T^2,15,6,9,24,23,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,0,6,7,0,0,15,0,10,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,2,0,7,3,0,0,11,0,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,2,6,4,6,7,15,15,12,33},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,1,0,0,2,0,0,3,0,6,4,6,15,9,23},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,1,2,2,0,T^2,4,3*T^2,7,3,6,11,15,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,0,0,2,T^2,0,0,3,0,7,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,2,4,7,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,0,7,0,6,15},{0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,2,0,3,6,6,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,0,0,T^2,0,3*T^2,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,4801)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 1 & 1 & 3 & 2 & 1 & 2 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, -1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{2,3,4},{1,3,4},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,3,4},{1,2,4},{0,3,4},{0,2,4},{1,3,3},{1,2,3},{0,3,3},{1,3,2},{0,2,3},{1,1,3},{0,1,3},{0,3,2},{1,2,2},{1,1,2},{0,2,2},{0,1,2},{1,2,1},{1,0,2},{0,0,2},{0,2,1},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,1,0},{0,1,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,4,10,7,10,18,16,29,16,28,49,46,82,60,70,118,92,112,175,168,266,215,318,336,504},{0,1,0,2,0,4,0,0,7,10,18,0,10,28,16,46,20,49,82,30,60,92,112,175,110,160,215,318},{0,0,1,2,1,2,4,4,10,3,16,10,10,16,28,49,28,22,70,60,49,112,70,168,112,215,168,336},{0,0,0,1,0,1,0,0,4,2,10,0,4,10,10,28,10,16,49,20,28,60,49,112,60,110,112,215},{0,0,0,0,1,2,2,4,4,3,6,7,10,16,18,29,28,22,40,46,49,82,70,118,112,175,168,266},{0,0,0,0,0,1,0,0,2,2,4,0,4,10,7,18,10,16,29,16,28,46,49,82,60,92,112,175},{0,0,0,0,0,0,1,1,2,0,3,4,2,3,10,16,10,4,22,28,16,49,22,70,49,112,70,168},{0,0,0,2*T^2,0,0,0,1,0,0,3*T^2,2,2,3,4,6,10,4,8+4*T^2,18,16,29,22,40,49,82,70,118},{0,0,0,0,0,0,0,0,1,0,2,0,1,2,4,10,4,3,16,10,10,28,16,49,28,60,49,112},{0,0,0,0,0,0,0,0,0,1,2,0,0,4,0,7,0,10,18,0,10,16,28,46,20,30,60,92},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,2,10,0,4,10,10,28,10,20,28,60},{0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,1,0,0,2,3,2,4*T^3,4,10,3,16,4,22,16,49,22,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4,4,3,6,7,10,18,16,29,28,46,49,82},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,4,0,4,7,10,18,10,16,28,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,0,3,4,2,10,3,16,10,28,16,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,1,4,2,10,4,10,10,28},{0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,0,3*T^2,2,2,4,3,6,10,18,16,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,4,7,0,0,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,0,4,10},{0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,1,0,2,0,3,2,10,3,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4,4,7,10,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,4,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5126)$ |
3 |
23 |
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9: $\begin{pmatrix}0 & -1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 3 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{4, 5}, {1, 2, 3, 6, 7}, {2, 3, 5, 6, 7}, {0, 1, 8}, {0, 4, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{3,4,5},{3,5,6},{0,4,5},{2,5,6},{0,1,4},{1,3,4},{0,2,5}},{2,1,2})
Cox degrees: {{0,0,1},{-1,1,1},{0,1,1},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,3,5},{0,4,5},{0,3,5},{1,3,4},{0,4,4},{1,2,4},{0,3,4},{1,3,3},{1,2,3},{0,2,4},{1,1,3},{0,3,3},{0,2,3},{1,2,2},{0,1,3},{1,1,2},{0,2,2},{1,0,2},{0,1,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,2,3,3,7,9,6,18,13,28,21,39,34,49,64,80,84,120,115,140,175,226,301,301,532},{0,1,1,1,3,1,7,3,7,7,7,18,28,18,28,28,64,28,84,64,84,84,175,210,175,406},{0,0,1,0,0,1,3,0,3,7,7,6,18,6,28,18,34,28,64,34,84,64,115,175,115,301},{0,0,0,1,1,1,2,3,7,2,7,9,13,18,13,28,39,28,49,64,49,84,120,140,175,301},{0,0,0,0,1,0,1,1,1,1,1,7,7,7,7,7,28,7,28,28,28,28,84,84,84,210},{0,0,0,0,0,1,1,0,3,2,7,3,9,6,13,18,21,28,39,34,49,64,80,120,115,226},{0,0,0,0,0,0,1,0,1,1,1,3,7,3,7,7,18,7,28,18,28,28,64,84,64,175},{0,0,3*T^2,0,0,0,0,1,1,6*T^2,1,2,2,7,2+10*T^2,7,13,7,13,28,13+15*T^2,28,49,49,84,140},{0,0,0,0,0,0,0,0,1,0,1,1,2,3,2,7,9,7,13,18,13,28,39,49,64,120},{0,0,0,0,0,0,0,0,0,1,1,0,3,0,7,3,6,7,18,6,28,18,34,64,34,115},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,3,3,7,9,6,13,18,21,39,34,80},{0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,7,1,7,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,1,7,3,7,7,18,28,18,64},{0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,1,6*T^2,1,2,1,2,7,2+10*T^2,7,13,13,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,7,3,6,18,6,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,3,2,7,9,13,18,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,3,3,9,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,7,3,18},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,1,6*T^2,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5162)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 4 & 3 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 2 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4}, {2, 3, 4, 5, 7}, {5, 6, 7}, {0, 1, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1},{1,1,2}},{{4,5,6},{0,3,5},{3,5,6},{2,3,6},{1,4,5},{0,1,5},{2,4,6}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (35): {{3,4,5},{3,3,5},{3,4,4},{2,4,4},{3,4,3},{3,3,4},{2,3,4},{2,4,3},{3,3,3},{3,2,4},{2,2,4},{3,2,3},{2,3,3},{1,3,3},{2,3,2},{2,2,3},{1,2,3},{1,3,2},{2,2,2},{2,1,3},{1,1,3},{2,1,2},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{0,2,1},{1,1,1},{1,0,2},{0,1,1},{1,0,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,3,5,9,5,8,8,15,14,17,21,25,32,42,34,50,47,63,78,74,84,107,120,140,131,182,166,232,263,343,329,505},{0,1,0,0,0,2,3,0,3,5,9,8,5,6,7,17,21,9,25,32,42,50,34,38,47,74,84,56,107,120,131,182,232,179,329},{0,0,1,1,2,2,2,3,5,3,3,8,9,9,17,15,15,21,32,21,21,47,42,42,74,63,63,84,120,84,140,166,196,232,343},{0,0,0,1,0,0,2,2,0,0,3,0,5,9,8,8,15,17,14,11,21,20,32,42,50,47,63,74,78,62,120,106,166,182,263},{0,3*T^2,0,0,1,0,0,1,2,3*T^2,6*T^2,3,2,2,9,3,3,9,15,4+6*T^2,4+10*T^2,21,15,15,42,21,21,42,63,27+10*T^2,63,84,84,140,196},{0,0,0,0,0,1,1,0,2,2,2,5,3,3,5,9,9,6,17,15,15,32,21,21,34,42,42,38,74,63,84,120,140,131,232},{0,0,0,0,0,0,1,0,0,0,2,0,2,3,3,5,9,5,8,8,15,14,17,21,25,32,42,34,50,47,74,78,120,107,182},{0,T^2,0,0,0,0,0,1,0,T^2,3*T^2,0,2,2,5,3,3,9,8,4+3*T^2,4+6*T^2,11,15,15,32,21,21,42,47,27+6*T^2,63,62,84,120,166},{0,0,0,0,0,0,0,0,1,0,0,2,1,1,3,2,2,3,9,3,3,15,9,9,21,15,15,21,42,21,42,63,63,84,140},{0,0,0,2*T^2,0,0,0,4*T^2,0,1,1,2,0,3*T^2,0,3,3,6*T^2,5,9,9,17,6,6+4*T^2,9,21,21,10+8*T^2,34,42,38,74,84,56,131},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,3,0,3,5,9,8,5,6,7,17,21,9,25,32,34,50,74,47,107},{0,0,0,0,0,0,0,2*T^2,0,0,0,1,0,0,0,1,1,3*T^2,3,2,2,9,3,3,6,9,9,6+4*T^2,21,15,21,42,42,38,84},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,3,5,3,3,8,9,9,17,15,15,21,32,21,42,47,63,74,120},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,3,0,5,9,8,8,15,17,14,11,32,20,47,50,78},{0,T^2,0,0,0,0,0,0,0,T^2,3*T^2,0,0,0,1,0,0,1,2,3*T^2,6*T^2,3,2,2,9,3,3,9,15,4+6*T^2,15,21,21,42,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,2,2,5,3,3,5,9,9,6,17,15,21,32,42,34,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,3,3,5,9,5,8,8,17,14,32,25,50},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,T^2,3*T^2,0,2,2,5,3,3,9,8,4+3*T^2,15,11,21,32,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,1,3,2,2,3,9,3,9,15,15,21,42},{0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,2*T^2,0,0,0,4*T^2,0,1,1,2,0,3*T^2,0,3,3,6*T^2,5,9,6,17,21,9,34},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,3,0,3,5,5,8,17,7,25},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,1,0,0,0,1,1,3*T^2,3,2,3,9,9,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,3,5,3,9,8,15,17,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,5,0,8,8,14},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,3*T^2,0,0,0,1,0,0,1,2,3*T^2,2,3,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,2,3,5,9,5,17},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,T^2,2,0,3,5,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,3,9},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,2*T^2,0,0,0,4*T^2,0,1,0,2,3,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,1,1,0,3},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5213)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & -1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}4 & 3 & 4 & 3 & 4 & 4 & 3 & 2 & 4 & 3 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 2 & 0 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 1 & 0 & 1 & -1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {1, 1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (23): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{0, 1, 2, 3, 4}, {2, 3, 4, 5, 7}, {5, 6, 7}, {0, 1, 8}, {6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{1,3,4},{0,2,5},{0,1,4},{3,4,5}},{2,1,1})
Cox degrees: {{1,-1,0},{1,-1,0},{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{4,1,1},{3,2,1},{4,0,1},{3,1,1},{4,0,0},{4,-1,1},{3,0,1},{2,2,1},{4,-1,0},{3,1,0},{2,1,1},{3,0,0},{3,-1,1},{2,0,1},{1,2,1},{3,-1,0},{2,1,0},{1,1,1},{2,0,0},{2,-1,1},{1,0,1},{0,2,1},{2,-1,0},{1,1,0},{0,1,1},{1,0,0},{0,1,0},{1,-1,0},{0,0,0}}
Ext matrix: {{1,2,2,7,3,3,12,12,5,9,27,19,17,42,42,29,39,77,69,57,112,112,99,119,182,189,294,259,434},{0,1,0,2,0,3*T^2,3,7,0,3,12,5,4+6*T^2,17,27,7,19,42,29,22+10*T^2,57,77,39,69,112,99,189,129,259},{0,0,1,2,1,2,7,3,3,2,12,9,12,27,17,19,15,42,39,42,77,57,69,59,112,119,169,189,294},{0,0,0,1,0,0,2,2,0,1,7,3,3,12,12,5,9,27,19,17,42,42,29,39,77,69,119,99,189},{0,0,0,0,1,0,0,0,2,2,0,7,0,0,0,12,12,0,27,0,0,0,42,42,0,77,112,112,182},{0,3*T^2,0,0,0,1,2,6*T^2,1,0,3,2,7,12,4+10*T^2,9,3,17,15,27,42,22+15*T^2,39,21,57,59,79,119,169},{0,0,0,0,0,0,1,0,0,0,2,1,2,7,3,3,2,12,9,12,27,17,19,15,42,39,59,69,119},{0,0,0,0,0,T^2,0,1,0,0,2,0,3*T^2,3,7,0,3,12,5,4+6*T^2,17,27,7,19,42,29,69,39,99},{0,3*T^2,0,0,0,0,0,6*T^2,1,0,0,2,0,0,10*T^2,7,3,0,12,0,0,15*T^2,27,17,0,42,57,77,112},{0,0,0,0,0,3*T^2,0,0,0,1,0,2,6*T^2,0,0,3,7,0,12,10*T^2,0,0,17,27,0,42,77,57,112},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,1,7,3,3,12,12,5,9,27,19,39,29,69},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,7,0,0,0,12,12,0,27,42,42,77},{0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,1,2,6*T^2,1,0,3,2,7,12,4+10*T^2,9,3,17,15,21,39,59},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,2,7,3,3,2,12,9,15,19,39},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,2,0,3*T^2,3,7,0,3,12,5,19,7,29},{0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,1,0,0,2,0,0,10*T^2,7,3,0,12,17,27,42},{0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,1,0,2,6*T^2,0,0,3,7,0,12,27,17,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,1,7,3,9,5,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,7,12,12,27},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,1,2,6*T^2,1,0,3,2,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,2,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,2,0,3,0,5},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,1,0,0,2,3,7,12},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,1,0,2,7,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5228)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 2 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
35: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 7 & 6 & 7 & 5 & 6 & 5 & 6 & 4 & 5 & 4 & 5 & 3 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-3, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (23): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {0, 5, 7}, {3, 4, 5, 6, 7}, {1, 2, 8}, {2, 3, 4, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,3,2},{1,3,3}},{{3,4,5},{2,3,5},{1,3,4},{0,4,5},{0,2,5},{0,1,4}},{1,1,1})
Cox degrees: {{1,3,2},{1,0,0},{0,0,1},{0,1,1},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (35): {{1,7,6},{1,6,6},{1,7,5},{1,5,6},{1,6,5},{1,5,5},{1,6,4},{1,4,5},{1,5,4},{1,4,4},{1,5,3},{1,3,4},{0,4,4},{1,4,3},{0,4,3},{1,4,2},{1,3,3},{0,3,4},{0,3,3},{1,2,3},{1,3,2},{0,2,3},{1,3,1},{0,3,2},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,7,12,12,17,27,42,42,57,43,77,79,112,112,59,119,147,182,159,252,194,252,279,378,322,364,504,420,581,742,826,1106},{0,1,0,2,2,7,3,12,12,27,17,42,27,42,42,57,77,43,79,112,112,119,147,115,182,194,252,252,279,378,269,420,581,561,826},{0,0,1,0,2,3,7,4+T^2,12,17,27,22+3*T^2,17,42,43,77,57,22,59,72+6*T^2,112,75,182,119,147,159,252,182+10*T^2,199,322,279,364,449,581,742},{0,0,10*T^2,1,0,2,15*T^2,7,3,12,4+21*T^2,27,12,17,17,22+28*T^2,42,27,42,77,57,79,72+36*T^2,57,112,115,147,182,194,252,151,269,420,344,561},{0,0,0,0,1,2,2,3,7,12,12,17,12,27,27,42,42,17,43,57,77,59,112,79,112,119,182,147,159,252,194,279,364,420,581},{0,0,0,0,0,1,0,2,2,7,3,12,7,12,12,17,27,12,27,42,42,43,57,42,77,79,112,112,119,182,115,194,279,269,420},{0,0,0,0,0,0,1,0,2,3,7,4+T^2,3,12,12,27,17,4,17,22+3*T^2,42,22,77,43,57,59,112,72+6*T^2,75,147,119,159,199,279,364},{0,0,6*T^2,0,0,0,10*T^2,1,0,2,15*T^2,7,2,3,3,4+21*T^2,12,7,12,27,17,27,22+28*T^2,17,42,42,57,77,79,112,57,115,194,151,269},{0,0,0,0,0,0,0,0,1,2,2,3,2,7,7,12,12,3,12,17,27,17,42,27,42,43,77,57,59,112,79,119,159,194,279},{0,0,0,0,0,0,0,0,0,1,0,2,1,2,2,3,7,2,7,12,12,12,17,12,27,27,42,42,43,77,42,79,119,115,194},{0,0,0,T^4,0,0,0,0,0,0,1,0,0,2,2,7,3,0,3,4+T^2,12,4,27,12,17,17,42,22+3*T^2,22,57,43,59,75,119,159},{0,0,3*T^2,0,0,0,6*T^2,0,0,0,10*T^2,1,0,0,0,15*T^2,2,1,2,7,3,7,4+21*T^2,3,12,12,17,27,27,42,17,42,79,57,115},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,2,7,0,0,12,0,12,0,27,0,0,42,0,42,77,112,112,182},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,0,2,3,7,3,12,7,12,12,27,17,17,42,27,43,59,79,119},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,0,0,2,6*T^2,0,3,0,7,0,12,0,10*T^2,17,0,27,42,57,77,112},{0,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,0,1,0,0,0,0,2,0,7,2,3,3,12,4+T^2,4,17,12,17,22,43,59},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,3,2,7,7,12,12,12,27,12,27,43,42,79},{0,0,3*T^2,0,0,0,6*T^2,0,0,0,10*T^2,0,0,0,0,15*T^2,0,1,2,0,0,7,21*T^2,3,0,12,0,0,27,0,17,42,77,57,112},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,0,7,0,0,12,0,12,27,42,42,77},{T^4,0,T^2+2*T^4,0,0,0,3*T^2,0,0,0,6*T^2,0,T^4,0,2*T^4,10*T^2,0,0,0,1,0,1,15*T^2,0,2,2,3,7,7,12,3,12,27,17,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,2,7,3,3,12,7,12,17,27,43},{0,0,T^2,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,10*T^2,0,0,0,0,0,1,15*T^2,0,0,2,0,0,7,0,3,12,27,17,42},{0,T^4,0,8*T^4,0,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,T^4,0,0,0,0,1,0,0,0,2,0,0,3,2,3,4,12,17},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,1,0,2,0,6*T^2,3,0,7,12,17,27,42},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,1,2,2,2,7,2,7,12,12,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,7,12,12,27},{T^5,0,0,T^4,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,3,7,12},{3*T^4,0,8*T^4,0,T^4,0,T^2+2*T^4,0,0,0,3*T^2,0,3*T^4,0,8*T^4,6*T^2,0,0,T^4,0,0,0,10*T^2,2*T^4,0,0,0,1,1,2,0,2,7,3,12},{0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,0,0,0,10*T^2,0,0,0,0,0,1,0,0,2,7,3,12},{2*T^5,T^5,3*T^4,0,0,0,T^4,0,0,0,0,0,2*T^5,0,3*T^4,0,0,T^5,0,0,0,0,0,T^4,0,0,0,0,0,1,0,1,2,2,7},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,1,2,3,7,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,3*T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5229)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 4 & 5 & 3 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-2, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (23): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {0, 5, 7}, {3, 4, 5, 6, 7}, {1, 2, 8}, {2, 3, 4, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,1},{1,2,2}},{{3,4,5},{0,4,5},{2,3,5},{1,3,4},{0,1,4},{0,2,5}},{1,1,1})
Cox degrees: {{1,2,1},{1,0,0},{0,0,1},{0,1,1},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (31): {{1,6,5},{1,5,5},{1,6,4},{1,4,5},{1,5,4},{1,4,4},{1,5,3},{1,3,4},{0,4,4},{1,4,3},{0,4,3},{1,4,2},{1,3,3},{0,3,4},{0,3,3},{1,2,3},{1,3,2},{0,2,3},{1,3,1},{0,3,2},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,7,12,12,17,13,27,29,42,42,19,49,57,77,69,112,89,112,139,182,147,189,252,224,329,434,490,686},{0,1,0,2,2,7,3,12,7,12,12,17,27,13,29,42,42,49,57,45,77,89,112,112,139,182,129,224,329,309,490},{0,0,1,T^2,2,3,7,4+3*T^2,3,12,13,27,17,4,19,22+6*T^2,42,25,77,49,57,69,112,72+10*T^2,89,147,139,189,239,329,434},{0,0,6*T^2,1,0,2,10*T^2,7,2,3,3,4+15*T^2,12,7,12,27,17,29,22+21*T^2,17,42,45,57,77,89,112,61,129,224,169,309},{0,0,0,0,1,2,2,3,2,7,7,12,12,3,13,17,27,19,42,29,42,49,77,57,69,112,89,139,189,224,329},{0,0,0,0,0,1,0,2,1,2,2,3,7,2,7,12,12,13,17,12,27,29,42,42,49,77,45,89,139,129,224},{0,0,0,0,0,0,1,T^2,0,2,2,7,3,0,3,4+3*T^2,12,4,27,13,17,19,42,22+6*T^2,25,57,49,69,89,139,189},{0,0,3*T^2,0,0,0,6*T^2,1,0,0,0,10*T^2,2,1,2,7,3,7,4+15*T^2,3,12,12,17,27,29,42,17,45,89,61,129},{0,0,0,0,0,0,0,0,1,0,2,0,0,2,7,0,0,12,0,12,0,27,0,0,42,0,42,77,112,112,182},{0,0,0,0,0,0,0,0,0,1,1,2,2,0,2,3,7,3,12,7,12,13,27,17,19,42,29,49,69,89,139},{0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,0,0,2,6*T^2,0,3,0,7,0,12,0,10*T^2,17,0,27,42,57,77,112},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,T^2,2,0,7,2,3,3,12,4+3*T^2,4,17,13,19,25,49,69},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,3,2,7,7,12,12,13,27,12,29,49,45,89},{0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,10*T^2,0,1,2,0,0,7,15*T^2,3,0,12,0,0,27,0,17,42,77,57,112},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,0,7,0,0,12,0,12,27,42,42,77},{0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,1,0,1,10*T^2,0,2,2,3,7,7,12,3,12,29,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,2,7,3,3,12,7,13,19,29,49},{0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,0,0,1,10*T^2,0,0,2,0,0,7,0,3,12,27,17,42},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,T^2,0,3,2,3,4,13,19},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,1,0,2,0,6*T^2,3,0,7,12,17,27,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,7,2,7,13,12,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,7,12,12,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,3,7,13},{T^4,0,2*T^4,0,0,0,T^2,0,T^4,0,2*T^4,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,0,1,1,2,0,2,7,3,12},{0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,0,0,1,0,0,2,7,3,12},{0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,1,2,3,7,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5231)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & -1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 0 & 1 & 3 & 2 & 0 & 1 & 2 & 3 & 0 & 2 & 1 & 0 & 2 & 1 & 3 & 2 & 0 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 0 \\ 5 & 5 & 4 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}, {0, 0, 1, 1, 1, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 1, 7}, {2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,2},{1,0,3}},{{1,2,4},{2,3,5},{0,3,5},{2,4,5},{0,1,4},{0,4,5}},{1,1,2})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,-1,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,3,5},{1,2,5},{1,3,4},{1,1,5},{1,2,4},{1,0,5},{1,1,4},{1,3,3},{1,2,3},{1,0,4},{1,1,3},{0,2,3},{1,3,2},{1,0,3},{1,2,2},{0,1,3},{0,0,3},{0,2,2},{1,1,2},{1,3,1},{1,2,1},{1,0,2},{0,1,2},{0,0,2},{1,1,1},{0,2,1},{1,0,1},{0,1,1},{0,0,1},{0,2,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,6,6,15,10,28,21,46,45,81,47,56,126,111,84,132,117,186,126,231,281,201,309,371,252,546,417,627,490,783,1152},{0,1,1,3,6,6,15,6,21,28,46,21,21,81,56,47,84,57,111,56,126,186,117,201,231,132,371,252,417,273,490,783},{0,0,1,0,3,0,6,6,15,10,28,15,21,45,46,28,45,47,81,56,111,126,84,132,186,117,281,201,309,252,417,627},{0,0,0,1,1,3,6,1,6,15,21,6,6,46,21,21,47,21,56,21,56,111,57,117,126,57,231,132,252,132,273,490},{0,0,0,0,1,0,3,1,6,6,15,6,6,28,21,15,28,21,46,21,56,81,47,84,111,57,186,117,201,132,252,417},{T^2,0,3*T^2,0,0,1,1,6*T^2,1,6,6,1+T^2,1+10*T^2,21,6,6,21,6+3*T^2,21,6+15*T^2,21,56,21,57,56,21+6*T^2,126,57,132,57+10*T^2,132,273},{0,0,0,0,0,0,1,0,1,3,6,1,1,15,6,6,15,6,21,6,21,46,21,47,56,21,111,57,117,57,132,252},{0,0,0,0,0,0,0,1,3,0,6,3,6,10,15,6,10,15,28,21,46,45,28,45,81,47,126,84,132,117,201,309},{0,0,0,0,0,0,0,0,1,0,3,1,1,6,6,3,6,6,15,6,21,28,15,28,46,21,81,47,84,57,117,201},{0,0,T^2,0,0,0,0,3*T^2,0,1,1,0,6*T^2,6,1,1,6,1+T^2,6,1+10*T^2,6,21,6,21,21,6+3*T^2,56,21,57,21+6*T^2,57,132},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,1,3,1,6,1,6,15,6,15,21,6,46,21,47,21,57,117},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,6,0,0,0,0,15,28,0,21,0,46,81,56,111,186},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,3,6,6,15,10,6,10,28,15,45,28,45,47,84,132},{0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,1,0,0,1,0,1,6*T^2,1,6,1,6,6,1+T^2,21,6,21,6+3*T^2,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,6,6,3,6,15,6,28,15,28,21,47,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,0,0,6,15,0,6,0,21,46,21,56,111},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,6,0,1,0,6,21,6,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6,0,6,0,15,28,21,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,6,1,15,6,15,6,21,47},{0,T^3,0,3*T^3,0,6*T^3,0,0,0,0,0,0,0,0,0,T^3,3*T^3,0,0,1,3,0,0,0,6,3,10,6,10,15,28,45},{0,0,0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,0,0,0,3,1,6,3,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,1,0,1,1,0,6,1,6,1+T^2,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,0,6,15,6,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,6,1,6,21},{T^5,0,0,0,0,T^3,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6,6,15,28},{3*T^5,T^5,0,0,0,0,0,0,0,0,0,3*T^5,0,0,0,T^5,0,0,0,T^2,0,0,0,0,0,0,1,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5238)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 3 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 1 & 0 \\ 3 & 3 & 2 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 1, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {2, 3, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{1,1,1}},{{1,3,4},{0,2,4},{1,2,4},{0,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,1,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,4,3},{2,3,3},{2,4,2},{2,2,3},{1,3,3},{2,4,1},{2,3,2},{1,2,3},{1,3,2},{2,3,1},{2,2,2},{1,1,3},{1,2,2},{2,2,1},{1,3,1},{0,2,2},{1,1,2},{1,3,0},{1,2,1},{0,1,2},{0,2,1},{1,2,0},{1,1,1},{0,0,2},{0,1,1},{1,1,0},{0,2,0},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,4,6,9,9,13,18,18,16,30,36,27,34,54,46,63,66,73,108,114,109,144,196,127,240,253,424},{0,1,0,3,1,0,3,4,3,6,9,9,13,18,6,13,30,10,27,34,27,46,63,66,73,108,46,144,127,253},{0,0,1,0,0,3,3,0,4,9,6,0,9,18,13,10,16,27,30,19,34,63,54,31,66,114,73,109,144,240},{0,0,0,1,0,0,0,1,0,0,3,4,3,6,0,3,13,0,6,13,6,10,27,34,27,46,10,73,46,127},{0,0,0,0,1,0,0,3,3,0,0,6,9,0,6,13,18,10,18,30,27,30,36,54,63,60,46,114,108,196},{0,0,0,0,T^2,1,0,3*T^2,0,3,0,6*T^2,0,6,4,T^2,0,13,9,3*T^2,10,30,16,6*T^2,19,54,34,31,66,109},{0,0,0,0,0,0,1,0,1,3,3,0,4,9,3,4,9,6,13,10,13,27,30,19,34,63,27,66,73,144},{0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,3,9,0,6,13,6,10,18,30,27,30,10,63,46,108},{0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,4,6,6,9,9,13,18,18,16,30,36,27,54,63,114},{0,0,0,0,0,0,0,T^2,0,1,0,3*T^2,0,3,1,0,0,3,4,T^2,4,13,9,3*T^2,10,30,13,19,34,66},{0,0,0,0,0,0,0,0,0,0,1,0,1,3,0,1,4,0,3,4,3,6,13,10,13,27,6,34,27,73},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,3,0,0,6,13,6,10,0,27,10,46},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,3,4,3,6,9,9,13,18,6,30,27,63},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,0,0,1,0,1,3,4,T^2,4,13,3,10,13,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,4,9,6,0,9,18,13,16,30,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,9,0,6,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,3,4,3,6,0,13,6,27},{0,0,0,0,T^2,0,0,3*T^2,0,0,0,6*T^2,0,0,0,T^2,0,1,0,3*T^2,0,3,0,6*T^2,0,6,4,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,0,4,9,3,9,13,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,6,9,18},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,T^2,0,1,0,3*T^2,0,3,1,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,0,4,3,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5241)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 1 & 4 & 3 & 2 & 2 & 3 & 1 & 3 & 1 & 2 & 2 & 1 & 0 & 3 & 2 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 1, 0, 1, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 5, 6}, {2, 4, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{0,4,5},{1,2,5},{1,2,3},{0,2,3},{0,2,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{1,1,1},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (33): {{2,4,4},{2,4,3},{2,3,4},{2,4,2},{2,3,3},{2,4,1},{2,2,4},{1,3,3},{2,3,2},{1,3,2},{2,2,3},{2,3,1},{1,2,3},{1,3,1},{2,2,2},{1,2,2},{2,2,1},{1,3,0},{1,1,3},{0,2,2},{1,2,1},{0,2,1},{1,1,2},{1,2,0},{0,1,2},{0,2,0},{1,1,1},{0,1,1},{1,1,0},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,5,6,12,10,15,14,22,28,31,35,41,47,53,77,81,71,95,80,125,134,167,185,182,203,261,297,377,360,443,568,829},{0,1,1,3,5,6,5,5,12,14,15,22,17,28,31,41,53,47,45,41,77,80,95,125,98,134,167,182,261,205,297,360,568},{0,0,1,0,3,0,5,3,6,6,12,10,14,10,22,28,35,15,41,28,47,47,77,71,80,71,125,134,185,182,203,297,443},{0,0,0,1,1,3,1,1,5,5,5,12,5,14,15,17,31,28,17,17,41,41,45,77,45,80,95,98,167,103,182,205,360},{0,0,0,0,1,0,1,1,3,3,5,6,5,6,12,14,22,10,17,14,28,28,41,47,41,47,77,80,125,98,134,182,297},{T^2,0,2*T^2,0,0,1,3*T^2,2*T^2,1,1,1,5,1+4*T^2,5,5,5,15,14,5+6*T^2,5+3*T^2,17,17,17,41,17+6*T^2,41,45,45,95,45+9*T^2,98,103,205},{0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,6,10,0,14,6,10,10,28,15,28,15,47,47,71,80,71,134,203},{0,0,0,0,0,0,0,1,0,3,0,0,5,6,0,12,0,10,15,14,22,28,31,35,41,47,53,77,81,95,125,167,261},{0,0,0,0,0,0,0,0,1,1,1,3,1,3,5,5,12,6,5,5,14,14,17,28,17,28,41,41,77,45,80,98,182},{0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,5,0,6,5,5,12,14,15,22,17,28,31,41,53,45,77,95,167},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,0,5,3,6,6,14,10,14,10,28,28,47,41,47,80,134},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,1,2*T^2,1,1,1,5,3,1+4*T^2,1,5,5,5,14,5+3*T^2,14,17,17,41,17+6*T^2,41,45,98},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,5,3,6,6,12,10,14,10,22,28,35,41,47,77,125},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,1,1,5,5,5,12,5,14,15,17,31,17,41,45,95},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,1,1,3,3,5,6,5,6,14,14,28,17,28,41,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,3,5,6,5,6,12,14,22,17,28,41,77},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,2*T^2,0,1,1,1,3,1,3,5,5,14,5+3*T^2,14,17,41},{0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,1,3*T^2,2*T^2,1,1,1,5,1+4*T^2,5,5,5,15,5+6*T^2,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,6,10,14,10,28,47},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,5,6,0,12,0,15,22,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,1,3,5,5,12,5,14,17,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,5,0,5,12,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,5,6,14,28},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,1,2*T^2,1,1,1,5,1+4*T^2,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,2*T^2,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5255)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 5 & 4 & 5 & 4 & 5 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -2, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,2}},{{2,3,4},{1,3,4},{0,2,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,2,2},{1,0,0},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (32): {{1,5,6},{1,4,6},{1,5,5},{1,4,5},{1,5,4},{1,3,5},{1,4,4},{1,3,4},{1,4,3},{1,2,4},{0,3,4},{1,3,3},{0,2,4},{0,3,3},{1,2,3},{1,3,2},{1,1,3},{0,3,2},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,8,6,13,18,33,32,48,34,63,50,66,98,103,133,109,106,168,146,186,258,238,271,378,290,356,441,602,656,924},{0,1,0,3,0,8,6,18,10,33,18,32,34,32,63,50,98,50,66,103,106,109,153,168,186,258,163,271,290,441,418,656},{0,0,1,2,3,3,8,13,18,18,13,33,18,34,48,63,63,66,50,98,66,106,168,133,146,238,186,186,271,356,441,602},{0,0,0,1,0,2,3,8,6,13,8,18,13,18,33,32,48,32,34,63,50,66,103,98,106,168,109,146,186,271,290,441},{0,2*T^2,0,0,1,3*T^2,2,3,8,4+4*T^2,3,13,4+6*T^2,13,18,33,23+5*T^2,34,18,48,23+8*T^2,50,98,63,66,133,106,82+10*T^2,146,186,271,356},{0,0,0,0,0,1,0,3,0,8,3,6,8,6,18,10,33,10,18,32,34,32,50,63,66,103,50,106,109,186,163,290},{0,0,0,0,0,0,1,2,3,3,2,8,3,8,13,18,18,18,13,33,18,34,63,48,50,98,66,66,106,146,186,271},{0,0,0,0,0,0,0,1,0,2,1,3,2,3,8,6,13,6,8,18,13,18,32,33,34,63,32,50,66,106,109,186},{0,T^2,0,0,0,2*T^2,0,0,1,3*T^2,0,2,4*T^2,2,3,8,4+4*T^2,8,3,13,4+6*T^2,13,33,18,18,48,34,23+8*T^2,50,66,106,146},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,0,8,0,3,6,8,6,10,18,18,32,10,34,32,66,50,109},{0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,0,6,8,0,13,18,0,0,33,0,32,48,63,98,103,168},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,3,3,2,8,3,8,18,13,13,33,18,18,34,50,66,106},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,8,6,0,0,18,0,10,33,32,63,50,103},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,0,3,8,0,0,13,0,18,18,33,48,63,98},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,3,2,3,6,8,8,18,6,13,18,34,32,66},{0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,2*T^2,0,0,1,3*T^2,1,0,2,4*T^2,2,8,3,3,13,8,4+6*T^2,13,18,34,50},{0,0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,T^3,0,0,1,3*T^3,0,0,1,0,0,3,3,6,0,8,6,18,10,32},{0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,0,0,3*T^2,2,0,0,3,0,8,4+4*T^2,13,18,33,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,8,0,6,13,18,33,32,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,2,8,3,3,8,13,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,8,6,18,10,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,3,8,13,18,33},{0,0,0,0,0,0,0,0,0,T^2,0,0,T^2,0,0,0,2*T^2,0,0,0,2*T^2,0,1,0,0,2,1,4*T^2,2,3,8,13},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,1,3,0,2,3,8,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,8,6,18},{T^5,0,0,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,3*T^2,2,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5263)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{1,3,4},{0,1,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,4,5},{1,3,5},{1,4,4},{1,3,4},{1,4,3},{1,2,4},{0,3,4},{1,3,3},{0,2,4},{0,3,3},{1,2,3},{1,3,2},{1,1,3},{0,3,2},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,8,6,13,9,18,15,21,33,32,48,38,41,63,61,81,103,98,131,168,135,181,231,336,361,546},{0,1,0,3,0,8,3,6,9,6,18,10,33,10,21,32,41,38,50,63,81,103,60,131,135,231,203,361},{0,0,1,2,3,3,2,8,3,9,13,18,18,21,15,33,21,41,63,48,61,98,81,81,131,181,231,336},{0,0,0,1,0,2,1,3,2,3,8,6,13,6,9,18,15,21,32,33,41,63,38,61,81,131,135,231},{0,2*T^2,0,0,1,3*T^2,0,2,5*T^2,2,3,8,4+4*T^2,9,3,13,4+7*T^2,15,33,18,21,48,41,27+9*T^2,61,81,131,181},{0,0,0,0,0,1,0,0,1,0,3,0,8,0,3,6,9,6,10,18,21,32,10,41,38,81,60,135},{0,0,0,0,0,0,1,0,2,3,0,0,0,6,8,0,13,18,0,0,33,0,32,48,63,98,103,168},{0,0,0,0,0,0,0,1,0,1,2,3,3,3,2,8,3,9,18,13,15,33,21,21,41,61,81,131},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,8,6,0,0,18,0,10,33,32,63,50,103},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,0,3,8,0,0,13,0,18,18,33,48,63,98},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,3,2,3,6,8,9,18,6,15,21,41,38,81},{0,T^2,0,0,0,2*T^2,0,0,3*T^2,0,0,1,3*T^2,1,0,2,5*T^2,2,8,3,3,13,9,4+7*T^2,15,21,41,61},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,3,3,6,0,9,6,21,10,38},{0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,0,0,3*T^2,2,0,0,3,0,8,4+4*T^2,13,18,33,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,8,0,6,13,18,33,32,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,2,8,3,3,9,15,21,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,8,6,18,10,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,3,8,13,18,33},{0,0,0,0,0,T^2,0,0,T^2,0,0,0,2*T^2,0,0,0,3*T^2,0,1,0,0,2,1,5*T^2,2,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,2,3,9,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,8,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,3,9},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,3*T^2,2,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5264)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 3 & 2 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,3,4},{1,2,4},{0,3,4},{1,3,3},{0,2,4},{1,3,2},{0,3,3},{1,2,3},{0,3,2},{1,1,3},{1,2,2},{0,2,3},{0,2,2},{0,1,3},{1,1,2},{1,2,1},{0,2,1},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,4,6,6,8,12,13,18,16,36,26,33,32,64,66,48,63,126,96,103,98,196,168,206,336},{0,1,0,0,2,0,0,3,0,8,6,6,12,16,18,10,20,36,33,32,64,66,50,63,126,103,100,206},{0,0,1,0,2,0,3,0,6,0,0,8,18,13,0,0,32,33,0,0,63,48,0,0,98,0,103,168},{0,0,0,1,0,3,2,2,6,3,8,4,16,6,13,18,36,26,18,33,66,36,63,48,96,98,126,196},{0,0,0,0,1,0,0,0,0,0,0,3,6,8,0,0,10,18,0,0,32,33,0,0,63,0,50,103},{0,2*T^2,0,0,4*T^2,1,0,0,2,3*T^2,2,0,4,6*T^2,3,8,16,6,4+4*T^2,13,26,8+8*T^2,33,18,36,48,66,96},{0,0,0,0,0,0,1,0,3,0,0,2,8,3,0,0,18,13,0,0,33,18,0,0,48,0,63,98},{0,0,0,0,0,0,0,1,0,2,3,2,6,4,8,6,12,16,13,18,36,26,32,33,66,63,64,126},{0,0,0,0,2*T^2,0,0,0,1,0,0,0,2,3*T^2,0,0,8,3,0,0,13,4+4*T^2,0,0,18,0,33,48},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,0,0,6,8,6,12,16,10,18,36,32,20,64},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,3,6,4,3,8,16,6,18,13,26,33,36,66},{0,0,0,0,0,0,0,0,0,0,0,1,3,2,0,0,6,8,0,0,18,13,0,0,33,0,32,63},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,0,0,8,3,0,0,13,0,18,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,6,8,0,0,18,0,10,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,3,6,4,6,8,16,18,12,36},{0,T^2,0,0,2*T^2,0,0,0,0,2*T^2,0,0,0,4*T^2,0,1,2,0,3*T^2,2,4,6*T^2,8,3,6,13,16,26},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,0,1,0,0,0,2,3*T^2,0,0,3,0,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,0,0,8,0,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,6,6,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,3,2,4,8,6,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,2*T^2,0,0,4*T^2,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5266)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 2 & 2 & 0 & 0 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 5 & 3 & 4 & 4 & 2 & 3 & 4 & 3 & 3 & 2 & 2 & 4 & 3 & 1 & 2 & 3 & 2 & 2 & 3 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, -1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 4, 5}, {3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{-1,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{3,4,5},{0,4,6},{2,3,5},{1,2,5},{1,5,6},{0,1,6},{4,5,6}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,1},{-1,1,0},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,2,5},{1,2,5},{2,2,4},{1,2,4},{2,2,3},{2,1,5},{1,2,3},{0,2,4},{2,1,4},{1,2,2},{0,2,3},{1,1,4},{2,1,3},{1,1,3},{0,2,2},{2,1,2},{2,0,4},{0,1,3},{0,2,1},{1,1,2},{2,0,3},{0,1,2},{2,0,2},{1,0,3},{1,1,1},{0,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,3,5,6,2,12,5,9,22,15,11,21,32,31,38,15,35,53,65,42,81,84,53,110,149,120,136,218,239,269,455},{0,1,0,3,0,1,6,5,3,10,12,9,6,21,22,10,9,32,35,38,21,65,38,42,60,110,84,120,141,167,218,347},{0,0,1,1,3,0,5,1,2,12,5,2,9,11,15,21,3,11,31,32,15,35,42,17,65,81,53,56,120,149,136,269},{0,0,0,1,0,0,3,1,1,6,5,2,3,9,12,6,2,11,22,21,9,32,21,15,38,65,42,53,84,110,120,218},{0,2*T^2,0,0,1,3*T^2,1,3*T^2,0,5,1,5*T^2,2,2,5,9,6*T^2,2+7*T^2,15,11,3,11,15,3+9*T^2,32,35,17,17+12*T^2,53,81,56,136},{0,0,0,0,0,1,0,0,3,0,0,5,6,12,0,10,9,15,0,22,21,31,38,32,35,53,65,81,110,81,149,239},{0,0,0,0,0,0,1,0,0,3,1,0,1,2,5,3,0,2,12,9,2,11,9,3,21,32,15,17,42,65,53,120},{0,0,0,0,0,0,0,1,0,0,3,1,0,3,6,0,1,9,10,6,3,21,6,9,10,38,21,42,38,60,84,141},{0,0,0,0,0,0,0,0,1,0,0,1,3,5,0,6,2,5,0,12,9,15,21,11,22,31,32,35,65,53,81,149},{0,T^2,0,0,0,T^2,0,2*T^2,0,1,0,3*T^2,0,0,1,1,3*T^2,5*T^2,5,2,0,2,2,6*T^2,9,11,3,3+9*T^2,15,32,17,53},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,0,2,6,3,1,9,3,2,6,21,9,15,21,38,42,84},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,1,5,0,6,3,12,6,9,10,22,21,32,38,35,65,110},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,0,1,0,5,2,5,9,2,12,15,11,11,32,31,35,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,3,1,5,3,2,6,12,9,11,21,22,32,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,2,1,0,3,9,2,3,9,21,15,42},{0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,1,3*T^2,3*T^2,0,1,0,1,2,5*T^2,5,5,2,2+7*T^2,11,15,11,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,5,0,0,12,15,22,0,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,1,0,6,3,9,6,10,21,38},{0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,0,T^2,3*T^2,1,0,0,0,0,3*T^2,1,2,0,6*T^2,2,9,3,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,3,5,2,2,9,12,11,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,0,0,5,5,12,0,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,2,3,6,9,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,5,6,0,12,22},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,2*T^2,0,0,0,0,0,3*T^2,1,1,0,5*T^2,2,5,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,0,0,0,3*T^2,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5277)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 4 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,2},{1,2,2}},{{2,3,4},{0,4,5},{0,2,4},{3,4,5},{0,1,5},{1,3,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,1},{0,1,1},{1,1,2},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,4,7},{1,4,6},{1,3,6},{1,4,5},{1,3,5},{1,4,4},{1,2,5},{0,3,5},{1,3,4},{0,3,4},{1,3,3},{1,2,4},{0,3,3},{1,2,3},{1,1,4},{0,2,4},{0,2,3},{1,1,3},{1,2,2},{0,2,2},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,6,15,10,21,16,28,31,45,46,51,81,56,52,96,111,126,154,132,186,232,281,287,362,482,732},{0,1,1,3,6,6,6,6,15,16,28,21,31,46,21,22,52,56,81,96,62,111,132,186,147,232,287,482},{0,0,1,0,3,0,6,3,6,6,10,15,10,28,21,16,31,46,45,51,52,81,96,126,132,154,232,362},{0,0,0,1,1,3,1,1,6,6,15,6,16,21,6,6,22,21,46,52,22,56,62,111,62,132,147,287},{0,0,0,0,1,0,1,1,3,3,6,6,6,15,6,6,16,21,28,31,22,46,52,81,62,96,132,232},{T^2,0,3*T^2,0,0,1,6*T^2,T^2,1,1,6,1,6,6,1+10*T^2,1+3*T^2,6,6,21,22,6+6*T^2,21,22,56,22+10*T^2,62,62,147},{0,0,0,0,0,0,1,0,0,0,0,3,0,6,6,3,6,15,10,10,16,28,31,45,52,51,96,154},{0,0,0,0,0,0,0,1,0,3,0,0,6,0,0,6,15,0,0,28,21,0,46,0,56,81,111,186},{0,0,0,0,0,0,0,0,1,1,3,1,3,6,1,1,6,6,15,16,6,21,22,46,22,52,62,132},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,1,6,0,0,15,6,0,21,0,21,46,56,111},{0,0,T^2,0,0,0,3*T^2,0,0,0,1,0,1,1,6*T^2,T^2,1,1,6,6,1+3*T^2,6,6,21,6+6*T^2,22,22,62},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,6,6,6,6,15,16,28,22,31,52,96},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,6,1,0,6,0,6,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,3,1,6,6,15,6,16,22,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,3,6,6,10,16,10,31,51},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,6,0,15,0,21,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,6,0,6,15,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,3,6,6,6,16,31},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,1,1,T^2,1,1,6,1+3*T^2,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,6,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,T^2,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5280)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{2,3,4},{3,4,5},{0,1,5},{0,3,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,1},{0,1,1},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,3,6},{1,3,5},{1,2,5},{0,3,5},{1,3,4},{0,3,4},{1,3,3},{1,2,4},{0,3,3},{1,2,3},{1,1,4},{0,2,4},{0,2,3},{1,1,3},{1,2,2},{0,2,2},{0,1,3},{1,0,3},{1,1,2},{0,1,2},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,4,6,9,10,15,16,28,21,21,43,46,45,73,67,56,81,127,126,111,167,186,207,297,467},{0,1,1,1,3,4,6,6,9,15,6,7,21,21,28,43,27,21,46,67,81,56,77,111,127,167,297},{0,0,1,0,0,0,0,3,0,6,6,4,9,15,10,16,21,21,28,43,45,46,67,81,73,127,207},{0,0,0,1,0,3,0,0,6,0,0,6,15,0,0,28,21,0,0,46,0,0,56,0,81,111,186},{0,0,0,0,1,1,3,1,4,6,1,1,7,6,15,21,7,6,21,27,46,21,27,56,67,77,167},{0,0,0,0,0,1,0,0,3,0,0,1,6,0,0,15,6,0,0,21,0,0,21,0,46,56,111},{T^2,0,3*T^2,T^2,0,0,1,0,1,1,6*T^2,3*T^2,1,1,6,7,1+6*T^2,1+10*T^2,6,7,21,6,7+10*T^2,21,27,27,77},{0,0,0,0,0,0,0,1,0,3,1,1,4,6,6,9,7,6,15,21,28,21,27,46,43,67,127},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,6,1,0,0,6,0,0,6,0,21,21,56},{0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,4,1,1,6,7,15,6,7,21,21,27,67},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,4,6,6,9,10,15,21,28,16,43,73},{0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,6,0,0,15,0,0,21,0,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,0,6,0,0,6,0,15,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,4,6,6,7,15,9,21,43},{0,0,T^2,0,0,0,0,0,0,0,3*T^2,T^2,0,0,1,1,3*T^2,6*T^2,1,1,6,1,1+6*T^2,6,7,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6,0,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,1,6,4,7,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,6,15},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,T^2,3*T^2,0,0,1,0,3*T^2,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5281)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 2 & 3 & 3 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 5 & 4 & 5 & 3 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {2, 3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{3,4,5},{0,2,5},{0,4,5},{1,3,4},{0,1,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,1},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,3,5},{1,2,5},{1,3,4},{0,3,5},{1,3,3},{1,2,4},{0,3,4},{1,2,3},{1,1,4},{0,3,3},{0,2,4},{1,1,3},{1,2,2},{1,1,2},{0,2,3},{1,0,3},{0,2,2},{1,0,2},{1,1,1},{0,1,3},{0,1,2},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,3,2,6,6,9,15,6,21,12,21,28,46,36,21,74,56,81,42,102,111,112,186,192,237,417},{0,1,0,1,0,3,3,6,6,6,9,15,10,28,21,21,38,46,45,36,74,81,102,126,126,192,312},{0,0,1,0,3,1,2,6,1,9,2,6,15,21,12,6,36,21,46,12,42,56,42,111,102,112,237},{0,0,0,1,0,0,3,0,0,6,6,0,0,0,15,0,28,0,0,21,46,0,56,0,81,111,186},{0,3*T^2,0,3*T^2,1,0,0,1,6*T^2,2,6*T^2,1,6,6,2,1+10*T^2,12,6,21,2+10*T^2,12,21,12+15*T^2,56,42,42,112},{0,0,0,0,0,1,1,3,1,3,2,6,6,15,9,6,21,21,28,12,36,46,42,81,74,102,192},{0,0,0,0,0,0,1,0,0,3,1,0,0,0,6,0,15,0,0,6,21,0,21,0,46,56,111},{0,0,0,0,0,0,0,1,0,1,0,1,3,6,2,1,9,6,15,2,12,21,12,46,36,42,102},{0,0,0,0,0,0,0,0,1,0,1,3,0,6,3,6,6,15,10,9,21,28,36,45,38,74,126},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,6,0,0,1,6,0,6,0,21,21,56},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,0,0,6,15,0,21,0,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,6,6,2,9,15,12,28,21,36,74},{0,T^2,0,T^2,0,0,0,0,3*T^2,0,3*T^2,0,1,1,0,6*T^2,2,1,6,6*T^2,2,6,2+10*T^2,21,12,12,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,0,2,6,2,15,9,12,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,1,6,0,6,0,15,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,3,6,9,10,6,21,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,6,3,9,21},{0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,0,0,3*T^2,0,0,1,3*T^2,0,1,6*T^2,6,2,2,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,3*T^2,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5283)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,4,5},{2,3,5},{2,4,4},{2,3,4},{2,4,3},{2,2,4},{1,3,4},{2,3,3},{1,2,4},{1,3,3},{2,3,2},{2,2,3},{1,2,3},{2,2,2},{1,3,2},{1,1,3},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,7,6,11,9,15,15,21,26,25,39,45,38,57,42,75,63,84,123,115,136,195,141,188,240,345,375,555},{0,1,0,3,0,7,3,6,9,6,10,15,21,26,10,39,21,38,42,38,60,75,84,123,60,136,141,240,213,375},{0,0,1,2,3,3,2,7,3,9,15,11,15,25,21,21,15,39,21,42,75,57,63,115,84,84,136,188,240,345},{0,0,0,1,0,2,1,3,2,3,6,7,9,15,6,15,9,21,15,21,38,39,42,75,38,63,84,136,141,240},{0,T^2,0,0,1,T^2,0,2,3*T^2,2,7,3,3,11,9,4+3*T^2,3,15,4+6*T^2,15,39,21,21,57,42,27+6*T^2,63,84,136,188},{0,0,0,0,0,1,0,0,1,0,0,3,3,6,0,9,3,6,9,6,10,21,21,38,10,42,38,84,60,141},{0,0,0,0,0,0,1,0,2,3,0,0,7,0,6,11,9,15,15,21,26,25,39,45,38,57,75,115,123,195},{0,0,0,0,0,0,0,1,0,1,3,2,2,7,3,3,2,9,3,9,21,15,15,39,21,21,42,63,84,136},{0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,7,3,6,9,6,10,15,21,26,10,39,38,75,60,123},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,3,2,7,3,9,15,11,15,25,21,21,39,57,75,115},{0,T^2,0,0,0,T^2,0,0,3*T^2,0,1,0,0,2,1,3*T^2,0,2,6*T^2,2,9,3,3,15,9,4+6*T^2,15,21,42,63},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,2,1,3,2,3,6,9,9,21,6,15,21,42,38,84},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,3,2,3,6,7,9,15,6,15,21,39,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,3,2,2,9,3,3,9,15,21,42},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,T^2,0,2,3*T^2,2,7,3,3,11,9,4+3*T^2,15,21,39,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,3,3,6,0,9,6,21,10,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,7,0,6,11,15,25,26,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,2,7,3,3,9,15,21,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,7,6,15,10,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,3,7,11,15,25},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,0,3*T^2,0,1,0,0,2,1,3*T^2,2,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,2,3,9,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,7,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,T^2,2,3,7,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5287)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 1 & 1 & 0 & 2 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 0 & 2 & 0 & 1 & 0 & 1 & 2 & 1 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 2 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, -1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{0,1,4},{2,3,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,2,3},{2,1,3},{1,2,3},{1,1,3},{0,2,3},{2,2,2},{2,1,2},{0,1,3},{1,2,2},{1,1,2},{2,2,1},{0,2,2},{2,0,2},{1,0,2},{0,1,2},{1,2,1},{2,1,1},{2,0,1},{1,1,1},{0,2,1},{0,0,2},{2,1,0},{0,1,1},{1,0,1},{0,0,1},{1,1,0},{2,0,0},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,5,11,12,12,27,15,22,17,42,50,31,35,56,74,53,78,85,128,120,209,161,140,269,263,443},{0,1,0,3,0,0,5,6,0,12,0,0,11,27,22,0,15,35,31,0,50,35,53,74,128,65,85,161,105,263},{0,0,1,2,3,1,2,6,5,11,5,12,3,17,27,15,11,17,35,31,42,35,74,56,120,85,56,140,161,269},{0,0,0,1,0,0,1,3,0,5,0,0,2,11,12,0,5,11,15,0,27,15,31,35,74,35,35,85,65,161},{0,0,0,0,1,0,0,2,1,2,1,5,0,3,11,5,2,3,11,15,17,11,35,17,56,35,17,56,85,140},{0,0,0,0,0,1,2,0,3,6,5,6,3,9,12,12,11,17,27,22,18,35,50,42,78,74,56,120,128,209},{0,0,0,0,0,0,1,0,0,3,0,0,2,6,6,0,5,11,12,0,12,15,22,27,50,31,35,74,53,128},{0,0,0,0,0,0,0,1,0,1,0,0,0,2,5,0,1,2,5,0,11,5,15,11,35,15,11,35,35,85},{0,0,0,0,0,0,0,0,1,2,1,3,0,3,6,5,2,3,11,12,9,11,27,17,42,35,17,56,74,120},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,0,1,2,5,0,6,5,12,11,27,15,11,35,31,74},{0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,0,T^2,0,3,2,3,6,6,3*T^2,11,12,9,18,27,17,42,50,78},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,2,5,3,2,11,3,17,11,3,17,35,56},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,0,5,0,0,6,0,0,12,22,0,15,31,0,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,3,0,0,5,12,0,5,15,0,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,2,1,5,2,11,5,2,11,15,35},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,0,2,3,T^2,2,6,3,9,11,3,17,27,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,0,5,6,6,12,12,11,27,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,6,0,5,12,0,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,6,5,2,11,12,27},{0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,1,0,0,2,0,3,2,0,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,1,5,0,15},{0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,1,0,0,0,3,2,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,1,5,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5289)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & -1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & -1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}2 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 1 & 0 \\ 1 & 2 & 1 & 1 & 3 & 2 & 2 & 0 & 3 & 1 & 1 & 0 & 2 & 2 & 0 & 1 & -1 & 1 & 2 & 0 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & 1 & -1 & -1 & 0 & 0 & -1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, 1, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 4, 5}, {1, 3, 6, 7}, {3, 5, 6, 7}, {0, 1, 8}, {0, 2, 4, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{3,4,5},{0,4,5},{2,5,6},{0,2,5},{0,1,4},{1,3,4},{3,5,6}},{2,1,2})
Cox degrees: {{0,0,1},{-1,1,1},{1,-1,0},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{2,1,4},{1,2,4},{1,1,4},{2,1,3},{0,3,4},{1,2,3},{0,2,4},{2,0,3},{0,3,3},{1,1,3},{2,1,2},{1,0,3},{0,2,3},{1,2,2},{2,0,2},{0,1,3},{2,-1,2},{1,1,2},{0,2,2},{1,0,2},{2,0,1},{1,1,1},{0,1,2},{2,-1,1},{1,-1,2},{1,0,1},{0,0,2},{0,1,1},{2,-1,0},{1,-1,1},{0,0,1},{1,0,0},{1,-1,0},{0,0,0}}
Ext matrix: {{1,2,3,4,3,7,5,7,10,15,10,18,23,16,22,31,28,40,58,58,50,82,91,74,64,133,109,196,155,165,259,253,341,504},{0,1,1,1,2,4,3,1,7,7,4,7,15,10,7,18,7,22,40,28,22,50,58,28,28,74,64,133,74,84,165,155,195,341},{0,0,1,0,0,0,2,1,0,4,0,7,7,0,4,15,7,10,16,22,10,20,40,22,28,50,58,82,50,74,133,95,155,253},{0,0,0,1,0,2,0,1,3,3,4,3,5,7,7,6,7,15,23,18,22,40,31,28,18,58,34,91,74,64,109,133,165,259},{0,0,0,0,1,1,1,0,4,1,1,1,7,4,1,7,1,7,22,7,7,22,28,7,7,28,28,74,28,28,84,74,84,195},{0,0,0,0,0,1,0,0,2,1,1,1,3,4,1,3,1,7,15,7,7,22,18,7,7,28,18,58,28,28,64,74,84,165},{0,0,0,0,0,0,1,0,0,1,0,1,4,0,1,7,1,4,10,7,4,10,22,7,7,22,28,50,22,28,74,50,74,155},{0,0,0,0,0,0,0,1,0,2,0,3,3,0,4,5,7,7,10,15,10,16,23,22,18,40,31,58,50,58,91,82,133,196},{0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,0,1,7,1,1,7,7,1,1,7,7,28,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,1,0,1,2,0,1,3,1,4,7,7,4,10,15,7,7,22,18,40,22,28,58,50,74,133},{0,0,2*T^2,0,0,0,4*T^2,0,0,0,1,3*T^2,0,2,1,6*T^2,1,3,5,3,7,15,6,7,3+4*T^2,18,6+8*T^2,31,28,18,34,58,64,109},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,0,4,0,0,7,4,7,10,15,16,10,22,40,20,50,82},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,4,1,1,4,7,1,1,7,7,22,7,7,28,22,28,74},{0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,1,0,3*T^2,0,1,3,1,1,7,3,1,1,7,3+4*T^2,18,7,7,18,28,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,3,4,7,5,7,3,15,6,23,22,18,31,40,58,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,4,1,1,4,7,10,4,7,22,10,22,50},{0,0,0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,1,0,0,2,0,0,3,4,3,7,5,10,10,15,23,16,40,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,1,4,3,1,1,7,3,15,7,7,18,22,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,1,1,7,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,1,4,3,7,4,7,15,10,22,40},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,2*T^2,0,0,0,4*T^2,0,0,0,0,1,2,0,1,3*T^2,3,6*T^2,5,7,3,6,15,18,31},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,0,0,0,1,3*T^2,3,1,1,3,7,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,1,1,7,4,7,22},{0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,3,4,3,5,7,15,23},{0,0,0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,4,7,0,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,3,4,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,T^3,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,0,0,0,2*T^2,0,4*T^2,0,1,0,0,2,3,5},{0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,1,3},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5290)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 0 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 4 & 3 & 4 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 3 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 4 & 3 & 3 & 2 & 4 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 3, 4}, {3, 4, 5, 7}, {2, 5, 6, 7}, {0, 1, 8}, {0, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1},{1,1,2}},{{4,5,6},{1,4,5},{2,4,6},{3,5,6},{2,3,6},{0,1,5},{0,3,5}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,1},{0,1,1},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,4,5},{2,3,5},{2,4,4},{1,4,4},{2,4,3},{2,3,4},{1,4,3},{2,3,3},{2,2,4},{1,3,4},{1,3,3},{2,2,3},{2,3,2},{1,2,4},{0,3,3},{1,2,3},{2,1,3},{2,2,2},{1,3,2},{0,2,3},{0,3,2},{1,2,2},{2,1,2},{1,1,3},{1,2,1},{1,1,2},{0,2,2},{0,1,2},{0,2,1},{1,1,1},{1,0,2},{0,1,1},{1,0,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,3,6,5,10,10,9,18,20,14,15,21,36,30,30,27,42,35,60,50,54,84,100,78,130,117,150,140,210,225,315,294,465},{0,1,0,0,0,2,0,3,6,3,5,10,4,9,6,18,20,14,7,21,9,27,30,36,36,60,35,78,49,84,100,117,150,210,156,294},{0,0,1,1,2,2,3,6,3,2,9,10,10,3,9,15,14,20,18,15,21,36,30,21,60,54,42,63,78,100,72,130,140,182,210,315},{0,0,0,1,0,0,2,0,0,2,6,0,0,3,9,10,0,0,10,15,18,20,0,14,30,30,36,54,60,50,40,100,70,140,150,225},{0,3*T^2,0,0,1,0,1,2,5*T^2,0,2,3,6,6*T^2,2,3,4+7*T^2,10,9,3,9,15,14,4+9*T^2,36,21,15,21,42,54,27+12*T^2,63,72,84,130,182},{0,0,0,0,0,1,0,2,2,1,3,6,3,2,3,9,10,10,5,9,6,18,20,15,27,36,21,42,35,60,54,78,100,130,117,210},{0,2*T^2,0,0,0,0,1,0,3*T^2,0,2,0,0,5*T^2,2,3,4*T^2,0,6,3,9,10,0,4+7*T^2,20,14,15,21,36,30,18+9*T^2,54,40,72,100,140},{0,0,0,0,0,0,0,1,0,0,1,2,2,0,1,2,3,6,3,2,3,9,10,3,18,15,9,15,21,36,21,42,54,63,78,130},{0,0,0,0,0,0,0,0,1,0,0,2,0,1,0,3,6,3,0,3,0,5,10,9,7,18,6,21,9,27,36,35,60,78,49,117},{0,0,0,0,0,0,0,0,0,1,2,0,0,2,3,6,0,0,3,9,5,10,0,10,14,20,18,36,27,30,30,60,50,100,84,150},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,0,0,2,2,3,6,0,3,10,10,9,15,18,20,14,36,30,54,60,100},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,2,0,1,0,3,6,2,5,9,3,9,6,18,15,21,36,42,35,78},{0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,1,3*T^2,0,0,5*T^2,2,1,0,1,2,3,6*T^2,9,3,2,3,9,15,4+9*T^2,15,21,21,42,63},{0,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,1,0,2,0,0,0,3,0,3,0,6,4,10,5,18,7,14,20,27,30,60,36,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,0,0,0,0,0,6,10,10,0,0,20,0,30,30,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,2,0,2,3,6,3,9,5,10,10,18,20,36,27,60},{0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,0,T^3,0,1,0,0,0,2*T^3,0,2,1,0,3,0,3,0,5,9,6,18,21,9,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,0,3,2,1,2,3,9,3,9,15,15,21,42},{0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,3*T^2,0,1,0,1,2,0,5*T^2,6,3,2,3,9,10,4+7*T^2,15,14,21,36,54},{0,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,1,0,0,0,0,0,0,2,6,3,0,0,10,0,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,1,0,0,3*T^2,0,0,2,3,6,0,4*T^2,10,0,14,20,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,1,2,3,6,3,9,10,15,18,36},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,1,0,1,0,3,2,3,9,9,6,21},{0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,1,0,2,0,3,0,3,6,5,10,18,7,27},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,0,0,3*T^2,1,0,0,0,1,2,5*T^2,2,3,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,2,3,6,9,5,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,0,6,0,10,10,20},{0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,0,3*T^2,2,0,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,3,9},{0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,1,0,2,3,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,6},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5295)$ |
3 |
27 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 3 & 1 & 2 & 3 & 0 & 2 & 1 & 1 & 0 & 3 & 2 & 0 & 3 & 1 & 0 & 2 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 0 \\ 2 & 1 & 0 & 2 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {-1, 1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4}, {2, 3, 4, 5, 7}, {5, 6, 7}, {0, 1, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{-1,0,1},{1,0,1},{0,1,1}},{{0,5,6},{3,5,6},{2,4,6},{0,2,6},{1,3,4},{1,3,5},{3,4,6},{0,1,5}},{2,1,3})
Cox degrees: {{-1,0,1},{1,-1,0},{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (32): {{3,2,2},{3,1,2},{3,0,2},{2,2,2},{2,1,2},{3,2,1},{2,0,2},{1,2,2},{3,1,1},{1,1,2},{2,2,1},{3,0,1},{0,2,2},{2,1,1},{1,0,2},{1,2,1},{0,1,2},{3,1,0},{2,0,1},{0,0,2},{3,0,0},{1,1,1},{0,2,1},{2,1,0},{1,0,1},{0,1,1},{2,0,0},{0,0,1},{1,1,0},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,5,9,6,13,15,12,25,21,18,35,39,35,55,55,42,57,75,63,95,120,110,135,195,162,270,240,345,462,648},{0,1,2,1,5,1,9,5,6,15,6,12,15,21,25,21,35,22,39,55,42,55,55,61,95,120,110,195,141,240,286,462},{0,0,1,0,1,0,5,1,1,5,1,6,5,6,15,6,15,6,21,35,22,21,21,22,55,55,61,120,61,141,141,286},{0,0,0,1,2,1,3,5,2,9,6,3,15,12,13,21,25,12,18,35,18,39,55,42,57,95,63,135,110,162,240,345},{0,0,0,0,1,0,2,1,1,5,1,2,5,6,9,6,15,6,12,25,12,21,21,22,39,55,42,95,61,110,141,240},{0,0,T^2,0,0,1,3*T^2,0,2,0,5,3,0,9,6*T^2,15,0,12,13,10*T^2,18,25,35,39,35,55,57,75,95,135,195,270},{0,0,0,0,0,0,1,0,0,1,0,1,1,1,5,1,5,1,6,15,6,6,6,6,21,21,22,55,22,61,61,141},{0,0,0,0,0,0,0,1,0,2,1,0,5,2,3,6,9,2,3,13,3,12,21,12,18,39,18,57,42,63,110,162},{0,0,0,0,0,0,0,0,1,0,1,2,0,5,0,5,0,6,9,0,12,15,15,21,25,35,39,55,55,95,120,195},{0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,1,5,1,2,9,2,6,6,6,12,21,12,39,22,42,61,110},{0,0,0,0,0,0,T^2,0,0,0,1,0,0,2,3*T^2,5,0,2,3,6*T^2,3,9,15,12,13,25,18,35,39,57,95,135},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,5,0,6,5,5,6,15,15,21,35,21,55,55,120},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,0,0,3,0,2,6,2,3,12,3,18,12,18,42,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,2,0,2,5,5,6,9,15,12,25,21,39,55,95},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,0,1,T^4,1,5,1,1,1,1,6,6,6,21,6,22,22,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,0,0,3*T^2,0,2,5,2,3,9,3,13,12,18,39,57},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,1,T^4,0,2,0,1,1,1,2,6,2,12,6,12,22,42},{0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,6*T^2,0,0,1,0,10*T^2,2,0,0,5,0,0,9,0,15,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,5,5,6,15,6,21,21,55},{T^4,0,0,0,0,6*T^4,0,0,T^4,0,T^4,0,0,0,0,0,0,6*T^4,0,1,T^4,0,0,T^4,1,1,1,6,1,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,5,0,5,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,5,2,9,6,12,21,39},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,0,2,0,3,2,3,12,18},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,1,0,0,2,0,5,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,5,15},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,1,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5296)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 1 & 0 & 0 & 2 & 0 & 1 & 1 & 2 & 1 & 0 & 0 & 2 & 0 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4}, {2, 3, 4, 5, 7}, {5, 6, 7}, {0, 1, 8}, {0, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{1,3,4},{0,2,5},{3,4,5},{0,1,4}},{2,1,1})
Cox degrees: {{0,0,1},{1,-1,0},{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (31): {{3,2,2},{3,1,2},{3,2,1},{3,0,2},{2,2,2},{3,1,1},{2,1,2},{2,2,1},{3,1,0},{3,0,1},{2,0,2},{1,2,2},{3,0,0},{2,1,1},{1,1,2},{1,2,1},{2,1,0},{2,0,1},{1,0,2},{0,2,2},{2,0,0},{1,1,1},{0,1,2},{0,2,1},{1,1,0},{1,0,1},{0,1,1},{1,0,0},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,5,5,9,11,8,8,13,15,14,23,25,35,38,35,35,35,62,65,55,85,110,95,145,170,205,250,370},{0,1,0,2,1,2,5,2,3,5,9,5,8,11,15,11,17,23,25,15,38,35,35,35,56,65,85,110,145,140,250},{0,0,1,3*T^2,0,2,0,5,5,3,6*T^2,0,8,9,0,15,23,13,10*T^2,0,35,25,0,35,65,35,55,95,75,145,205},{0,0,0,1,0,0,1,0,0,2,5,1,3,2,5,2,3,11,15,5,17,11,15,11,17,35,35,56,85,56,140},{0,0,0,0,1,0,2,2,0,0,3,5,0,5,9,11,8,8,13,15,14,23,25,35,38,35,65,62,95,110,170},{0,0,0,0,0,1,0,1,2,2,0,0,5,5,0,5,11,9,0,0,23,15,0,15,35,25,35,65,55,85,145},{0,0,0,0,0,0,1,0,0,0,2,1,0,2,5,2,3,5,9,5,8,11,15,11,17,23,35,38,65,56,110},{0,0,0,T^2,0,0,0,1,0,0,3*T^2,0,0,2,0,5,5,3,6*T^2,0,8,9,0,15,23,13,25,35,35,65,95},{0,0,0,3*T^2,0,0,0,0,1,0,6*T^2,0,2,0,0,0,5,0,10*T^2,0,9,0,0,0,15,0,0,25,0,35,55},{0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,1,2,5,0,0,11,5,0,5,11,15,15,35,35,35,85},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,2,5,1,3,2,5,2,3,11,11,17,35,17,56},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,3,5,0,5,9,11,8,8,23,14,35,38,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,5,0,0,0,5,0,0,15,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,0,0,5,5,0,5,11,9,15,23,25,35,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,2,5,2,3,5,11,8,23,17,38},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,0,3*T^2,0,0,2,0,5,5,3,9,8,13,23,35},{0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,1,0,6*T^2,0,2,0,0,0,5,0,0,9,0,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,1,2,5,5,11,15,11,35},{0,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,2,2,3,11,3,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,5,0,8,8,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,5,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,5,5,9,11,23},{0,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,0,2,0,3,5,8},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,3*T^2,0,0,0,0,0,1,0,0,2,0,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,5,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5297)$ |
3 |
27 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
32: $\begin{pmatrix}2 & 2 & 2 & 1 & 3 & 1 & 2 & 3 & 0 & 1 & 2 & 1 & 3 & 2 & 0 & 0 & -1 & 1 & 3 & -1 & 2 & 1 & 0 & 2 & 0 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 2 & 1 & 0 & 2 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 2 & 1 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 1 & 2 & 2 & 2 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 1, 1}, {-1, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 6}, {4, 5, 7}, {2, 3, 4, 6, 7}, {0, 1, 8}, {0, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{0,3,5},{0,2,5},{1,3,4},{3,5,6},{0,1,3},{2,5,6},{3,4,6}},{2,1,3})
Cox degrees: {{-1,0,1},{1,-1,0},{1,0,0},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (32): {{2,2,2},{2,1,2},{2,0,2},{1,2,2},{3,1,1},{1,1,2},{2,2,1},{3,0,1},{0,2,2},{1,0,2},{2,1,1},{1,2,1},{3,1,0},{2,0,1},{0,1,2},{0,0,2},{-1,2,2},{1,1,1},{3,0,0},{-1,1,2},{2,1,0},{1,0,1},{0,2,1},{2,0,0},{0,1,1},{-1,2,1},{1,1,0},{0,0,1},{-1,1,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,5,3,9,7,5,15,13,16,25,18,25,25,35,35,49,32,55,61,73,65,100,115,140,154,165,230,238,325,480},{0,1,2,1,1,5,1,3,5,9,7,7,7,16,15,25,15,25,18,35,28,49,25,61,65,65,80,115,140,154,185,325},{0,0,1,0,0,1,0,1,1,5,1,1,1,7,5,15,5,7,7,15,7,25,7,28,25,25,28,65,65,80,80,185},{0,0,0,1,0,2,1,0,5,3,3,7,3,5,9,13,15,16,6,25,18,25,25,32,49,65,61,73,115,100,154,238},{0,0,0,0,1,0,1,2,0,0,5,5,7,9,0,0,0,15,16,0,25,25,15,49,35,35,65,55,70,115,140,230},{0,0,0,0,0,1,0,0,1,2,1,1,1,3,5,9,5,7,3,15,7,16,7,18,25,25,28,49,65,61,80,154},{0,0,3*T^2,0,0,0,1,0,0,6*T^2,2,5,3,3,0,10*T^2,0,9,5,0,16,13,15,25,25,35,49,35,55,73,115,165},{0,0,0,0,0,0,0,1,0,0,1,1,1,5,0,0,0,5,7,0,7,15,5,25,15,15,25,35,35,65,65,140},{0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,3,5,3,0,9,3,5,7,6,16,25,18,25,49,32,61,100},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,1,1,1,5,1,7,1,7,7,7,7,25,25,28,28,80},{0,0,0,0,0,0,0,0,0,0,1,1,1,2,0,0,0,5,3,0,7,9,5,16,15,15,25,25,35,49,65,115},{0,0,T^2,0,0,0,0,0,0,3*T^2,0,1,0,0,0,6*T^2,0,2,0,0,3,3,5,5,9,15,16,13,25,25,49,73},{0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,1,0,0,10*T^2,0,0,2,0,5,0,0,9,0,0,15,0,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,5,1,7,5,5,7,15,15,25,25,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,1,0,5,1,3,1,3,7,7,7,16,25,18,28,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,1,1,7,7,7,7,28},{0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,T^3,0,0,0,1,0,2*T^3,2,0,0,1,0,3,7,3,5,16,6,18,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,1,3,5,5,7,9,15,16,25,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,0,0,5,0,0,15,15,35},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,1,0,0,0,0,1,1,1,3,7,3,7,18},{0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,0,0,1,0,0,2,0,0,5,0,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,5,5,7,7,25},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,1,0,2,5,3,3,9,5,16,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,5,3,7,16},{0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,T^3,0,0,T^2,0,0,2*T^3,0,0,0,0,0,0,1,0,0,2,0,3,5},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,7},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5298)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}3 & 3 & 2 & 2 & 3 & 1 & 2 & 3 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 3 & 2 & 2 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 0 & 0 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 1, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 6}, {4, 5, 7}, {2, 3, 4, 6, 7}, {0, 1, 8}, {0, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{0,2,4},{2,4,5},{3,4,5},{0,1,3}},{2,1,2})
Cox degrees: {{0,0,1},{1,-1,0},{1,0,0},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{3,1,2},{3,0,2},{2,2,2},{2,1,2},{3,1,1},{1,2,2},{2,0,2},{3,0,1},{2,2,1},{3,1,0},{1,1,2},{2,1,1},{0,2,2},{1,0,2},{1,2,1},{3,0,0},{2,0,1},{2,1,0},{1,1,1},{0,1,2},{0,0,2},{0,2,1},{2,0,0},{1,0,1},{0,1,1},{1,1,0},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,1,5,3,5,9,9,3,6,15,15,15,25,15,21,33,30,45,35,55,45,72,85,105,90,180,180,210,375},{0,1,0,1,0,1,5,3,0,0,5,3,5,15,3,6,15,6,15,15,35,15,30,45,45,30,105,90,90,210},{0,0,1,2,1,5,3,2,3,3,9,9,15,13,15,9,15,21,33,25,35,45,42,51,85,72,125,124,180,285},{0,0,0,1,0,1,2,1,0,0,5,3,5,9,3,3,9,6,15,15,25,15,21,33,45,30,85,72,90,180},{0,0,0,0,1,0,0,2,1,3,0,5,0,0,5,9,9,15,15,0,0,15,33,25,35,45,55,85,105,180},{0,0,0,0,0,1,0,0,0,0,2,1,5,3,3,1,2,3,9,9,13,15,9,15,33,21,51,42,72,124},{0,0,0,0,0,0,1,0,0,0,1,0,1,5,0,0,3,0,3,5,15,3,6,15,15,6,45,30,30,90},{0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,3,5,3,5,0,0,5,15,15,15,15,35,45,45,105},{0,3*T^2,0,0,0,0,6*T^2,0,1,1,0,2,0,10*T^2,5,2,3,9,9,0,15*T^2,15,15,13,25,33,35,51,85,125},{0,3*T^2,0,0,0,0,6*T^2,0,0,1,0,0,0,10*T^2,0,2,0,5,0,0,15*T^2,0,9,0,0,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,1,0,1,2,0,0,1,0,3,5,9,3,3,9,15,6,33,21,30,72},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,3,5,0,0,5,9,9,15,15,25,33,45,85},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,2,3,3,1,2,9,3,15,9,21,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,5,0,0,3,3,0,15,6,6,30},{0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,1,0,0,1,2,0,10*T^2,5,2,3,9,9,13,15,33,51},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,5,0,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,3,5,5,3,15,15,15,45},{0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,1,0,0,10*T^2,0,2,0,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,5,3,9,9,15,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,1,3,0,9,3,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,1,0,0,2,1,3,2,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,3,3,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,3,9},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5299)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & -2 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & -1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
38: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 1 & 2 & 0 & 3 & 1 & 2 & 3 & 0 & 1 & 2 & 1 & 0 & -1 & 1 & -1 & 2 & 0 & 3 & 1 & 3 & 1 & 0 & 2 & 2 & 0 & -1 & 1 & -1 & 2 & 1 & 0 & 1 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 3 & 1 & 3 & 2 & 1 & 0 & 2 & 3 & 0 & 1 & 2 & 0 & 1 & 2 & 3 & 1 & 2 & 0 & 1 & 3 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -2, 1, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 3, 4}, {3, 4, 5, 7}, {2, 5, 6, 7}, {0, 1, 8}, {0, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-2,-1},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{2,3,4},{0,2,4},{3,4,5},{0,1,2},{0,1,5}},{4,1,1})
Cox degrees: {{0,0,1},{1,-2,-1},{0,1,1},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (38): {{2,3,3},{2,2,3},{2,3,2},{2,1,3},{2,2,2},{2,1,2},{2,2,1},{2,0,2},{1,3,3},{2,1,1},{1,2,3},{1,3,2},{2,0,1},{2,1,0},{1,2,2},{1,1,3},{2,0,0},{2,-1,1},{1,1,2},{2,-1,0},{1,2,1},{1,0,2},{0,3,3},{1,1,1},{0,3,2},{1,1,0},{1,0,1},{0,2,3},{0,2,2},{1,0,0},{1,-1,1},{0,1,2},{1,-1,0},{0,2,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,6,10,10,14,12,20,18,24,30,30,42,24,50,40,60,70,70,78,63,110,116,165,150,84,168,240,190,220,315,270,375,480,552,738},{0,1,0,2,2,6,3,10,6,10,12,10,20,14,24,18,30,30,42,50,36,60,42,70,70,98,110,63,116,165,150,168,240,174,270,375,378,552},{0,0,1,2*T^2,2,3,6,4+4*T^2,3,10,4,12,14,20,18,5+3*T^2,30,18+6*T^2,24,40,42,30+6*T^2,24,60,63,110,78,30,84,150,96+9*T^2,105,190,168,220,272,375,480},{0,0,0,1,0,2,0,6,2,3,6,3,10,4,10,12,14,20,24,30,14,42,24,36,36,48,70,42,70,98,110,116,165,98,174,270,232,378},{0,0,0,0,1,2,2,3,2,6,3,6,10,10,12,4,20,14,18,30,24,24,18,42,42,70,60,24,63,110,78,84,150,116,168,220,270,375},{0,0,0,0,0,1,0,2,1,2,2,2,6,3,6,3,10,10,12,20,10,18,12,24,24,36,42,18,42,70,60,63,110,70,116,168,174,270},{0,0,0,0,0,0,1,2*T^2,0,2,0,2,3,6,3,0,10,4+4*T^2,4,14,12,5+3*T^2,4,18,18,42,24,5,24,60,30+6*T^2,30,78,63,84,105,168,220},{0,0,0,0,0,0,0,1,0,0,1,0,2,0,2,2,3,6,6,10,3,12,6,10,10,14,24,12,24,36,42,42,70,36,70,116,98,174},{0,0,0,0,0,0,0,0,1,0,2,2,0,0,6,3,0,0,10,0,10,14,12,20,24,30,30,18,42,50,40,60,70,70,110,150,165,240},{0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,0,6,3,3,10,6,4,3,12,12,24,18,4,18,42,24,24,60,42,63,84,116,168},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,0,6,0,3,10,6,10,10,14,20,12,24,30,30,42,50,36,70,110,98,165},{0,0,0,T^2,0,0,0,2*T^2,0,0,0,1,0,0,2,2*T^2,0,3*T^2,3,0,6,4+4*T^2,3,10,12,20,14,4,18,30,18+6*T^2,24,40,42,60,78,110,150},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,2,2,6,2,3,2,6,6,10,12,3,12,24,18,18,42,24,42,63,70,116},{0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,1,0,3*T^3,2,2*T^2,0,3,2,0,0,3,3,12,4,0,4,18,5+3*T^2,5,24,18,24,30,63,84},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,2,3,2,6,6,10,10,3,12,20,14,18,30,24,42,60,70,110},{0,0,3*T^3,0,0,0,4*T^3,0,0,0,0,0,0,5*T^3,0,1,0,0,2,0,0,6,2,3,3,4,10,6,10,14,20,24,30,14,36,70,48,98},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,2,2,6,3,0,3,12,4,4,18,12,18,24,42,63},{T^3,0,2*T^3,0,0,0,0,0,2*T^3,0,0,4*T^3,0,0,0,0,0,1,1,2,0,2,1+3*T^3,2,2+6*T^3,3,6,2,6,10,12,12,24,10,24,42,36,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,2,3,6,2,6,10,10,12,20,10,24,42,36,70},{0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,0,0,0,1,1+3*T^3,2,2,0,2,6,3,3,12,6,12,18,24,42},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,1,2*T^2,0,2,2,6,3,0,3,10,4+4*T^2,4,14,12,18,24,42,60},{0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,0,0,0,0,0,1,0,0,0,0,2,1,2,3,6,6,10,3,10,24,14,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,2,6,0,0,10,0,10,20,30,30,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,0,2,6,3,3,10,6,12,18,24,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,1,0,0,0,2,0,3*T^2,3,0,6,10,14,20,30},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,T^2,0,0,0,0,0,0,0,1,0,0,0,2,2*T^2,0,3,2,3,4,12,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,6,2,6,12,10,24},{0,0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,4*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,6,0,3,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,6,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,3,6,12},{0,0,T^3,0,0,0,2*T^3,0,T^3,0,0,2*T^3,0,3*T^3,0,0,0,0,0,0,0,0,2*T^3,0,4*T^3,0,0,0,0,0,1,1,2,0,2,6,3,10},{0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,0,1,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,0,1,2,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5301)$ |
3 |
28 |
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9: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & -1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}3 & 2 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 3 & 3 & 2 & 1 & 1 & 2 & 3 & 2 & 0 & 0 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 3 & 1 & 2 & 1 & 0 & 1 & 2 & 3 & 0 & 0 & 2 & 0 & -1 & 1 & 1 & 2 & 0 & -1 & 1 & 3 & 2 & 1 & -1 & 0 & 1 & -1 & 0 & 2 & 1 & 0 & 1 & -1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 0 & 1 & 1 & 2 & 1 & 1 & 0 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {1, 1, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 1, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 3, 4}, {3, 4, 5, 7}, {2, 5, 6, 7}, {0, 1, 8}, {2, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{3,4,5},{0,1,4},{0,2,5},{1,3,4}},{2,1,1})
Cox degrees: {{1,-1,0},{1,-1,0},{0,1,1},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{3,2,2},{2,3,2},{3,1,2},{2,2,2},{3,1,1},{3,0,2},{2,1,2},{2,2,1},{1,3,2},{3,0,1},{2,0,2},{1,2,2},{3,0,0},{3,-1,1},{2,1,1},{1,1,2},{1,2,1},{2,0,1},{3,-1,0},{2,1,0},{0,3,2},{0,2,2},{1,1,1},{2,-1,1},{2,0,0},{1,1,0},{2,-1,0},{1,0,1},{0,2,1},{0,1,1},{1,0,0},{0,1,0},{1,-1,0},{0,0,0}}
Ext matrix: {{1,2,2,6,4,3,10,10,10,7,14,20,10,10,22,30,40,34,16,28,30,50,70,46,52,100,76,100,110,170,160,260,220,380},{0,1,0,2,0,4*T^2,3,4,6,0,4+6*T^2,10,0,6*T^2,7,14,22,10,0,10,20,30,34,13+9*T^2,16,52,22,46,70,100,76,160,100,220},{0,0,1,2,1,2,6,2,3,4,10,10,4,7,10,20,16,22,10,10,14,30,40,34,28,49,52,70,58,110,100,152,160,260},{0,0,0,1,0,0,2,1,2,0,3,6,0,0,4,10,10,7,0,4,10,20,22,10,10,28,16,34,40,70,52,100,76,160},{0,0,0,0,1,0,0,2,0,2,0,0,4,3,6,0,10,10,7,10,0,0,20,14,22,40,34,30,30,50,70,110,100,170},{0,0,0,0,0,1,2,0,0,1,6,3,1,4,2,10,3,10,4,2,4,14,16,22,10,16,28,40,22,58,49,70,100,152},{0,0,0,0,0,0,1,0,0,0,2,2,0,0,1,6,2,4,0,1,3,10,10,7,4,10,10,22,16,40,28,49,52,100},{0,0,0,0,0,2*T^2,0,1,0,0,3*T^2,0,0,4*T^2,2,0,6,3,0,4,0,0,10,4+6*T^2,7,22,10,14,20,30,34,70,46,100},{0,0,0,0,0,2*T^2,0,0,1,0,4*T^2,2,0,3*T^2,0,3,4,0,0,0,6,10,7,6*T^2,0,10,0,10,22,34,16,52,22,76},{0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,0,3,6,4,2,0,0,10,10,10,16,22,20,14,30,40,58,70,110},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,1,0,0,0,3,2,4,1,2,4,10,3,16,10,16,28,49},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,0,0,0,2,6,4,0,0,4,0,7,10,22,10,28,16,52},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,2,0,0,0,0,6,10,10,0,0,0,20,30,30,50},{0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,1,0,0,0,2,1,0,4*T^3,0,3,6,2,3,10,10,4,14,16,22,40,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,0,1,0,0,6,3,4,10,7,10,10,20,22,40,34,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,1,0,0,1,0,4,2,10,4,10,10,28},{0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,2*T^2,0,0,1,0,0,0,0,0,2,4*T^2,0,4,0,3,6,10,7,22,10,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,1,2,4,6,3,10,10,16,22,40},{0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,1,0,4*T^3,0,0,0,2,3,6,0,0,0,10,14,20,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,0,0,0,3*T^2,2,6,3,0,0,0,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,1,2,0,3*T^2,0,0,0,0,4,7,0,10,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,4,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,2,2,6,4,10,7,22},{0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,3*T^3,0,0,1,0,0,1,2,0,3,2,3,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,0,0,6,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,1,0,0,0,0,2,6,3,10},{0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,1,0,0,0,2,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,4,10},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,1,2,0,4,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5302)$ |
3 |
28 |
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9: $\begin{pmatrix}1 & 1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ -1 & -1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}2 & 1 & 2 & 3 & 1 & 0 & 3 & 2 & 1 & 3 & 1 & 0 & 2 & 0 & 2 & 2 & 3 & -1 & 1 & -1 & 0 & 0 & 1 & 2 & -1 & 2 & 1 & 1 & 0 & 1 & 0 & -1 & -1 & 1 & 0 & 0 \\ 1 & 2 & 0 & 0 & 1 & 3 & -1 & 1 & 2 & 0 & 0 & 2 & 0 & 1 & 1 & -1 & -1 & 3 & 1 & 2 & 2 & 0 & 0 & 0 & 1 & -1 & 1 & -1 & 1 & 0 & 0 & 2 & 1 & -1 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 2 & 2 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 2 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 1, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 3, 6}, {2, 4, 5, 7}, {3, 4, 6, 7}, {0, 1, 8}, {2, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{2,4,5},{3,4,5},{0,1,3},{0,2,4}},{2,1,2})
Cox degrees: {{1,-1,0},{1,-1,0},{-1,1,1},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{2,1,2},{1,2,2},{2,0,2},{3,0,1},{1,1,2},{0,3,2},{3,-1,1},{2,1,1},{1,2,1},{3,0,0},{1,0,2},{0,2,2},{2,0,1},{0,1,2},{2,1,0},{2,-1,1},{3,-1,0},{-1,3,2},{1,1,1},{-1,2,2},{0,2,1},{0,0,2},{1,0,1},{2,0,0},{-1,1,2},{2,-1,0},{1,1,0},{1,-1,1},{0,1,1},{1,0,0},{0,0,1},{-1,2,1},{-1,1,1},{1,-1,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,2,6,3,4,5,8,8,10,10,14,20,14,23,22,14,26,30,38,30,50,44,50,83,68,74,80,140,130,110,190,224,200,340},{0,1,0,0,2,2,0,2,5,3,3,6,4,10,8,6,6,10,14,20,26,14,23,22,30,36,44,32,50,83,74,80,130,122,140,224},{0,0,1,0,2,0,2,0,0,0,6,3,5,10,0,14,8,4,8,14,11,20,26,14,30,44,20,50,38,68,80,50,110,140,92,200},{0,0,0,1,0,0,2,2,3,5,0,0,6,0,8,10,14,0,10,0,14,0,20,26,0,50,38,30,30,80,50,40,70,130,110,190},{0,0,0,0,1,0,0,0,0,0,2,2,2,6,0,4,3,3,5,10,8,10,14,8,20,22,14,23,26,44,50,38,80,83,68,140},{0,0,4*T^2,0,0,1,6*T^2,0,2,0,6*T^2,2,0,3,3,9*T^2,0,6,4,10,14,4+8*T^2,6,6,14,9,22,8+12*T^2,23,36,32,50,74,50,83,122},{0,0,0,0,0,2*T^3,1,0,0,0,0,0,2,0,0,6,5,3*T^3,3,0,4,0,10,8,0,26,11,20,14,38,30,18,40,80,50,110},{0,0,0,0,0,0,0,1,2,2,0,0,2,0,5,3,4,0,6,0,10,0,10,14,0,23,26,14,20,50,30,30,50,74,80,130},{0,0,2*T^2,0,0,0,4*T^2,0,1,0,3*T^2,0,0,0,2,6*T^2,0,0,2,0,6,4*T^2,3,4,0,6,14,4+8*T^2,10,23,14,20,30,32,50,74},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,2,0,0,0,0,0,0,6,0,10,10,0,0,20,0,0,0,30,30,50},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,0,0,0,3,0,6,5,0,10,8,0,14,8,14,26,11,38,44,20,68},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,2,2,6,5,3,4,3,10,6,8,6,14,22,23,26,50,36,44,83},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,2,0,3,0,6,5,0,14,8,10,10,26,20,14,30,50,38,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,2,2,0,6,3,0,4,5,8,14,8,26,22,14,44},{0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,1,3*T^2,0,0,0,0,0,0,0,2,0,3,6,4*T^2,0,10,0,0,0,14,20,30},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,2*T^3,0,0,0,0,2,0,0,5,0,6,3,8,10,4,14,26,11,38},{0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,1,3*T^3,0,0,0,0,0,2,0,6,3,0,0,10,0,0,0,20,14,30},{0,0,2*T^2,2*T^3,0,0,3*T^2+3*T^3,0,0,2*T^3,4*T^2,0,0,0,0,6*T^2,3*T^3,1,0,2,2,6*T^2,0,0,3,0,3,9*T^2,4,6,6,14,23,9,22,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,2,0,4,5,3,6,14,10,10,20,23,26,50},{0,0,0,T^3,0,0,2*T^3,0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,1,0,0,0,0,2,0,0,0,2,3,4,5,14,6,8,22},{0,0,T^2,0,0,0,2*T^2,0,0,0,2*T^2,0,0,0,0,4*T^2,0,0,0,0,1,3*T^2,0,0,0,0,2,6*T^2,2,4,3,6,10,6,14,23},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,0,0,5,0,8,8,0,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,2,5,6,3,10,14,8,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,0,0,6,0,0,0,10,10,20},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,5,3,0,8},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,6,3,10},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,1,3*T^2,0,2,0,0,0,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,5,0,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,2,6,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,0,5},{0,0,0,T^3,0,0,2*T^3,0,0,T^3,T^2,0,0,0,0,2*T^2,2*T^3,0,0,0,0,2*T^2,0,0,0,0,0,4*T^2,0,0,0,1,2,0,2,4},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5303)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 0 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,2,3},{2,1,3},{1,2,3},{2,2,2},{1,1,3},{1,2,2},{0,2,3},{2,1,2},{2,2,1},{1,1,2},{0,1,3},{1,2,1},{2,1,1},{0,2,2},{2,0,2},{0,1,2},{0,2,1},{2,0,1},{2,1,0},{1,0,2},{1,1,1},{0,0,2},{0,1,1},{1,1,0},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,3,6,9,6,7,6,21,12,18,15,18,11,42,36,25,26,33,45,66,90,78,45,75,150,135,156,270},{0,1,0,0,3,0,0,3,0,9,6,0,6,0,7,18,0,15,10,21,18,42,36,30,26,45,90,78,60,156},{0,0,1,0,2,3,3,0,0,7,6,6,0,9,0,21,18,0,0,11,15,33,45,26,0,25,75,45,78,135},{0,0,0,1,0,3,0,2,3,6,0,9,7,6,3,12,18,11,15,9,21,18,42,45,25,33,66,75,90,150},{0,0,0,0,1,0,0,0,0,3,3,0,0,0,0,9,0,0,0,7,6,21,18,10,0,15,45,26,30,78},{0,0,0,0,0,1,0,0,0,2,0,3,0,3,0,6,9,0,0,3,7,9,21,15,0,11,33,25,45,75},{0,0,0,0,0,0,1,0,0,0,2,0,0,3,0,7,6,0,0,0,0,11,15,0,0,0,25,0,26,45},{0,0,0,0,0,0,0,1,0,3,0,0,3,0,2,6,0,7,6,6,9,12,18,18,15,21,42,45,36,90},{0,T^2,0,0,3*T^2,0,0,0,1,0,6*T^2,3,2,0,T^2,0,6,3,7,3*T^2,6,6*T^2,12,21,11,9,18,33,42,66},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,0,2,3,6,9,6,0,7,21,15,18,45},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,7,6,0,0,0,15,0,10,26},{0,0,0,0,T^2,0,0,0,0,0,3*T^2,1,0,0,0,0,3,0,0,T^2,2,3*T^2,6,7,0,3,9,11,21,33},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,3,0,3,0,6,9,7,6,12,21,18,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,0,0,3,7,0,0,0,11,0,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,0,6,0,0,6,9,18,18,0,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,3,0,0,0,7,0,6,15},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,0,0,0,0,T^2,2,0,0,0,3,0,7,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,6,9,0,18},{0,T^2,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,0,T^2,0,0,0,1,3*T^2,0,6*T^2,0,3,2,0,0,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,3,9,6,0,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,0,2,6,7,9,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,7},{0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,T^2,0,3*T^2,0,1,0,0,0,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5304)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
31: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 2 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 4, 5}, {3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{2,3,4},{3,4,5},{0,1,5},{0,3,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,1},{0,1,1},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (31): {{2,2,6},{2,2,5},{2,1,5},{1,2,5},{2,2,4},{1,2,4},{2,2,3},{2,1,4},{1,2,3},{1,1,4},{2,0,4},{2,1,3},{0,2,4},{1,1,3},{0,2,3},{2,0,3},{2,1,2},{1,2,2},{0,2,2},{1,1,2},{2,0,2},{1,0,3},{0,1,3},{0,1,2},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,5,5,6,12,10,12,22,22,15,22,15,46,31,31,35,35,53,79,53,61,61,115,121,115,160,187,187,280,436},{0,1,1,1,3,5,6,5,12,7,5,12,5,22,15,15,22,22,31,46,31,25,25,61,79,61,76,115,115,160,280},{0,0,1,0,0,0,0,3,0,5,5,6,0,12,0,12,10,0,0,22,22,22,15,31,35,46,61,79,53,115,187},{0,0,0,1,0,3,0,0,6,5,0,0,5,12,12,0,0,10,22,22,0,15,22,46,35,31,61,53,79,115,187},{0,0,0,0,1,1,3,1,5,1,1,5,1,7,5,5,12,12,15,22,15,7,7,25,46,25,28,61,61,76,160},{0,0,0,0,0,1,0,0,3,1,0,0,1,5,5,0,0,6,12,12,0,5,7,22,22,15,25,31,46,61,115},{T^2,0,2*T^2,2*T^2,0,0,1,0,1,4*T^2,3*T^2,1,3*T^2,1,1,1,5,5,5,7,5,1+6*T^2,1+6*T^2,7,22,7,7+9*T^2,25,25,28,76},{0,0,0,0,0,0,0,1,0,1,1,3,0,5,0,5,6,0,0,12,12,7,5,15,22,22,25,46,31,61,115},{0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,3,5,5,0,1,1,7,12,5,7,15,22,25,61},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,0,0,6,0,5,5,12,10,12,22,22,22,46,79},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,6,5,0,0,0,12,15,22,0,31,53},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,3,0,0,5,5,1,1,5,12,7,7,22,15,25,61},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,6,0,0,0,5,12,0,0,15,0,22,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,1,1,5,6,5,7,12,12,22,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,1,5,0,0,5,0,12,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,1,0,0,0,5,5,12,0,15,31},{0,0,T^2,0,0,0,0,0,0,2*T^2,2*T^2,0,0,0,0,0,1,0,0,1,1,4*T^2,3*T^2,1,5,1,1+6*T^2,7,5,7,25},{0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,2*T^2,0,0,0,0,1,1,1,0,3*T^2,4*T^2,1,5,1,1+6*T^2,5,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,1,1,5,5,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,5,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,5,6,0,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,5,0,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,5,12},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,2*T^2,2*T^2,0,1,0,4*T^2,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5305)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 2 & 1 & 1 & 0 & 2 & 2 & 0 & 0 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 2 & 2 & -1 & 0 & 1 & 0 & 2 & -1 & 0 & 2 & 1 & 0 & -1 & 1 & -1 & 0 & 1 & -1 & 1 & 0 & 0 & -1 & 0 & -1 & 0 \\ 4 & 4 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 2 & 4 & 3 & 2 & 2 & 3 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 0 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 4, 5}, {3, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{3,4,5},{0,2,5},{1,3,4},{0,1,4},{0,4,5}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,0},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (34): {{2,1,4},{2,0,4},{1,2,4},{2,1,3},{1,1,4},{2,1,2},{1,2,3},{2,0,3},{1,1,3},{1,2,2},{0,2,4},{2,-1,3},{2,0,2},{1,1,2},{1,0,3},{0,2,3},{2,-1,2},{2,0,1},{0,2,2},{0,1,3},{1,0,2},{2,-1,1},{1,1,1},{2,-1,0},{1,0,1},{0,1,2},{1,-1,2},{0,1,1},{0,0,2},{1,0,0},{1,-1,1},{0,0,1},{1,-1,0},{0,0,0}}
Ext matrix: {{1,1,2,3,3,6,6,5,13,12,5,5,12,30,15,21,15,22,48,28,42,31,54,53,84,75,45,147,87,141,101,189,183,336},{0,1,0,0,2,0,0,3,6,0,3,5,6,12,13,9,12,10,18,21,30,22,20,35,54,48,42,86,75,85,84,147,141,244},{0,0,1,0,1,0,3,0,5,6,3,0,0,12,5,13,0,0,30,15,15,0,22,0,31,42,15,84,45,53,35,101,65,183},{0,0,0,1,0,3,2,1,3,6,0,1,5,13,3,5,5,12,21,6,15,15,30,31,42,28,15,75,30,84,45,87,101,189},{0,0,0,0,1,0,0,0,3,0,2,0,0,6,5,6,0,0,12,13,12,0,10,0,22,30,15,54,42,35,31,84,53,141},{0,2*T^2,0,0,4*T^2,1,0,0,0,2,6*T^2,3*T^2,1,3,6*T^2,0,1,5,5,9*T^2,3,5,13,15,15,6,3+8*T^2,28,6+12*T^2,42,15,30,45,87},{0,0,0,0,0,0,1,0,1,3,0,0,0,5,1,3,0,0,13,3,5,0,12,0,15,15,5,42,15,31,15,45,35,101},{0,0,0,0,0,0,0,1,2,0,0,1,3,6,3,3,5,6,9,5,13,12,12,22,30,21,15,48,28,54,42,75,84,147},{0,0,0,0,0,0,0,0,1,0,0,0,0,3,1,2,0,0,6,3,5,0,6,0,12,13,5,30,15,22,15,42,31,84},{0,0,0,0,2*T^2,0,0,0,0,1,4*T^2,0,0,1,3*T^2,0,0,0,3,6*T^2,1,0,5,0,5,3,1+4*T^2,15,3+8*T^2,15,5,15,15,45},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,6,5,0,0,0,0,0,12,0,22,15,0,0,31,0,53},{0,0,3*T^2,0,0,0,6*T^2,0,0,10*T^2,3*T^2,1,0,0,2,6*T^2,3,0,10*T^2,3,6,6,0,10,12,9,13,18,21,20,30,48,54,86},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,1,3,3,0,3,5,6,12,13,5,3,21,6,30,15,28,42,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,1,0,3,0,5,3,1,13,3,12,5,15,15,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,3,0,0,0,6,6,5,12,13,10,12,30,22,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,0,0,0,0,5,0,12,5,0,0,15,0,31},{0,0,T^2,0,0,0,3*T^2,0,0,6*T^2,T^2,0,0,0,0,3*T^2,1,0,6*T^2,0,2,3,0,6,6,3,3,9,5,12,13,21,30,48},{0,T^2,0,0,2*T^2,0,0,0,0,0,3*T^2,2*T^2,0,0,4*T^2,0,0,1,0,6*T^2,0,1,2,5,3,0,6*T^2,5,9*T^2,13,3,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,5,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,6,5,0,0,12,0,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,2,1,6,3,6,5,13,12,30},{0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,T^2,0,0,3*T^2,0,0,1,0,3,2,0,0,3,0,6,3,5,13,21},{0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,2*T^2,0,0,0,0,4*T^2,0,0,1,0,1,0,3*T^2,3,6*T^2,5,1,3,5,15},{0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,2*T^2,0,0,0,T^2,3*T^2,0,0,0,1,0,0,4*T^2,0,6*T^2,2,0,0,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,1,3,5,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,0,0,5,0,12},{0,0,T^2,0,0,0,3*T^2,0,0,6*T^2,T^2,0,0,0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,0,0,1,0,2,0,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,0,2*T^2,0,4*T^2,1,0,0,1,3},{0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5306)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & -1 & -1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
33: $\begin{pmatrix}3 & 3 & 2 & 3 & 1 & 2 & 2 & 3 & 3 & 1 & 1 & 3 & 2 & 2 & 0 & 1 & 1 & 2 & 3 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 \\ -1 & -2 & 0 & -1 & 1 & -1 & 0 & -2 & -1 & 0 & 1 & -2 & 0 & -1 & 1 & 0 & 1 & -1 & -2 & -2 & -1 & 1 & -2 & -1 & 0 & 0 & 1 & 0 & -2 & -1 & 0 & -1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 2 & 3 & 2 & 1 & 1 & 0 & 2 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{1,3,4},{0,2,5},{3,4,5},{0,4,5},{0,1,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,0},{1,-1,0},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (33): {{3,-1,3},{3,-2,3},{2,0,3},{3,-1,2},{1,1,3},{2,-1,3},{2,0,2},{3,-2,2},{3,-1,1},{1,0,3},{1,1,2},{3,-2,1},{2,0,1},{2,-1,2},{0,1,3},{1,0,2},{1,1,1},{2,-1,1},{3,-2,0},{2,-2,2},{1,-1,2},{0,1,2},{2,-2,1},{2,-1,0},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{2,-2,0},{1,-1,1},{0,0,1},{1,-1,0},{0,0,0}}
Ext matrix: {{1,1,3,3,6,4,9,4,6,9,18,9,18,15,16,33,36,33,16,16,39,58,39,58,72,73,126,126,73,93,172,172,316},{0,1,0,0,0,3,0,3,0,6,0,6,0,9,10,18,0,18,10,15,33,30,33,30,36,58,60,60,58,72,126,126,220},{0,0,1,0,3,1,3,0,0,4,9,0,6,4,9,15,18,9,0,4,16,33,10,16,33,39,72,58,19,39,93,73,172},{0,0,0,1,0,0,3,1,3,0,6,4,9,4,0,9,18,15,9,4,10,16,16,33,33,19,58,72,39,39,73,93,172},{0,T^2,0,0,1,0,0,3*T^2,0,1,3,6*T^2,0,0,4,4,6,0,10*T^2,3*T^2,4,15,6*T^2,0,9,16,33,16,10*T^2,10,39,19,73},{0,0,0,0,0,1,0,0,0,3,0,0,0,3,6,9,0,6,0,4,15,18,9,10,18,33,36,30,16,33,72,58,126},{0,0,0,0,0,0,1,0,0,0,3,0,3,1,0,4,9,4,0,1,4,9,4,9,15,10,33,33,10,16,39,39,93},{0,0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,0,9,6,4,9,10,15,18,18,16,30,36,33,33,58,72,126},{0,T^2,0,0,0,3*T^2,0,0,1,6*T^2,0,1,3,0,10*T^2,0,6,4,4,3*T^2,6*T^2,0,4,15,9,10*T^2,16,33,16,10,19,39,73},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,0,0,0,0,4,9,0,0,6,15,18,10,0,9,33,16,58},{0,0,0,0,0,0,0,T^2,0,0,1,3*T^2,0,0,0,1,3,0,6*T^2,T^2,1,4,3*T^2,0,4,4,15,9,6*T^2,4,16,10,39},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,0,0,0,4,9,6,0,10,18,15,9,16,33,58},{0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,1,0,6*T^2,0,3,1,0,T^2,3*T^2,0,1,4,4,6*T^2,9,15,4,4,10,16,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,0,1,4,6,4,6,9,9,18,18,9,15,33,33,72},{0,T^2,0,0,0,0,0,3*T^2,0,0,0,6*T^2,0,0,1,0,0,0,10*T^2,3*T^2,0,3,6*T^2,0,0,4,6,0,10*T^2,0,9,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,0,0,3,4,9,6,0,4,15,9,33},{0,0,0,0,0,0,0,0,0,T^2,0,T^2,0,0,3*T^2,0,1,0,3*T^2,0,T^2,0,T^2,0,1,3*T^2,4,4,3*T^2,1,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,3,3,0,6,9,4,4,9,15,33},{0,T^2,0,0,0,3*T^2,0,0,0,6*T^2,0,0,0,0,10*T^2,0,0,0,1,3*T^2,6*T^2,0,0,3,0,10*T^2,0,6,4,0,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,3,0,0,6,0,0,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,3,9,6,18},{0,0,0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,6*T^2,T^2,0,1,3*T^2,0,0,1,3,0,6*T^2,0,4,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,6,9,18},{0,0,0,0,0,T^2,0,0,0,3*T^2,0,0,0,0,6*T^2,0,0,0,0,T^2,3*T^2,0,0,1,0,6*T^2,0,3,1,0,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,0,1,4,4,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,3*T^2,0,0,0,T^2,0,0,0,1,0,3*T^2,0,1,0,4},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,0,0,0,0,T^2,0,0,0,0,3*T^2,0,1,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5307)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 0 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 6}, {4, 5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{2,3,4},{0,1,3},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,2,3},{2,1,3},{1,2,3},{2,2,2},{1,1,3},{1,2,2},{0,2,3},{2,1,2},{2,2,1},{1,1,2},{0,1,3},{1,2,1},{2,1,1},{0,2,2},{2,0,2},{0,1,2},{0,2,1},{2,0,1},{2,1,0},{1,0,2},{1,1,1},{0,0,2},{0,1,1},{1,1,0},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,3,6,9,6,9,6,24,12,18,21,18,15,46,36,42,38,39,54,74,102,96,84,100,183,192,180,345},{0,1,0,0,3,0,0,3,0,9,6,0,6,0,9,18,0,21,10,24,18,46,36,30,38,54,102,96,60,180},{0,0,1,0,2,3,3,1,0,9,6,6,3,9,2,24,18,9,6,15,21,39,54,38,21,42,100,84,96,192},{0,0,0,1,0,3,0,2,3,6,0,9,9,6,3,12,18,15,21,9,24,18,46,54,42,39,74,100,102,183},{0,0,0,0,1,0,0,0,0,3,3,0,0,0,1,9,0,3,0,9,6,24,18,10,6,21,54,38,30,96},{0,0,0,0,0,1,0,0,0,2,0,3,1,3,0,6,9,2,3,3,9,9,24,21,9,15,39,42,54,100},{0,0,0,0,0,0,1,0,0,1,2,0,0,3,0,9,6,1,0,2,3,15,21,6,3,9,42,21,38,84},{0,0,0,0,0,0,0,1,0,3,0,0,3,0,2,6,0,9,6,6,9,12,18,18,21,24,46,54,36,102},{0,3*T^2,0,0,6*T^2,0,0,0,1,0,10*T^2,3,2,0,6*T^2,0,6,3,9,10*T^2,6,15*T^2,12,24,15,9,18,39,46,74},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,1,0,2,3,6,9,6,3,9,24,21,18,54},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,1,0,9,6,0,0,3,21,6,10,38},{0,T^2,0,0,3*T^2,0,0,0,0,0,6*T^2,1,0,0,3*T^2,0,3,0,1,6*T^2,2,10*T^2,6,9,2,3,9,15,24,39},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,3,0,3,0,6,9,9,6,12,24,18,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,0,1,3,9,3,1,2,15,9,21,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,0,6,0,0,6,9,18,18,0,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,3,0,0,1,9,3,6,21},{0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,T^2,0,1,0,0,3*T^2,0,6*T^2,2,1,0,0,3,2,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,6,9,0,18},{0,T^2,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,0,3*T^2,0,0,0,1,6*T^2,0,10*T^2,0,3,2,0,0,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,0,3,9,6,0,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,1,2,6,9,9,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,3,9},{0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,0,T^2,0,0,0,0,3*T^2,0,6*T^2,0,1,0,0,0,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,0,3*T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,5308)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
36: $\begin{pmatrix}1 & 1 & 0 & 2 & 1 & 2 & 0 & 0 & 1 & -1 & 2 & 0 & 0 & 1 & -1 & 1 & 2 & -1 & 0 & -1 & 1 & 2 & 2 & 0 & -1 & 1 & 0 & 0 & -1 & 1 & 0 & -1 & 1 & -1 & 0 & 0 \\ 2 & 1 & 3 & 1 & 2 & 0 & 2 & 1 & 1 & 3 & 1 & 3 & 2 & 2 & 2 & 0 & 0 & 1 & 1 & 3 & 1 & 1 & 0 & 2 & 2 & 0 & 0 & 1 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 \\ 3 & 3 & 3 & 2 & 2 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 3 & 2 & 1 & 3 & 2 & 2 & 1 & 0 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 3, 6}, {2, 4, 5, 7}, {3, 4, 6, 7}, {0, 1, 8}, {0, 2, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{2,4,5},{3,4,5},{0,1,3},{0,2,4}},{2,1,2})
Cox degrees: {{0,0,1},{1,-1,0},{-1,1,1},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (36): {{1,2,3},{1,1,3},{0,3,3},{2,1,2},{1,2,2},{2,0,2},{0,2,3},{0,1,3},{1,1,2},{-1,3,3},{2,1,1},{0,3,2},{0,2,2},{1,2,1},{-1,2,3},{1,0,2},{2,0,1},{-1,1,3},{0,1,2},{-1,3,2},{1,1,1},{2,1,0},{2,0,0},{0,2,1},{-1,2,2},{1,0,1},{0,0,2},{0,1,1},{-1,1,2},{1,1,0},{0,0,1},{-1,2,1},{1,0,0},{-1,1,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,1,2,4,4,4,7,12,4,7,4,16,10,10,20,20,16,34,16,34,16,52,40,40,67,52,91,72,72,154,100,154,188,188,336},{0,1,0,0,0,2,1,4,4,1,0,0,4,0,4,12,7,10,16,4,10,0,16,10,16,34,34,40,40,20,91,40,72,100,80,188},{0,0,1,0,2,0,2,3,4,4,3,4,12,7,7,6,6,10,20,16,20,10,28,34,34,33,28,67,52,52,100,91,100,154,154,252},{0,0,0,1,1,2,0,0,4,0,4,1,4,4,0,7,12,0,10,4,16,10,34,16,10,34,16,40,20,40,72,40,91,80,100,188},{0,0,0,0,1,0,0,0,2,0,2,1,4,4,0,3,4,0,7,4,12,7,20,16,10,20,10,34,16,34,52,40,67,72,91,154},{0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,4,4,0,4,1,4,0,10,4,4,16,10,16,10,10,40,16,40,40,40,100},{0,0,0,0,0,0,1,2,2,1,0,0,4,0,4,4,3,7,12,4,7,0,10,10,16,20,20,34,34,16,67,40,52,91,72,154},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,2,0,4,4,0,0,0,0,0,4,7,12,10,16,0,34,10,16,40,20,72},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,2,2,0,4,1,4,0,7,4,4,12,7,16,10,10,34,16,34,40,40,91},{0,0,0,4*T^2,0,6*T^2,0,0,0,1,6*T^2,0,2,0,2,0,9*T^2,3,4,4,3,8*T^2,4+12*T^2,7,12,6,6,20,20,10,33,34,28,67,52,100},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,0,0,0,4,4,12,4,0,7,0,10,0,16,16,10,34,20,40,72},{0,4*T^2,0,0,0,6*T^2,0,6*T^2,0,0,0,1,2,2,0,9*T^2,0,8*T^2,3,4,4,3,6,12,7,6,4+12*T^2,20,10,20,28,34,33,52,67,100},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,1,2,0,3,4,4,4,3,12,7,7,20,16,20,34,34,67},{0,2*T^2,0,0,0,4*T^2,0,3*T^2,0,0,0,0,0,1,0,6*T^2,0,4*T^2,0,0,2,2,4,4,0,3,8*T^2,7,0,12,10,10,20,16,34,52},{0,0,0,2*T^2,0,4*T^2,0,0,0,0,3*T^2,0,0,0,1,0,6*T^2,2,2,0,0,4*T^2,8*T^2,0,4,3,4,7,12,0,20,10,10,34,16,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,4,4,4,4,0,16,4,10,16,10,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,0,4,0,4,0,4,10,4,16,10,16,40},{0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,3*T^2,1,0,0,0,0,4*T^2,0,0,0,2,0,4,0,7,0,0,10,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,2,2,4,4,0,12,4,7,16,10,34},{0,2*T^2,0,2*T^2,0,6*T^2,0,4*T^2,0,0,4*T^2,0,0,0,0,6*T^2,6*T^2,6*T^2,0,1,0,6*T^2,9*T^2,2,2,0,9*T^2,4,3,3,6,12,6,20,20,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,2,0,4,0,4,7,4,12,10,16,34},{0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,3*T^2,0,0,0,0,0,1,2,0,0,0,4*T^2,0,0,4,0,0,7,0,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,4,0,4,10},{0,T^2,0,0,0,2*T^2,0,2*T^2,0,0,0,0,0,0,0,4*T^2,0,3*T^2,0,0,0,0,0,1,0,0,6*T^2,2,0,2,3,4,4,7,12,20},{0,0,0,T^2,0,2*T^2,0,0,0,0,2*T^2,0,0,0,0,0,4*T^2,0,0,0,0,3*T^2,6*T^2,0,1,0,0,2,2,0,4,4,3,12,7,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,1,4,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,4,4,12},{0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,1,0,2,0,0,4,0,7},{0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,3*T^2,0,0,1,0,0,2,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,0,0,0,0,0,0,T^2,0,0,T^2,0,0,0,0,2*T^2,2*T^2,2*T^2,0,0,0,2*T^2,4*T^2,0,0,0,4*T^2,0,0,0,0,1,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,6550)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 5, 6}, {0, 7}, {1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{1,1,1},{1,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{4,5,5},{4,4,5},{4,5,4},{4,4,4},{3,4,4},{3,3,4},{3,4,3},{3,3,3},{2,3,3},{2,2,3},{2,3,2},{2,2,2},{1,2,2},{1,1,2},{1,2,1},{1,1,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,4,8,14,14,25,35,56,56,92,112,168,168,259,294,420,420,616},{0,1,0,2,2,8,3,14,14,35,20,56,56,112,77,168,168,294,224,420},{0,0,1,2,2,3,8,14,14,20,35,56,56,77,112,168,168,224,294,420},{0,0,0,1,1,2,2,8,8,14,14,35,35,56,56,112,112,168,168,294},{0,0,0,0,1,2,2,4,8,14,14,25,35,56,56,92,112,168,168,259},{0,0,0,0,0,1,0,2,2,8,3,14,14,35,20,56,56,112,77,168},{0,0,0,0,0,0,1,2,2,3,8,14,14,20,35,56,56,77,112,168},{0,0,0,0,0,0,0,1,1,2,2,8,8,14,14,35,35,56,56,112},{0,0,0,0,0,0,0,0,1,2,2,4,8,14,14,25,35,56,56,92},{0,0,0,0,0,0,0,0,0,1,0,2,2,8,3,14,14,35,20,56},{0,0,0,0,0,0,0,0,0,0,1,2,2,3,8,14,14,20,35,56},{0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,8,8,14,14,35},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4,8,14,14,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,8,3,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,3,8,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7027)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 0 & 0 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 5}, {2, 3, 4, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{2,3,4},{1,3,4},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{0,1,1},{0,1,1},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,4,5},{0,4,5},{1,4,4},{0,4,4},{1,3,4},{0,3,4},{1,3,3},{1,2,3},{0,3,3},{1,2,2},{0,2,3},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,7,13,13,28,24,49,49,85,84,140,140,231,210,336,336,532},{0,1,0,2,1,7,2,7,13,13,28,49,28,84,49,140,84,210,140,336},{0,0,1,2,1,2,7,7,13,28,13,49,28,49,84,140,84,140,210,336},{0,0,0,1,0,1,1,1,7,7,7,28,7,28,28,84,28,84,84,210},{0,0,0,0,1,2,2,7,4,13,13,24,28,49,49,85,84,140,140,231},{0,0,0,0,0,1,0,1,2,2,7,13,7,28,13,49,28,84,49,140},{0,0,0,0,0,0,1,1,2,7,2,13,7,13,28,49,28,49,84,140},{0,0,0,0,0,0,0,1,0,2,2,4,7,13,13,24,28,49,49,85},{0,0,0,0,0,0,0,0,1,1,1,7,1,7,7,28,7,28,28,84},{0,0,0,0,0,0,0,0,0,1,0,2,1,2,7,13,7,13,28,49},{0,0,0,0,0,0,0,0,0,0,1,2,1,7,2,13,7,28,13,49},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,7,1,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4,7,13,13,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,7,2,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7209)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}4 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 5}, {6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{1,3,4},{0,2,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,1,1},{1,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{4,5,6},{4,5,5},{4,4,5},{3,4,5},{4,4,4},{3,4,4},{3,3,4},{2,3,4},{3,3,3},{2,3,3},{2,2,3},{1,2,3},{2,2,2},{1,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,3,7,5,13,18,28,29,49,64,84,100,140,175,210,266,336,406,602},{0,1,1,1,3,7,7,7,18,28,28,28,64,84,84,84,175,210,210,406},{0,0,1,1,2,2,7,7,13,13,28,28,49,49,84,84,140,140,210,336},{0,0,0,1,0,2,3,7,5,13,18,28,29,49,64,84,100,140,175,266},{0,0,0,0,1,1,1,1,7,7,7,7,28,28,28,28,84,84,84,210},{0,0,0,0,0,1,1,1,3,7,7,7,18,28,28,28,64,84,84,175},{0,0,0,0,0,0,1,1,2,2,7,7,13,13,28,28,49,49,84,140},{0,0,0,0,0,0,0,1,0,2,3,7,5,13,18,28,29,49,64,100},{0,0,0,0,0,0,0,0,1,1,1,1,7,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,1,1,1,3,7,7,7,18,28,28,64},{0,0,0,0,0,0,0,0,0,0,1,1,2,2,7,7,13,13,28,49},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,7,5,13,18,29},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,7,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7383)$ |
3 |
17 |
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9: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
17: $\begin{pmatrix}5 & 5 & 4 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 1 & 2 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (17): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{0, 1, 2, 3, 4, 5}, {1, 2, 3, 4, 5, 7}, {6, 7}, {0, 8}, {6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{3,4,5},{0,2,5},{0,1,4},{1,3,4}},{2,1,1})
Cox degrees: {{1,-1,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (17): {{5,1,1},{5,0,1},{4,1,1},{5,0,0},{4,0,1},{3,1,1},{4,0,0},{3,0,1},{2,1,1},{3,0,0},{2,0,1},{1,1,1},{2,0,0},{1,0,1},{0,1,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,6,2,6,21,12,21,56,42,56,126,112,126,252,252,504},{0,1,1,1,6,6,7,21,21,27,56,56,77,126,126,182,378},{0,0,1,0,1,6,2,6,21,12,21,56,42,56,126,112,252},{0,0,0,1,0,0,6,0,0,21,0,0,56,0,0,126,252},{0,0,0,0,1,1,1,6,6,7,21,21,27,56,56,77,182},{0,0,0,0,0,1,0,1,6,2,6,21,12,21,56,42,112},{0,0,0,0,0,0,1,0,0,6,0,0,21,0,0,56,126},{0,0,0,0,0,0,0,1,1,1,6,6,7,21,21,27,77},{0,0,0,0,0,0,0,0,1,0,1,6,2,6,21,12,42},{0,0,0,0,0,0,0,0,0,1,0,0,6,0,0,21,56},{0,0,0,0,0,0,0,0,0,0,1,1,1,6,6,7,27},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,6,2,12},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7418)$ |
3 |
17 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\ 3 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 9 & 8 & 8 & 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 8 & 8 & 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-4, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (17): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {0, 7}, {2, 3, 4, 5, 6, 7}, {1, 8}, {2, 3, 4, 5, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,4,3},{1,4,4}},{{3,4,5},{0,4,5},{0,2,5},{1,3,4},{2,3,5},{0,1,4}},{1,1,1})
Cox degrees: {{1,4,3},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,9,8},{1,8,8},{1,8,7},{1,7,7},{1,7,6},{1,6,6},{1,6,5},{1,5,5},{0,5,5},{1,5,4},{1,4,4},{0,4,4},{1,4,3},{1,3,3},{1,3,2},{0,3,3},{1,2,2},{0,2,2},{1,2,1},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,6,6,21,21,56,56,57,126,126,132,252,252,462,273,462,518,792,792,918,1539},{0,1,1,6,6,21,21,56,56,56,126,127,126,252,252,258,462,483,462,792,848,1413},{0,0,1,1,6,6,21,21,21,56,56,57,126,126,252,132,252,273,462,462,518,918},{0,0,0,1,1,6,6,21,21,21,56,56,56,126,126,127,252,258,252,462,483,848},{0,0,0,0,1,1,6,6,6,21,21,21,56,56,126,57,126,132,252,252,273,518},{0,0,0,0,0,1,1,6,6,6,21,21,21,56,56,56,126,127,126,252,258,483},{0,0,0,0,0,0,1,1,1,6,6,6,21,21,56,21,56,57,126,126,132,273},{0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,56,56,126,127,258},{0,0,0,0,0,0,0,0,1,0,0,6,0,0,0,21,0,56,0,0,126,252},{0,0,0,0,0,0,0,0,0,1,1,1,6,6,21,6,21,21,56,56,57,132},{0,0,0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,56,127},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,6,0,21,0,0,56,126},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,6,1,6,6,21,21,21,57},{T^5,0,0,0,0,0,0,0,T^5,0,0,0,0,1,1,1,6,6,6,21,21,56},{T^5,T^5,0,0,0,0,0,0,T^5,0,0,0,0,0,1,0,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,6,0,0,21,56},{6*T^5,T^5,T^5,0,0,0,0,0,6*T^5,0,0,T^5,0,0,0,0,1,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,21},{6*T^5,6*T^5,T^5,T^5,0,0,0,0,6*T^5,0,0,T^5,0,0,0,0,0,0,1,1,1,6},{21*T^5,6*T^5,6*T^5,T^5,T^5,0,0,0,21*T^5,0,0,6*T^5,0,0,0,T^5,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7419)$ |
3 |
17 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\ 2 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-3, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (17): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {0, 7}, {2, 3, 4, 5, 6, 7}, {1, 8}, {2, 3, 4, 5, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,3,2},{1,3,3}},{{3,4,5},{1,3,4},{0,1,4},{0,2,5},{0,4,5},{2,3,5}},{1,1,1})
Cox degrees: {{1,3,2},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,8,7},{1,7,7},{1,7,6},{1,6,6},{1,6,5},{1,5,5},{0,5,5},{1,5,4},{1,4,4},{0,4,4},{1,4,3},{1,3,3},{1,3,2},{0,3,3},{1,2,2},{0,2,2},{1,2,1},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,6,6,21,21,22,56,56,62,126,126,252,147,252,308,462,462,588,1044},{0,1,1,6,6,21,21,21,56,57,56,126,126,132,252,273,252,462,518,918},{0,0,1,1,6,6,6,21,21,22,56,56,126,62,126,147,252,252,308,588},{0,0,0,1,1,6,6,6,21,21,21,56,56,57,126,132,126,252,273,518},{0,0,0,0,1,1,1,6,6,6,21,21,56,22,56,62,126,126,147,308},{0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,57,56,126,132,273},{0,0,0,0,0,0,1,0,0,6,0,0,0,21,0,56,0,0,126,252},{0,0,0,0,0,0,0,1,1,1,6,6,21,6,21,22,56,56,62,147},{0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,57,132},{0,0,0,0,0,0,0,0,0,1,0,0,0,6,0,21,0,0,56,126},{0,0,0,0,0,0,0,0,0,0,1,1,6,1,6,6,21,21,22,62},{0,0,0,0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,6,0,0,21,56},{T^5,0,0,0,0,0,T^5,0,0,0,0,0,0,0,1,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,21},{T^5,T^5,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,1,1,1,6},{6*T^5,T^5,T^5,0,0,0,6*T^5,0,0,T^5,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7420)$ |
3 |
17 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-2, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (17): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {0, 7}, {2, 3, 4, 5, 6, 7}, {1, 8}, {2, 3, 4, 5, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,1},{1,2,2}},{{3,4,5},{0,1,4},{1,3,4},{0,2,5},{0,4,5},{2,3,5}},{1,1,1})
Cox degrees: {{1,2,1},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,7,6},{1,6,6},{1,6,5},{1,5,5},{0,5,5},{1,5,4},{1,4,4},{0,4,4},{1,4,3},{1,3,3},{1,3,2},{0,3,3},{1,2,2},{0,2,2},{1,2,1},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,6,6,7,21,21,27,56,56,126,77,126,182,252,252,378,714},{0,1,1,6,6,6,21,22,21,56,56,62,126,147,126,252,308,588},{0,0,1,1,1,6,6,7,21,21,56,27,56,77,126,126,182,378},{0,0,0,1,1,1,6,6,6,21,21,22,56,62,56,126,147,308},{0,0,0,0,1,0,0,6,0,0,0,21,0,56,0,0,126,252},{0,0,0,0,0,1,1,1,6,6,21,7,21,27,56,56,77,182},{0,0,0,0,0,0,1,1,1,6,6,6,21,22,21,56,62,147},{0,0,0,0,0,0,0,1,0,0,0,6,0,21,0,0,56,126},{0,0,0,0,0,0,0,0,1,1,6,1,6,7,21,21,27,77},{0,0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,22,62},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,6,6,7,27},{0,0,0,0,0,0,0,0,0,0,0,1,0,6,0,0,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{T^5,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7421)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 3 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 7 & 7 & 6 & 6 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 2 & 4 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 1, -3}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,3}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,2,7},{1,1,7},{1,2,6},{1,1,6},{1,2,5},{1,2,4},{1,1,5},{1,1,4},{1,2,3},{1,1,3},{0,1,4},{1,2,2},{0,0,4},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,35,30,70,70,140,71,126,107,145,210,252,220,420,267,408,455,700,730,1130},{0,1,0,5,0,0,15,35,0,70,35,0,71,70,0,126,145,210,126,267,210,455,330,730},{0,0,1,2,5,15,10,30,35,70,30,70,45,71,126,140,107,252,145,220,267,408,455,700},{0,0,0,1,0,0,5,15,0,35,15,0,30,35,0,70,71,126,70,145,126,267,210,455},{0,0,0,0,1,5,2,10,15,30,10,35,15,30,70,70,45,140,71,107,145,220,267,408},{0,0,0,0,0,1,0,2,5,10,2,15,3,10,35,30,15,70,30,45,71,107,145,220},{0,0,0,0,0,0,1,5,0,15,5,0,10,15,0,35,30,70,35,71,70,145,126,267},{0,0,0,0,0,0,0,1,0,5,1,0,2,5,0,15,10,35,15,30,35,71,70,145},{0,0,0,0,0,0,0,0,1,2,0,5,0,2,15,10,3,30,10,15,30,45,71,107},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5,2,15,5,10,15,30,35,71},{0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,0,10,0,15,30,35,70,70,140},{T^4,2*T^4,0,0,0,0,0,0,0,0,T^4,1,2*T^4,0,5,2,0,10,2,3,10,15,30,45},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,5,10,15,30,35,70},{5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,0,0,5*T^4,0,10*T^4,T^4,1,0,2*T^4,2,0,0,2,3,10,15},{0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,1,0,5,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,0,35},{0,5*T^4,0,T^4,0,0,0,0,0,0,0,0,5*T^4,0,0,0,T^4,1,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7424)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 7 & 7 & 6 & 5 & 6 & 5 & 4 & 5 & 3 & 4 & 5 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 7}, {1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,3,7},{2,2,7},{2,3,6},{2,3,5},{2,2,6},{2,2,5},{2,3,4},{1,2,5},{2,3,3},{2,2,4},{1,1,5},{2,2,3},{1,2,4},{1,2,3},{1,1,4},{1,1,3},{1,2,2},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,10,8,20,20,22,35,40,34,70,48,90,76,145,152,148,238,248,206,392,260,368,422,606,644,936},{0,1,0,0,4,10,0,10,0,20,22,35,20,35,48,90,56,90,84,152,148,238,152,260,238,422,352,644},{0,0,1,4,2,8,10,8,20,20,12,40,22,48,34,76,90,76,152,145,104,248,148,206,260,368,422,606},{0,0,0,1,0,2,4,2,10,8,3,20,8,22,12,34,48,34,90,76,46,145,76,104,148,206,260,368},{0,0,0,0,1,4,0,4,0,10,8,20,10,20,22,48,35,48,56,90,76,152,90,148,152,260,238,422},{0,0,0,0,0,1,0,1,0,4,2,10,4,10,8,22,20,22,35,48,34,90,48,76,90,148,152,260},{0,0,0,0,0,0,1,0,4,2,0,8,2,8,3,12,22,12,48,34,16,76,34,46,76,104,148,206},{0,0,0,0,0,0,0,1,0,0,2,0,4,10,8,20,20,22,35,40,34,70,48,76,90,145,152,248},{T^3,2*T^3,0,0,0,0,0,2*T^3,1,0,4*T^3,2,0,2,0,3,8,3+3*T^3,22,12,4+6*T^3,34,12,16,34,46,76,104},{0,0,0,0,0,0,0,0,0,1,0,4,1,4,2,8,10,8,20,22,12,48,22,34,48,76,90,148},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,0,10,0,20,22,35,20,48,35,90,56,152},{0,T^3,0,0,0,0,0,0,0,0,2*T^3,1,0,1,0,2,4,2,10,8,3+3*T^3,22,8,12,22,34,48,76},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8,10,8,20,20,12,40,22,34,48,76,90,145},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,2,10,8,3,20,8,12,22,34,48,76},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,8,20,10,22,20,48,35,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,8,10,22,20,48},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,0,8,2,3,8,12,22,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{0,0,0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,2*T^3,1,0,4*T^3,2,0,0,2,3,8,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,2,4,8,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7427)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 4 & 3 & 1 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 3 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 7}, {1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{1,1,1}},{{1,3,4},{0,3,4},{1,2,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,1,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{2,3,4},{2,2,4},{2,3,3},{1,2,4},{2,2,3},{2,3,2},{1,1,4},{1,2,3},{2,3,1},{2,2,2},{1,1,3},{1,2,2},{2,2,1},{0,1,3},{1,1,2},{1,2,1},{0,0,3},{0,1,2},{1,2,0},{1,1,1},{0,0,2},{1,1,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,3,8,10,5,13,20,20,22,34,40,27,58,70,41,73,125,120,112,215,154,238,280,435},{0,1,0,1,4,0,3,4,0,10,13,10,20,13,34,20,27,34,35,70,73,125,70,154,125,280},{0,0,1,0,2,4,0,3,10,8,5,13,20,6,22,34,9,27,70,58,41,120,73,112,154,238},{0,0,0,1,0,0,2,4,0,0,8,10,0,13,20,20,22,34,35,40,58,70,70,120,125,215},{0,0,0,0,1,0,0,1,0,4,3,4,10,3,13,10,6,13,20,34,27,70,34,73,70,154},{0,0,0,0,0,1,0,0,4,2,0,3,8,0,5,13,0,6,34,22,9,58,27,41,73,112},{0,0,0,0,0,0,1,0,0,0,4,0,0,4,10,0,13,10,0,20,34,35,20,70,35,125},{0,0,0,0,0,0,0,1,0,0,2,4,0,3,8,10,5,13,20,20,22,40,34,58,70,120},{0,0,0,T^3,0,0,2*T^3,0,1,0,0,0,2,T^3,0,3,2*T^3,0,13,5,0,22,6,9,27,41},{0,0,0,0,0,0,0,0,0,1,0,1,4,0,3,4,0,3,10,13,6,34,13,27,34,73},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,3,4,0,10,13,20,10,34,20,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,3,10,8,5,20,13,22,34,58},{0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,1,T^3,0,4,3,0,13,3,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,0,8,0,10,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,3,10,4,13,10,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,8,3,5,13,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20},{0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,T^3,0,0,2*T^3,0,1,0,0,2,0,0,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,3,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,1,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7431)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & -2 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 0 & 1 & -1 & 2 & 3 & 0 & 1 & 2 & -1 & 3 & 0 & 1 & -1 & 2 & 3 & 0 & 1 & -1 & 2 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, 1, -2, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 5}, {4, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-2,1,1}},{{0,2,3},{2,3,4},{1,3,4},{0,1,3}},{2,3,3})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{1,0,0},{-2,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,2,3},{2,2,3},{3,2,2},{1,2,3},{2,2,2},{3,1,2},{0,2,3},{1,2,2},{-1,2,3},{2,1,2},{3,1,1},{0,2,2},{1,1,2},{2,1,1},{-1,2,2},{3,0,1},{0,1,2},{1,1,1},{-1,1,2},{2,0,1},{3,0,0},{0,1,1},{1,0,1},{-1,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,2,10,8,13,20,20,35,32,25,40,65,60,70,71,116,120,189,140,129,212,249,343,248,408,433,700},{0,1,0,4,2,4,10,8,20,13,8,20,32,25,40,32,65,60,116,71,60,120,140,212,129,249,248,433},{0,0,1,0,4,1,0,10,0,4,13,20,10,32,35,13,20,65,35,32,71,116,65,189,140,116,249,408},{0,0,0,1,0,1,4,2,10,4,2,8,13,8,20,13,32,25,65,32,25,60,71,120,60,140,129,248},{0,0,0,0,1,0,0,4,0,1,4,10,4,13,20,4,10,32,20,13,32,65,32,116,71,65,140,249},{0,0,0,0,0,1,0,0,0,4,2,0,10,8,0,13,20,20,35,32,25,40,65,70,60,116,120,212},{0,0,0,0,0,0,1,0,4,1,0,2,4,2,8,4,13,8,32,13,8,25,32,60,25,71,60,129},{0,0,0,0,0,0,0,1,0,0,1,4,1,4,10,1,4,13,10,4,13,32,13,65,32,32,71,140},{T^3,0,2*T^3,0,0,3*T^3,0,0,1,0,5*T^3,0,1,0,2,1+6*T^3,4,2,13,4,2+9*T^3,8,13,25,8,32,25,60},{0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,4,10,8,20,13,8,20,32,40,25,65,60,120},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,1,0,10,0,4,13,20,10,35,32,20,65,116},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,1,4,4,1,4,13,4,32,13,13,32,71},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,2,10,4,2,8,13,20,8,32,25,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,1,4,10,4,20,13,10,32,65},{0,0,T^3,0,0,T^3,0,0,0,0,3*T^3,0,0,0,1,3*T^3,0,1,1,0,1+6*T^3,4,1,13,4,4,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,0,10,0,8,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,2,4,8,2,13,8,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,10,4,4,13,32},{0,0,0,0,0,T^3,0,0,0,0,2*T^3,0,0,0,0,3*T^3,0,0,1,0,5*T^3,0,1,2,0,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,2,10,8,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,8},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,3*T^3,0,0,1,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7432)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 3 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 3 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 7 & 7 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, 1, -3, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {1, 2, 3, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,3,3}},{{2,3,4},{1,3,4},{0,1,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,1,1},{0,1,1},{0,1,1},{1,3,3},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,7,8},{1,7,7},{1,6,7},{1,6,6},{1,5,6},{1,5,5},{1,4,5},{0,4,5},{1,4,4},{0,4,4},{1,3,4},{1,3,3},{0,3,4},{0,3,3},{1,2,3},{0,2,3},{1,2,2},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,6,11,21,36,56,57,91,93,126,196,132,207,252,273,378,414,462,518,672,763,918,1318},{0,1,1,6,6,21,21,21,56,57,56,126,57,132,126,132,252,273,252,273,462,518,518,918},{0,0,1,2,6,11,21,21,36,36,56,91,57,93,126,132,196,207,252,273,378,414,518,763},{0,0,0,1,1,6,6,6,21,21,21,56,21,57,56,57,126,132,126,132,252,273,273,518},{0,0,0,0,1,2,6,6,11,11,21,36,21,36,56,57,91,93,126,132,196,207,273,414},{0,0,0,0,0,1,1,1,6,6,6,21,6,21,21,21,56,57,56,57,126,132,132,273},{0,0,0,0,0,0,1,1,2,2,6,11,6,11,21,21,36,36,56,57,91,93,132,207},{0,0,0,0,0,0,0,1,0,2,0,0,6,11,0,21,0,36,0,56,0,91,126,196},{0,0,0,0,0,0,0,0,1,1,1,6,1,6,6,6,21,21,21,21,56,57,57,132},{0,0,0,0,0,0,0,0,0,1,0,0,1,6,0,6,0,21,0,21,0,56,56,126},{0,0,0,0,0,0,0,0,0,0,1,2,1,2,6,6,11,11,21,21,36,36,57,93},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,6,6,6,6,21,21,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,6,0,11,0,21,0,36,56,91},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,0,6,0,21,21,56},{0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,1,1,2,2,6,6,11,11,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,6,0,11,21,36},{T^5,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,1,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,6,21},{T^5,4*T^4,0,T^4,0,0,0,T^5,0,4*T^4,0,0,0,T^4,0,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,6,11},{6*T^5,T^5,T^5,0,0,0,0,6*T^5,0,T^5,0,0,T^5,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7447)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5, 6}, {0, 7}, {1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{1,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,4,5},{3,3,5},{3,4,4},{3,3,4},{3,4,3},{2,3,4},{3,3,3},{2,2,4},{2,3,3},{2,2,3},{2,3,2},{1,2,3},{2,2,2},{1,1,3},{1,2,2},{1,1,2},{1,2,1},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,9,12,15,21,36,38,42,66,63,84,130,141,140,222,196,252,363,399,585},{0,1,0,3,0,3,6,9,6,21,10,21,38,42,38,84,60,84,141,140,141,252,213,399},{0,0,1,2,3,2,6,3,9,15,21,15,36,21,42,63,84,63,130,84,140,196,252,363},{0,0,0,1,0,1,3,2,3,9,6,9,21,15,21,42,38,42,84,63,84,140,141,252},{0,0,0,0,1,0,2,0,2,3,9,3,15,4,15,21,42,21,63,27,63,84,140,196},{0,0,0,0,0,1,0,2,3,6,6,9,12,15,21,36,38,42,66,63,84,130,141,222},{0,0,0,0,0,0,1,0,1,2,3,2,9,3,9,15,21,15,42,21,42,63,84,140},{0,0,0,0,0,0,0,1,0,3,0,3,6,9,6,21,10,21,38,42,38,84,60,141},{0,0,0,0,0,0,0,0,1,2,3,2,6,3,9,15,21,15,36,21,42,63,84,130},{0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,9,6,9,21,15,21,42,38,84},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,3,9,3,15,4,15,21,42,63},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,9,12,15,21,36,38,66},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,2,9,3,9,15,21,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,9,6,21,10,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,2,6,3,9,15,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,9,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,3,9,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7461)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 1 & 1 & 0 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 5}, {3, 4, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{1,3,4},{0,1,3},{2,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{0,1,1},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,3,4},{1,3,4},{2,3,3},{0,3,4},{2,2,3},{1,3,3},{1,2,3},{2,2,2},{0,3,3},{1,2,2},{0,2,3},{2,1,2},{0,2,2},{2,1,1},{1,1,2},{0,1,2},{1,1,1},{2,0,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,2,6,7,6,18,13,12,33,34,28,62,49,64,115,110,84,196,140,175,301,286,487},{0,1,0,3,1,2,7,2,6,13,18,7,33,13,28,64,49,28,110,49,84,175,140,286},{0,0,1,0,1,3,3,7,6,18,6,7,34,28,18,34,64,28,115,84,64,115,175,301},{0,0,0,1,0,0,1,0,2,2,7,1,13,2,7,28,13,7,49,13,28,84,49,140},{0,0,0,0,1,0,3,2,0,6,6,7,12,13,18,34,33,28,62,49,64,115,110,196},{0,0,0,0,0,1,1,1,3,7,3,1,18,7,7,18,28,7,64,28,28,64,84,175},{0,0,0,0,0,0,1,0,0,2,3,1,6,2,7,18,13,7,33,13,28,64,49,110},{0,0,0,0,0,0,0,1,0,3,0,1,6,7,3,6,18,7,34,28,18,34,64,115},{0,0,0,0,0,0,0,0,1,1,1,0,7,1,1,7,7,1,28,7,7,28,28,84},{0,0,0,0,0,0,0,0,0,1,0,0,3,1,1,3,7,1,18,7,7,18,28,64},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,7,2,1,13,2,7,28,13,49},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,7,12,13,18,34,33,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,7,1,1,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,6,7,3,6,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,1,6,2,7,18,13,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,1,7,2,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7464)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 2 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 2 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 7 & 7 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 8 & 7 & 7 & 6 & 6 & 6 & 5 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, 0, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {1, 2, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,2}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,1,1},{0,1,1},{1,2,2},{1,2,2},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,7,8},{2,7,7},{2,6,7},{2,6,6},{2,5,6},{1,5,6},{2,5,5},{1,5,5},{2,4,5},{2,4,4},{1,4,5},{1,4,4},{2,3,4},{1,3,4},{2,3,3},{0,3,4},{1,3,3},{0,3,3},{1,2,3},{1,2,2},{0,2,3},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,5,9,15,17,25,29,35,55,45,73,70,100,105,103,155,161,196,292,211,319,350,395,504,579,687,979},{0,1,1,5,5,5,15,17,15,35,17,45,35,45,70,45,100,103,100,196,103,211,196,211,350,395,395,687},{0,0,1,2,5,5,9,9,15,25,17,29,35,45,55,45,73,73,100,155,103,161,196,211,292,319,395,579},{0,0,0,1,1,1,5,5,5,15,5,17,15,17,35,17,45,45,45,100,45,103,100,103,196,211,211,395},{0,0,0,0,1,1,2,2,5,9,5,9,15,17,25,17,29,29,45,73,45,73,100,103,155,161,211,319},{0,0,0,0,0,1,0,2,0,0,5,9,0,15,0,17,25,29,35,55,45,73,70,100,105,155,196,292},{0,0,0,0,0,0,1,1,1,5,1,5,5,5,15,5,17,17,17,45,17,45,45,45,100,103,103,211},{0,0,0,0,0,0,0,1,0,0,1,5,0,5,0,5,15,17,15,35,17,45,35,45,70,100,100,196},{0,0,0,0,0,0,0,0,1,2,1,2,5,5,9,5,9,9,17,29,17,29,45,45,73,73,103,161},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,1,5,5,5,17,5,17,17,17,45,45,45,103},{0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,5,9,9,15,25,17,29,35,45,55,73,100,155},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,5,15,5,17,15,17,35,45,45,100},{0,T^3,0,0,0,0,0,2*T^3,0,0,0,0,1,1,2,1,2,2+3*T^3,5,9,5,9,17,17,29,29,45,73},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,5,9,5,9,15,17,25,29,45,73},{T^4,0,0,0,0,2*T^4,0,0,0,0,0,0,0,0,1,3*T^4,1,1,1,5,1,5,5,5,17,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,5,9,0,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,1,5,5,5,15,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,5,5,9,9,17,29},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,1,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7466)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 0 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, -1, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {1, 2, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,1,4},{1,3,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,1,1},{0,1,1},{1,0,0},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{2,4,5},{1,4,5},{2,4,4},{1,4,4},{2,3,4},{2,3,3},{1,3,4},{1,3,3},{0,3,4},{2,2,3},{1,2,3},{0,3,3},{2,2,2},{2,1,2},{1,2,2},{0,2,3},{0,2,2},{1,1,2},{2,1,1},{0,1,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,5,9,11,20,17,15,35,31,25,35,59,56,95,85,55,140,135,224,175,295,265,450},{0,1,0,2,0,0,5,9,11,0,15,20,0,0,25,35,59,35,0,85,55,135,70,175,105,265},{0,0,1,2,1,5,2,11,3,5,11,17,15,15,35,17,56,35,35,56,85,140,85,140,175,295},{0,0,0,1,0,0,1,5,2,0,5,11,0,0,15,11,35,15,0,35,35,85,35,85,70,175},{0,0,0,0,1,2,2,4,3,5,11,6,9,15,20,17,31,35,25,56,59,95,85,140,135,224},{0,0,0,0,0,1,0,2,0,1,2,3,5,5,11,3,17,11,15,17,35,56,35,56,85,140},{0,0,0,0,0,0,1,2,2,0,5,4,0,0,9,11,20,15,0,35,25,59,35,85,55,135},{0,0,0,0,0,0,0,1,0,0,1,2,0,0,5,2,11,5,0,11,15,35,15,35,35,85},{0,0,0,0,0,0,0,0,1,0,0,2,0,0,0,5,9,0,0,15,0,25,0,35,0,55},{0,0,0,0,0,0,0,0,0,1,2,0,2,5,4,3,6,11,9,17,20,31,35,56,59,95},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,4,5,0,11,9,20,15,35,25,59},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,5,0,0,5,0,15,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,3,2,5,3,11,17,11,17,35,56},{0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,1,0,0,0,2,2,3,4,6,11,17,20,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,2,5,11,5,11,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,5,0,9,0,15,0,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,4,5,11,9,20},{0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,1,0,2,3,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,5,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5},{0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7498)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -2, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2}, {3, 4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,2}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,2,2},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,6,7},{1,6,6},{1,5,6},{1,5,5},{1,4,5},{0,4,5},{1,4,4},{0,4,4},{1,3,4},{1,3,3},{0,3,4},{0,3,3},{1,2,3},{0,2,3},{1,2,2},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,6,11,21,22,36,38,56,91,62,102,126,147,196,232,252,308,378,469,588,868},{0,1,1,6,6,6,21,22,21,56,22,62,56,62,126,147,126,147,252,308,308,588},{0,0,1,2,6,6,11,11,21,36,22,38,56,62,91,102,126,147,196,232,308,469},{0,0,0,1,1,1,6,6,6,21,6,22,21,22,56,62,56,62,126,147,147,308},{0,0,0,0,1,1,2,2,6,11,6,11,21,22,36,38,56,62,91,102,147,232},{0,0,0,0,0,1,0,2,0,0,6,11,0,21,0,36,0,56,0,91,126,196},{0,0,0,0,0,0,1,1,1,6,1,6,6,6,21,22,21,22,56,62,62,147},{0,0,0,0,0,0,0,1,0,0,1,6,0,6,0,21,0,21,0,56,56,126},{0,0,0,0,0,0,0,0,1,2,1,2,6,6,11,11,21,22,36,38,62,102},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,6,6,6,6,21,22,22,62},{0,0,0,0,0,0,0,0,0,0,1,2,0,6,0,11,0,21,0,36,56,91},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,0,6,0,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,6,6,11,11,22,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,6,0,11,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,6,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,6,21},{0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,6,11},{T^5,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7499)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2}, {3, 4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,1,1},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,5,6},{1,5,5},{1,4,5},{0,4,5},{1,4,4},{0,4,4},{1,3,4},{1,3,3},{0,3,4},{0,3,3},{1,2,3},{0,2,3},{1,2,2},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,6,7,11,13,21,36,27,47,56,77,91,127,126,182,196,287,378,574},{0,1,1,1,6,7,6,21,7,27,21,27,56,77,56,77,126,182,182,378},{0,0,1,1,2,2,6,11,7,13,21,27,36,47,56,77,91,127,182,287},{0,0,0,1,0,2,0,0,6,11,0,21,0,36,0,56,0,91,126,196},{0,0,0,0,1,1,1,6,1,7,6,7,21,27,21,27,56,77,77,182},{0,0,0,0,0,1,0,0,1,6,0,6,0,21,0,21,0,56,56,126},{0,0,0,0,0,0,1,2,1,2,6,7,11,13,21,27,36,47,77,127},{0,0,0,0,0,0,0,1,0,1,1,1,6,7,6,7,21,27,27,77},{0,0,0,0,0,0,0,0,1,2,0,6,0,11,0,21,0,36,56,91},{0,0,0,0,0,0,0,0,0,1,0,1,0,6,0,6,0,21,21,56},{0,0,0,0,0,0,0,0,0,0,1,1,2,2,6,7,11,13,27,47},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,6,0,11,21,36},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,6,7,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7500)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{1, 2}, {3, 4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,4,5},{0,4,5},{1,4,4},{0,4,4},{1,3,4},{0,3,4},{1,3,3},{1,2,3},{0,3,3},{1,2,2},{0,2,3},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,6,12,11,21,22,36,42,72,56,112,91,182,126,252,196,392},{0,1,0,2,0,6,0,0,11,0,21,36,0,56,0,91,0,126,0,196},{0,0,1,2,1,2,6,6,12,21,12,42,21,42,56,112,56,112,126,252},{0,0,0,1,0,1,0,0,6,0,6,21,0,21,0,56,0,56,0,126},{0,0,0,0,1,2,2,6,4,11,12,22,21,42,36,72,56,112,91,182},{0,0,0,0,0,1,0,0,2,0,6,11,0,21,0,36,0,56,0,91},{0,0,0,0,0,0,1,1,2,6,2,12,6,12,21,42,21,42,56,112},{0,0,0,0,0,0,0,1,0,2,2,4,6,12,11,22,21,42,36,72},{0,0,0,0,0,0,0,0,1,0,1,6,0,6,0,21,0,21,0,56},{0,0,0,0,0,0,0,0,0,1,0,2,1,2,6,12,6,12,21,42},{0,0,0,0,0,0,0,0,0,0,1,2,0,6,0,11,0,21,0,36},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,0,6,0,21},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4,6,12,11,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,6,0,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7501)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {1, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,2,4},{1,3,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,1,1},{1,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,5,6},{3,5,5},{3,4,5},{2,4,5},{3,4,4},{2,4,4},{3,3,4},{2,3,4},{3,3,3},{1,3,4},{2,3,3},{1,3,3},{2,2,3},{1,2,3},{2,2,2},{0,2,3},{1,2,2},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,4,7,7,13,10,22,16,28,37,49,50,74,78,84,120,140,155,195,236,306,381,567},{0,1,1,1,4,7,4,7,10,7,22,28,22,28,50,28,74,84,74,84,155,195,195,381},{0,0,1,1,2,2,4,7,7,7,13,13,22,28,37,28,49,49,74,84,120,140,195,306},{0,0,0,1,0,2,0,4,0,7,7,13,10,22,16,28,37,49,50,74,78,120,155,236},{0,0,0,0,1,1,1,1,4,1,7,7,7,7,22,7,28,28,28,28,74,84,84,195},{0,0,0,0,0,1,0,1,0,1,4,7,4,7,10,7,22,28,22,28,50,74,74,155},{0,0,0,0,0,0,1,1,2,1,2,2,7,7,13,7,13,13,28,28,49,49,84,140},{0,0,0,0,0,0,0,1,0,1,2,2,4,7,7,7,13,13,22,28,37,49,74,120},{0,0,0,0,0,0,0,0,1,0,1,1,1,1,7,1,7,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,1,0,2,0,4,0,7,7,13,10,22,16,37,50,78},{0,0,0,0,0,0,0,0,0,0,1,1,1,1,4,1,7,7,7,7,22,28,28,74},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,4,7,4,7,10,22,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,2,2,7,7,13,13,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,4,7,7,13,22,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,4,7,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7502)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & 1 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 6 & 4 & 3 & 5 & 4 & 2 & 3 & 4 & 1 & 3 & 2 & 0 & 4 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {-1, 1, 1, 1, 1, -2}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,3,0},{0,1,-1},{0,0,1},{1,1,2}},{{1,4,5},{1,2,3},{0,4,5},{0,2,5},{1,2,5},{0,2,3}},{1,2,1})
Cox degrees: {{0,1,-1},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,2,6},{1,2,5},{1,1,6},{1,2,4},{1,2,3},{1,1,5},{1,1,4},{1,2,2},{1,1,3},{0,1,4},{1,2,1},{0,1,3},{1,1,2},{1,2,0},{0,0,4},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,15,35,20,50,70,105,51,126,110,196,210,126,211,336,251,540,371,456,610,771,1231},{0,1,1,5,15,6,20,35,50,20,70,51,105,126,56,110,196,126,336,211,251,371,456,771},{0,0,1,0,0,5,15,0,35,15,0,35,70,0,51,70,126,110,210,126,211,210,371,610},{0,0,0,1,5,1,6,15,20,6,35,20,50,70,21,51,105,56,196,110,126,211,251,456},{0,0,0,0,1,0,1,5,6,1,15,6,20,35,6,20,50,21,105,51,56,110,126,251},{0,0,0,0,0,1,5,0,15,5,0,15,35,0,20,35,70,51,126,70,110,126,211,371},{0,0,0,0,0,0,1,0,5,1,0,5,15,0,6,15,35,20,70,35,51,70,110,211},{0,0,0,0,0,0,0,1,1,0,5,1,6,15,1,6,20,6,50,20,21,51,56,126},{0,0,0,0,0,0,0,0,1,0,0,1,5,0,1,5,15,6,35,15,20,35,51,110},{0,0,0,0,0,0,0,0,0,1,0,5,0,0,6,15,0,20,0,35,50,70,105,196},{T^4,0,T^4,0,0,0,0,0,0,T^4,1,0,1,5,T^4,1,6,1,20,6,6,20,21,56},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,0,15,20,35,50,105},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,1,15,5,6,15,20,51},{5*T^4,T^4,6*T^4,0,0,T^4,0,0,0,5*T^4,0,T^4,0,1,6*T^4,0,1,T^4,6,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,6,15,20,50},{0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,T^4,0,1,0,5,1,1,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,5*T^4,0,0,T^4,0,0,0,0,0,0,0,0,5*T^4,0,0,T^4,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7510)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ -2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 3 & 5 & 2 & 4 & 1 & 3 & 4 & 0 & 3 & -1 & 2 & 2 & 1 & 1 & 4 & 0 & 3 & -1 & 0 & 2 & -1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {-2, 1, 1, 1, 1, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{2,3,0},{0,1,-2},{0,0,1},{1,1,1}},{{1,4,5},{1,2,5},{0,2,5},{1,2,3},{0,2,3},{0,4,5}},{1,3,1})
Cox degrees: {{0,1,-2},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (25): {{1,2,5},{1,2,4},{1,2,3},{1,1,5},{1,2,2},{1,1,4},{1,2,1},{1,1,3},{0,1,4},{1,2,0},{0,1,3},{1,2,-1},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,4},{1,1,0},{0,0,3},{1,1,-1},{0,1,0},{0,0,2},{0,1,-1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,15,16,35,40,70,85,41,126,90,210,161,176,280,315,182,456,335,705,526,576,831,936,1451},{0,1,5,5,15,16,35,40,16,70,41,126,85,90,161,176,91,280,182,456,315,335,526,576,936},{0,0,1,1,5,5,15,16,5,35,16,70,40,41,85,90,41,161,91,280,176,182,315,335,576},{0,0,0,1,0,5,0,15,5,0,15,0,35,35,70,70,41,126,90,210,126,176,210,315,526},{0,0,0,0,1,1,5,5,1,15,5,35,16,16,40,41,16,85,41,161,90,91,176,182,335},{0,0,0,0,0,1,0,5,1,0,5,0,15,15,35,35,16,70,41,126,70,90,126,176,315},{0,0,0,0,0,0,1,1,0,5,1,15,5,5,16,16,5,40,16,85,41,41,90,91,182},{0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,15,5,35,16,70,35,41,70,90,176},{0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,16,0,40,0,70,85,126,161,280},{T^4,0,0,T^4,0,0,0,0,T^4,1,0,5,1,1,5,5,1+T^4,16,5,40,16,16,41,41,91},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,5,0,16,0,35,40,70,85,161},{5*T^4,T^4,0,5*T^4,0,T^4,0,0,6*T^4,0,T^4,1,0,0,1,1,6*T^4,5,1+T^4,16,5,5,16,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,5,1,15,5,35,15,16,35,41,90},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,5,0,15,16,35,40,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,1,15,5,5,15,16,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,0,35,70},{0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,T^4,1,0,5,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,5*T^4,0,T^4,0,0,T^4,0,0,0,0,0,0,0,6*T^4,0,T^4,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7511)$ |
3 |
20 |
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9: $\begin{pmatrix}-3 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}4 & 3 & 2 & 1 & 0 & 4 & 4 & 3 & -1 & -2 & 2 & 3 & 2 & 1 & 0 & 1 & 4 & 0 & -1 & -1 & 3 & -2 & -2 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {-3, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 5}, {6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-3,0,1},{0,1,1}},{{0,2,4},{2,3,4},{1,3,4},{0,1,4}},{1,1,4})
Cox degrees: {{-3,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{4,1,2},{3,1,2},{2,1,2},{1,1,2},{0,1,2},{4,1,1},{4,0,1},{3,1,1},{-1,1,2},{-2,1,2},{2,1,1},{3,0,1},{2,0,1},{1,1,1},{0,1,1},{1,0,1},{4,0,0},{0,0,1},{-1,1,1},{-1,0,1},{3,0,0},{-2,1,1},{-2,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,15,35,70,36,37,75,126,210,141,80,156,245,400,280,282,470,621,747,480,925,1135,777,1205,1801},{0,1,5,15,35,15,15,36,70,126,75,37,80,141,245,156,156,280,400,470,282,621,747,480,777,1205},{0,0,1,5,15,5,5,15,35,70,36,15,37,75,141,80,80,156,245,280,156,400,470,282,480,777},{0,0,0,1,5,1,1,5,15,35,15,5,15,36,75,37,37,80,141,156,80,245,280,156,282,480},{0,0,0,0,1,0,0,1,5,15,5,1,5,15,36,15,15,37,75,80,37,141,156,80,156,282},{0,0,0,0,0,1,1,5,0,0,15,5,15,35,70,35,37,70,126,126,80,210,210,156,280,470},{0,0,0,0,0,0,1,0,0,0,0,5,15,0,0,35,36,70,0,126,75,0,210,141,245,400},{0,0,0,0,0,0,0,1,0,0,5,1,5,15,35,15,15,35,70,70,37,126,126,80,156,280},{T^4,0,0,0,0,T^4,2*T^4,0,1,5,1,0,1,5,15,5,5+2*T^4,15,36,37,15,75,80,37,80,156},{5*T^4,T^4,0,0,0,5*T^4,10*T^4,T^4,0,1,0,2*T^4,0,1,5,1,1+10*T^4,5,15,15,5+2*T^4,36,37,15,37,80},{0,0,0,0,0,0,0,0,0,0,1,0,1,5,15,5,5,15,35,35,15,70,70,37,80,156},{0,0,0,0,0,0,0,0,0,0,0,1,5,0,0,15,15,35,0,70,36,0,126,75,141,245},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,5,15,0,35,15,0,70,36,75,141},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,1,1,5,15,15,5,35,35,15,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,5,1,15,15,5,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,0,15,5,0,35,15,36,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,0,15,5,15,36},{0,0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,0,2*T^4,0,1,1,0,5,5,1,5,15},{0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,1,0,0,5,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15,35},{0,0,0,0,0,5*T^4,5*T^4,T^4,0,0,0,T^4,0,0,0,0,10*T^4,0,0,0,2*T^4,1,1,0,1,5},{0,0,0,0,0,0,5*T^4,0,0,0,0,T^4,0,0,0,0,5*T^4,0,0,0,T^4,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7512)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 2 & 4 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 1, -2}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,6},{1,1,6},{1,2,5},{1,2,4},{1,1,5},{1,1,4},{1,2,3},{1,1,3},{0,1,4},{1,2,2},{0,0,4},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,5,15,10,30,35,70,31,70,47,75,126,140,115,252,155,240,287,448,490,770},{0,1,0,0,5,15,0,35,15,0,31,35,0,70,75,126,70,155,126,287,210,490},{0,0,1,5,2,10,15,30,10,35,15,31,70,70,47,140,75,115,155,240,287,448},{0,0,0,1,0,2,5,10,2,15,3,10,35,30,15,70,31,47,75,115,155,240},{0,0,0,0,1,5,0,15,5,0,10,15,0,35,31,70,35,75,70,155,126,287},{0,0,0,0,0,1,0,5,1,0,2,5,0,15,10,35,15,31,35,75,70,155},{0,0,0,0,0,0,1,2,0,5,0,2,15,10,3,30,10,15,31,47,75,115},{0,0,0,0,0,0,0,1,0,0,0,1,0,5,2,15,5,10,15,31,35,75},{0,0,0,0,0,0,0,0,1,0,2,5,0,0,10,0,15,30,35,70,70,140},{0,0,0,0,0,0,0,0,0,1,0,0,5,2,0,10,2,3,10,15,31,47},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,5,10,15,30,35,70},{T^4,2*T^4,0,0,0,0,0,0,T^4,0,2*T^4,0,1,0,0,2,0,0,2,3,10,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,2,5,10,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,0,35},{0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7518)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 3 & 4 & 1 & 3 & 2 & 0 & 4 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {-1, 1, 1, 1, 1, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{0,4,5},{0,2,3},{1,2,5},{0,2,5},{1,2,3}},{1,2,1})
Cox degrees: {{0,1,-1},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,5},{1,2,4},{1,1,5},{1,2,3},{1,1,4},{1,2,2},{1,1,3},{0,1,4},{1,2,1},{0,1,3},{1,1,2},{1,2,0},{0,0,4},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,15,20,35,50,21,70,55,105,126,61,120,196,140,336,231,281,406,511,862},{0,1,1,5,6,15,20,6,35,21,50,70,22,55,105,61,196,120,140,231,281,511},{0,0,1,0,5,0,15,5,0,15,35,0,21,35,70,55,126,70,120,126,231,406},{0,0,0,1,1,5,6,1,15,6,20,35,6,21,50,22,105,55,61,120,140,281},{0,0,0,0,1,0,5,1,0,5,15,0,6,15,35,21,70,35,55,70,120,231},{0,0,0,0,0,1,1,0,5,1,6,15,1,6,20,6,50,21,22,55,61,140},{0,0,0,0,0,0,1,0,0,1,5,0,1,5,15,6,35,15,21,35,55,120},{0,0,0,0,0,0,0,1,0,5,0,0,6,15,0,20,0,35,50,70,105,196},{0,0,0,0,0,0,0,0,1,0,1,5,0,1,6,1,20,6,6,21,22,61},{0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,0,15,20,35,50,105},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,1,15,5,6,15,21,55},{T^4,0,T^4,0,0,0,0,T^4,0,0,0,1,T^4,0,1,0,6,1,1,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,6,15,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,1,5,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,T^4,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7519)$ |
3 |
20 |
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9: $\begin{pmatrix}-2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}4 & 3 & 2 & 1 & 4 & 4 & 3 & 0 & -1 & 3 & 2 & 1 & 2 & 4 & 0 & 1 & 0 & -1 & 3 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {-2, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 5}, {6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,1}},{{0,2,4},{2,3,4},{0,1,4},{1,3,4}},{1,1,3})
Cox degrees: {{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (23): {{4,1,2},{3,1,2},{2,1,2},{1,1,2},{4,1,1},{4,0,1},{3,1,1},{0,1,2},{-1,1,2},{3,0,1},{2,1,1},{1,1,1},{2,0,1},{4,0,0},{0,1,1},{1,0,1},{0,0,1},{-1,1,1},{3,0,0},{-1,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,15,35,16,17,40,70,126,45,85,161,100,102,280,196,350,456,206,582,380,652,1055},{0,1,5,15,5,5,16,35,70,17,40,85,45,45,161,100,196,280,102,350,206,380,652},{0,0,1,5,1,1,5,15,35,5,16,40,17,17,85,45,100,161,45,196,102,206,380},{0,0,0,1,0,0,1,5,15,1,5,16,5,5,40,17,45,85,17,100,45,102,206},{0,0,0,0,1,1,5,0,0,5,15,35,15,17,70,35,70,126,45,126,100,196,350},{0,0,0,0,0,1,0,0,0,5,0,0,15,16,0,35,70,0,40,126,85,161,280},{0,0,0,0,0,0,1,0,0,1,5,15,5,5,35,15,35,70,17,70,45,100,196},{0,0,0,0,0,0,0,1,5,0,1,5,1,1,16,5,17,40,5,45,17,45,102},{T^4,0,0,0,T^4,2*T^4,0,0,1,0,0,1,0,2*T^4,5,1,5,16,1,17,5,17,45},{0,0,0,0,0,0,0,0,0,1,0,0,5,5,0,15,35,0,16,70,40,85,161},{0,0,0,0,0,0,0,0,0,0,1,5,1,1,15,5,15,35,5,35,17,45,100},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,5,15,1,15,5,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,15,0,5,35,16,40,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,15,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,5,1,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,1,15,5,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,5,16},{0,0,0,0,T^4,T^4,0,0,0,0,0,0,0,2*T^4,0,0,0,1,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15,35},{0,0,0,0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7520)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 3 & 4 & 2 & 4 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 1, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 7}, {1, 2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,5},{1,1,5},{1,2,4},{1,1,4},{1,2,3},{1,1,3},{0,1,4},{1,2,2},{0,0,4},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,30,11,35,17,35,70,70,55,140,85,135,175,280,322,518},{0,1,0,5,0,15,5,0,11,15,0,35,35,70,35,85,70,175,126,322},{0,0,1,2,5,10,2,15,3,11,35,30,17,70,35,55,85,135,175,280},{0,0,0,1,0,5,1,0,2,5,0,15,11,35,15,35,35,85,70,175},{0,0,0,0,1,2,0,5,0,2,15,10,3,30,11,17,35,55,85,135},{0,0,0,0,0,1,0,0,0,1,0,5,2,15,5,11,15,35,35,85},{0,0,0,0,0,0,1,0,2,5,0,0,10,0,15,30,35,70,70,140},{0,0,0,0,0,0,0,1,0,0,5,2,0,10,2,3,11,17,35,55},{0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,35,0,70},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,5,10,15,30,35,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,1,0,5,1,2,5,11,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7521)$ |
3 |
20 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}4 & 3 & 2 & 4 & 1 & 4 & 3 & 0 & 2 & 3 & 4 & 1 & 2 & 0 & 3 & 1 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {-1, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 5}, {6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{1,3,4},{0,1,4},{2,3,4}},{1,1,2})
Cox degrees: {{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{4,1,2},{3,1,2},{2,1,2},{4,1,1},{1,1,2},{4,0,1},{3,1,1},{0,1,2},{2,1,1},{3,0,1},{4,0,0},{1,1,1},{2,0,1},{0,1,1},{3,0,0},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,15,6,35,7,20,70,50,25,27,105,65,196,75,140,266,170,336,602},{0,1,5,1,15,1,6,35,20,7,7,50,25,105,27,65,140,75,170,336},{0,0,1,0,5,0,1,15,6,1,1,20,7,50,7,25,65,27,75,170},{0,0,0,1,0,1,5,0,15,5,7,35,15,70,25,35,70,65,140,266},{0,0,0,0,1,0,0,5,1,0,0,6,1,20,1,7,25,7,27,75},{0,0,0,0,0,1,0,0,0,5,6,0,15,0,20,35,70,50,105,196},{0,0,0,0,0,0,1,0,5,1,1,15,5,35,7,15,35,25,65,140},{0,0,0,0,0,0,0,1,0,0,0,1,0,6,0,1,7,1,7,27},{0,0,0,0,0,0,0,0,1,0,0,5,1,15,1,5,15,7,25,65},{0,0,0,0,0,0,0,0,0,1,1,0,5,0,6,15,35,20,50,105},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,35,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,1,5,1,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,15,6,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,1,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7522)$ |
3 |
20 |
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9: $\begin{pmatrix}-2 & 1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}3 & 2 & 1 & 4 & 4 & 0 & 3 & -1 & 3 & 2 & -2 & 1 & 2 & 4 & 0 & 1 & 3 & -1 & 0 & 2 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {-2, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 6}, {5, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,1},{-1,1,1}},{{0,2,4},{2,4,5},{0,1,4},{1,3,5},{2,3,5},{1,4,5}},{1,1,3})
Cox degrees: {{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (23): {{3,1,2},{2,1,2},{1,1,2},{4,1,1},{4,0,1},{0,1,2},{3,1,1},{-1,1,2},{3,0,1},{2,1,1},{-2,1,2},{1,1,1},{2,0,1},{4,0,0},{0,1,1},{1,0,1},{3,0,0},{-1,1,1},{0,0,1},{2,0,0},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,15,5,6,35,16,70,21,40,126,85,55,56,161,120,126,280,231,251,406,456,771},{0,1,5,1,1,15,5,35,6,16,70,40,21,21,85,55,56,161,120,126,231,251,456},{0,0,1,0,0,5,1,15,1,5,35,16,6,6,40,21,21,85,55,56,120,126,251},{0,0,0,1,1,0,5,0,5,15,0,35,15,21,70,35,55,126,70,120,126,231,406},{0,0,0,0,1,0,0,0,5,0,0,0,15,16,0,35,40,0,70,85,126,161,280},{0,0,0,0,0,1,0,5,0,1,15,5,1,1,16,6,6,40,21,21,55,56,126},{0,0,0,0,0,0,1,0,1,5,0,15,5,6,35,15,21,70,35,55,70,120,231},{0,0,0,T^4,T^4,0,0,1,0,0,5,1,0,T^4,5,1,1,16,6,6,21,21,56},{0,0,0,0,0,0,0,0,1,0,0,0,5,5,0,15,16,0,35,40,70,85,161},{0,0,0,0,0,0,0,0,0,1,0,5,1,1,15,5,6,35,15,21,35,55,120},{T^4,0,0,5*T^4,6*T^4,0,T^4,0,T^4,0,1,0,0,6*T^4,1,0,T^4,5,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,1,15,5,6,15,21,55},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,0,15,16,35,40,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,1,5,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,T^4,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7523)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}4 & 3 & 4 & 2 & 3 & 4 & 1 & 2 & 4 & 3 & 0 & 1 & 3 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 5}, {6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{4,1,2},{3,1,2},{4,1,1},{2,1,2},{3,1,1},{4,0,1},{1,1,2},{2,1,1},{4,0,0},{3,0,1},{0,1,2},{1,1,1},{3,0,0},{2,0,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,2,15,10,3,35,30,5,15,70,70,25,45,140,75,105,210,175,350},{0,1,0,5,2,0,15,10,0,3,35,30,5,15,70,25,45,105,75,175},{0,0,1,0,5,1,0,15,3,5,0,35,15,15,70,45,35,70,105,210},{0,0,0,1,0,0,5,2,0,0,15,10,0,3,30,5,15,45,25,75},{0,0,0,0,1,0,0,5,0,1,0,15,3,5,35,15,15,35,45,105},{0,0,0,0,0,1,0,0,2,5,0,0,10,15,0,30,35,70,70,140},{0,0,0,0,0,0,1,0,0,0,5,2,0,0,10,0,3,15,5,25},{0,0,0,0,0,0,0,1,0,0,0,5,0,1,15,3,5,15,15,45},{0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,10,15,35,30,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,3,0,5},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,1,5,3,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,15,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7524)$ |
3 |
20 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}3 & 2 & 4 & 1 & 4 & 3 & 0 & 2 & 3 & -1 & 1 & 4 & 2 & 0 & 3 & 1 & -1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {-1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 6}, {5, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{0,2,4},{0,1,4},{2,4,5},{1,4,5},{2,3,5}},{1,1,2})
Cox degrees: {{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (21): {{3,1,2},{2,1,2},{4,1,1},{1,1,2},{4,0,1},{3,1,1},{0,1,2},{2,1,1},{3,0,1},{-1,1,2},{1,1,1},{4,0,0},{2,0,1},{0,1,1},{3,0,0},{1,0,1},{-1,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,1,15,2,6,35,20,11,70,50,12,35,105,41,85,196,105,175,225,427},{0,1,0,5,0,1,15,6,2,35,20,2,11,50,12,35,105,41,85,105,225},{0,0,1,0,1,5,0,15,5,0,35,11,15,70,35,35,126,85,70,175,322},{0,0,0,1,0,0,5,1,0,15,6,0,2,20,2,11,50,12,35,41,105},{0,0,0,0,1,0,0,0,5,0,0,6,15,0,20,35,0,50,70,105,196},{0,0,0,0,0,1,0,5,1,0,15,2,5,35,11,15,70,35,35,85,175},{0,0,0,0,0,0,1,0,0,5,1,0,0,6,0,2,20,2,11,12,41},{0,0,0,0,0,0,0,1,0,0,5,0,1,15,2,5,35,11,15,35,85},{0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,15,0,20,35,50,105},{0,0,T^4,0,T^4,0,0,0,0,1,0,T^4,0,1,0,0,6,0,2,2,12},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,1,15,2,5,11,35},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,6,15,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,1,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,6,20},{0,0,T^4,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7525)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}4 & 3 & 4 & 2 & 3 & 4 & 1 & 2 & 4 & 3 & 0 & 1 & 3 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4, 6}, {5, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{0,1,3},{2,3,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{4,1,2},{3,1,2},{4,1,1},{2,1,2},{3,1,1},{4,0,1},{1,1,2},{2,1,1},{4,0,0},{3,0,1},{0,1,2},{1,1,1},{3,0,0},{2,0,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,5,2,15,10,7,35,30,13,25,70,70,45,65,140,115,140,266,245,462},{0,1,0,5,2,1,15,10,2,7,35,30,13,25,70,45,65,140,115,245},{0,0,1,0,5,1,0,15,7,5,0,35,25,15,70,65,35,70,140,266},{0,0,0,1,0,0,5,2,0,1,15,10,2,7,30,13,25,65,45,115},{0,0,0,0,1,0,0,5,1,1,0,15,7,5,35,25,15,35,65,140},{0,0,0,0,0,1,0,0,2,5,0,0,10,15,0,30,35,70,70,140},{0,0,0,0,0,0,1,0,0,0,5,2,0,1,10,2,7,25,13,45},{0,0,0,0,0,0,0,1,0,0,0,5,1,1,15,7,5,15,25,65},{0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,10,15,35,30,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,1,7,2,13},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,1,5,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,15,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7526)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ -1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 4 & 1 & 3 & 3 & 2 & 4 & 1 & 2 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {-1, 1, 1, 1, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 7}, {1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{1,2,3},{0,2,5},{0,2,3},{0,4,5},{1,2,5}},{1,2,1})
Cox degrees: {{0,1,-1},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{2,3,5},{2,3,4},{2,2,5},{2,3,3},{2,2,4},{2,3,2},{1,2,4},{2,3,1},{2,2,3},{1,2,3},{2,2,2},{1,1,4},{2,2,1},{1,2,2},{1,1,3},{1,2,1},{0,1,3},{1,2,0},{1,1,2},{0,1,2},{1,1,1},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,5,10,14,20,16,35,30,38,55,44,91,75,93,131,96,210,171,183,285,204,442,315,367,502,607,940},{0,1,1,4,5,10,5,20,14,16,30,17,55,38,44,75,44,131,93,96,171,102,285,183,204,315,367,607},{0,0,1,0,4,0,4,0,10,10,20,16,35,20,38,35,38,56,75,75,131,96,210,131,183,210,315,502},{0,0,0,1,1,4,1,10,5,5,14,5,30,16,17,38,17,75,44,44,93,45,171,96,102,183,204,367},{0,0,0,0,1,0,1,0,4,4,10,5,20,10,16,20,16,35,38,38,75,44,131,75,96,131,183,315},{0,0,0,0,0,1,0,4,1,1,5,1,14,5,5,16,5,38,17,17,44,17,93,44,45,96,102,204},{0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,16,35,30,38,55,44,91,75,93,131,171,285},{T^3,0,T^3,0,0,0,2*T^3,1,0,0,1,2*T^3,5,1,1,5,1+3*T^3,16,5,5,17,5+3*T^3,44,17,17,44,45,102},{0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,5,20,16,16,38,17,75,38,44,75,96,183},{0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,5,20,14,16,30,17,55,38,44,75,93,171},{0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,1,10,5,5,16,5,38,16,17,38,44,96},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,10,20,16,35,20,38,35,75,131},{0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,0,4,1,1,5,1+3*T^3,16,5,5,16,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,5,5,14,5,30,16,17,38,44,93},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,5,20,10,16,20,38,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,5,1,14,5,5,16,17,44},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,30,55},{0,0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,2*T^3,1,0,0,1,2*T^3,5,1,1,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,16,38},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7527)$ |
3 |
24 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 3 & 3 & 2 & 0 & -1 & 1 & 2 & 3 & 0 & 1 & 0 & 3 & 2 & -1 & 2 & 1 & -1 & 3 & 1 & 0 & -1 & 2 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 2 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 1, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 5}, {4, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1},{-1,1,2}},{{0,2,4},{2,3,6},{4,5,6},{1,4,5},{0,1,4},{2,4,6},{3,5,6}},{1,1,2})
Cox degrees: {{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,2,3},{1,2,3},{3,2,2},{3,1,2},{2,2,2},{0,2,3},{-1,2,3},{1,2,2},{2,1,2},{3,1,1},{0,2,2},{1,1,2},{0,1,2},{3,0,1},{2,1,1},{-1,2,2},{2,0,1},{1,1,1},{-1,1,2},{3,0,0},{1,0,1},{0,1,1},{-1,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,1,2,5,10,20,14,10,11,30,28,60,16,34,55,49,78,110,55,112,150,257,133,215,267,473},{0,1,0,0,1,4,10,5,2,2,14,10,28,3,11,30,16,34,60,17,49,78,150,55,112,133,267},{0,0,1,1,4,0,0,10,4,10,20,10,20,10,28,35,28,60,35,49,60,110,182,112,110,215,368},{0,0,0,1,0,0,0,0,4,5,0,10,20,10,14,0,28,30,35,34,60,55,91,78,110,150,257},{0,0,0,0,1,0,0,4,1,2,10,4,10,2,10,20,10,28,20,16,28,60,110,49,60,112,215},{0,0,0,0,0,1,4,1,0,0,5,2,10,0,2,14,3,11,28,3,16,34,78,17,49,55,133},{0,0,T^3,2*T^3,0,0,1,0,0,2*T^3,1,0,2,3*T^3,0,5,0,2,10,3*T^3,3,11,34,3,16,17,55},{0,0,0,0,0,0,0,1,0,0,4,1,4,0,2,10,2,10,10,3,10,28,60,16,28,49,112},{0,0,0,0,0,0,0,0,1,1,0,4,10,2,5,0,10,14,20,11,28,30,55,34,60,78,150},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,4,10,0,10,10,20,35,28,20,60,110},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,0,2,4,0,2,10,28,3,10,16,49},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,0,2,5,10,2,10,14,30,11,28,34,78},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,0,2,5,14,2,10,11,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,5,10,0,0,14,20,30,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,2,4,10,20,10,10,28,60},{0,0,T^3,T^3,0,0,0,0,0,2*T^3,0,0,0,2*T^3,0,1,0,0,1,3*T^3,0,2,10,0,2,3,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,0,5,10,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,10,2,4,10,28},{0,0,0,T^3,0,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,1,2*T^3,0,1,5,0,2,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,2,10},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7528)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 \\ 2 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 7 & 7 & 6 & 6 & 6 & 5 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0 \\ 8 & 7 & 7 & 6 & 6 & 6 & 6 & 5 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 1, 1, -2, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 4, 5}, {4, 5, 7}, {1, 2, 3, 6, 7}, {0, 8}, {1, 2, 3, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,2},{1,2,2},{1,2,3}},{{3,5,6},{4,5,6},{1,3,5},{2,3,6},{2,4,6},{0,4,5},{0,2,4},{0,1,5}},{1,1,1})
Cox degrees: {{1,1,2},{0,1,1},{0,1,1},{0,1,1},{1,2,2},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,7,8},{2,7,7},{2,6,7},{2,6,6},{1,6,6},{2,5,6},{1,5,6},{2,5,5},{1,5,5},{2,4,5},{2,4,4},{1,4,5},{1,4,4},{2,3,4},{1,3,4},{0,4,4},{2,3,3},{2,2,3},{1,3,3},{0,3,3},{1,2,3},{1,2,2},{0,2,2},{1,1,2},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,5,5,6,15,17,15,21,35,35,45,55,70,100,57,70,126,120,131,196,231,266,350,406,491,841},{0,1,1,5,5,5,5,15,17,15,35,17,45,35,45,45,70,70,100,103,100,196,211,196,350,395,687},{0,0,1,1,1,5,5,5,6,15,15,17,21,35,45,21,35,70,55,57,100,120,131,196,231,266,491},{0,0,0,1,1,1,1,5,5,5,15,5,17,15,17,17,35,35,45,45,45,100,103,100,196,211,395},{0,0,0,0,1,0,1,0,5,0,0,5,15,0,15,17,0,0,35,45,35,70,100,70,126,196,350},{0,0,0,0,0,1,1,1,1,5,5,5,6,15,17,6,15,35,21,21,45,55,57,100,120,131,266},{0,0,0,0,0,0,1,0,1,0,0,5,5,0,15,6,0,0,15,21,35,35,55,70,70,120,231},{0,0,0,0,0,0,0,1,1,1,5,1,5,5,5,5,15,15,17,17,17,45,45,45,100,103,211},{0,0,0,0,0,0,0,0,1,0,0,1,5,0,5,5,0,0,15,17,15,35,45,35,70,100,196},{0,0,0,0,0,0,0,0,0,1,1,1,1,5,5,1,5,15,6,6,17,21,21,45,55,57,131},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,5,5,5,5,5,17,17,17,45,45,103},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,1,0,0,5,6,15,15,21,35,35,55,120},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,5,5,5,15,17,15,35,45,100},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,T^4,1,5,1,1,5,6,6,17,21,21,57},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,5,6,15,15,21,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{T^4,0,0,0,2*T^4,0,2*T^4,0,0,0,0,0,0,0,0,3*T^4,1,1,1,1,1,5,5,5,17,17,45},{T^4,T^4,0,0,6*T^4,0,2*T^4,0,T^4,0,0,0,0,0,0,7*T^4,0,1,0,T^4,1,1,1,5,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,T^4,0,T^4,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7531)$ |
3 |
24 |
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9: $\begin{pmatrix}-1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 0 & 2 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {-1, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3}, {4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{1,3,4},{2,3,4},{0,1,4}},{1,1,2})
Cox degrees: {{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,3,4},{1,3,4},{0,3,4},{2,3,3},{1,3,3},{2,2,3},{0,3,3},{1,2,3},{2,2,2},{0,2,3},{2,1,2},{1,2,2},{0,2,2},{1,1,2},{0,1,2},{2,1,1},{2,0,1},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,4,9,7,16,18,22,34,28,46,79,64,115,74,84,145,241,175,301,195,361,582},{0,1,3,1,4,1,9,7,7,18,7,22,46,28,64,28,28,74,145,84,175,84,195,361},{0,0,1,0,1,0,4,1,1,7,1,7,22,7,28,7,7,28,74,28,84,28,84,195},{0,0,0,1,3,1,6,3,7,6,7,18,34,18,34,28,28,64,115,64,115,84,175,301},{0,0,0,0,1,0,3,1,1,3,1,7,18,7,18,7,7,28,64,28,64,28,84,175},{0,0,0,0,0,1,0,3,4,6,7,9,16,18,34,22,28,46,79,64,115,74,145,241},{0,0,0,0,0,0,1,0,0,1,0,1,7,1,7,1,1,7,28,7,28,7,28,84},{0,0,0,0,0,0,0,1,1,3,1,4,9,7,18,7,7,22,46,28,64,28,74,145},{0,0,0,0,0,0,0,0,1,0,1,3,6,3,6,7,7,18,34,18,34,28,64,115},{0,0,0,0,0,0,0,0,0,1,0,1,4,1,7,1,1,7,22,7,28,7,28,74},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,6,4,7,9,16,18,34,22,46,79},{0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,1,1,7,18,7,18,7,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,7,1,7,1,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,1,4,9,7,18,7,22,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,7,1,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,6,3,6,7,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6,4,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,3,1,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7532)$ |
3 |
25 |
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9: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 3 & 1 & 3 & 2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 1, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 3, 4, 5}, {3, 4, 5, 7}, {1, 2, 6, 7}, {0, 8}, {1, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1},{1,1,2}},{{4,5,6},{1,4,5},{0,1,5},{2,3,6},{0,3,5},{2,4,6},{3,5,6}},{1,1,1})
Cox degrees: {{1,0,1},{0,1,1},{0,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{3,5,6},{3,5,5},{2,5,5},{3,4,5},{3,4,4},{2,4,5},{2,4,4},{3,3,4},{2,3,4},{1,4,4},{3,3,3},{1,3,4},{3,2,3},{2,3,3},{1,3,3},{2,2,3},{1,2,3},{0,3,3},{2,2,2},{2,1,2},{1,2,2},{0,2,2},{1,1,2},{1,1,1},{0,1,1},{1,0,1},{0,0,0}}
Ext matrix: {{1,1,2,4,4,7,10,10,22,13,10,28,20,28,43,50,74,49,60,95,102,130,155,200,276,281,507},{0,1,1,1,4,1,7,4,7,7,10,7,10,22,28,22,28,28,50,50,74,84,74,155,195,155,381},{0,0,1,0,0,1,4,0,4,7,0,7,0,10,22,10,22,28,20,20,50,74,50,95,155,95,281},{0,0,0,1,1,1,2,4,7,2,4,7,10,10,13,22,28,13,28,50,43,49,74,102,130,155,276},{0,0,0,0,1,0,1,1,1,1,4,1,4,7,7,7,7,7,22,22,28,28,28,74,84,74,195},{0,0,0,0,0,1,1,0,4,2,0,7,0,4,10,10,22,13,10,20,28,43,50,60,102,95,200},{0,0,0,0,0,0,1,0,1,1,0,1,0,4,7,4,7,7,10,10,22,28,22,50,74,50,155},{0,0,0,0,0,0,0,1,1,0,1,1,4,2,2,7,7,2,10,22,13,13,28,43,49,74,130},{0,0,0,0,0,0,0,0,1,0,0,1,0,1,2,4,7,2,4,10,10,13,22,28,43,50,102},{0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,0,4,7,0,0,10,22,10,20,50,20,95},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,7,7,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,2,0,0,4,10,10,10,28,20,60},{0,0,2*T^3,0,0,0,0,0,0,3*T^3,0,0,1,0,0,1,1,4*T^3,2,7,2,2,7,13,13,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,4,4,7,7,7,22,28,22,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,4,7,4,10,22,10,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,2,2,7,10,13,22,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,2,4,4,10,10,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,7,7,7,28},{0,0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,1,0,0,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,7,4,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7534)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & -1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}4 & 3 & 4 & 3 & 2 & 4 & 2 & 3 & 1 & 4 & 3 & 1 & 2 & 0 & 3 & 2 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 0 \\ 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, -1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 2, 3, 4, 5}, {2, 3, 4, 5, 7}, {1, 6, 7}, {0, 8}, {1, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{-1,1,1}},{{0,4,5},{3,5,6},{1,3,4},{0,1,4},{3,4,5},{0,2,5},{2,5,6}},{2,1,2})
Cox degrees: {{1,-1,0},{-1,1,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{4,1,2},{3,2,2},{4,1,1},{3,1,2},{2,2,2},{4,0,1},{2,1,2},{3,1,1},{1,2,2},{4,0,0},{3,0,1},{1,1,2},{2,1,1},{0,2,2},{3,0,0},{2,0,1},{0,1,2},{1,1,1},{2,0,0},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,2,5,5,7,15,11,15,13,25,35,35,35,46,65,70,85,120,140,175,266,260,497},{0,1,1,1,5,1,5,7,15,7,7,15,25,35,28,25,35,65,80,65,140,140,185,371},{0,0,1,0,0,1,0,5,0,7,5,0,15,0,25,15,0,35,65,35,70,70,140,266},{0,0,0,1,1,1,5,2,5,2,7,15,11,15,13,25,35,35,46,65,85,140,120,260},{0,0,0,0,1,0,1,1,5,1,1,5,7,15,7,7,15,25,28,25,65,65,80,185},{0,0,0,0,0,1,0,1,0,2,5,0,5,0,11,15,0,15,35,35,35,70,85,175},{0,0,0,0,0,0,1,0,1,0,1,5,2,5,2,7,15,11,13,25,35,65,46,120},{0,0,0,0,0,0,0,1,0,1,1,0,5,0,7,5,0,15,25,15,35,35,65,140},{0,0,0,0,0,0,0,0,1,0,0,1,1,5,1,1,5,7,7,7,25,25,28,80},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,15,0,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,5,0,5,11,15,15,35,35,85},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,2,2,7,11,25,13,46},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,5,7,5,15,15,25,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,5,5,15,11,35},{0,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,1,0,0,1,2,7,2,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7535)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & -2 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}3 & 2 & 2 & 1 & 4 & 3 & 1 & 0 & 3 & 2 & 0 & 4 & -1 & 2 & 1 & -1 & -2 & 1 & 3 & 0 & 2 & 0 & -1 & 1 & 0 \\ 1 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 0, 0, 0, 1}, {0, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 2, 3, 4, 6}, {1, 5, 7}, {2, 3, 4, 6, 7}, {0, 8}, {1, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-2,1,1},{-1,1,1}},{{0,3,4},{2,5,6},{0,1,3},{1,3,5},{2,4,6},{3,5,6},{0,2,4},{3,4,6}},{2,1,4})
Cox degrees: {{1,-1,0},{-2,1,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (25): {{3,1,2},{2,2,2},{2,1,2},{1,2,2},{4,0,1},{3,1,1},{1,1,2},{0,2,2},{3,0,1},{2,1,1},{0,1,2},{4,0,0},{-1,2,2},{2,0,1},{1,1,1},{-1,1,2},{-2,2,2},{1,0,1},{3,0,0},{0,1,1},{2,0,0},{0,0,1},{-1,1,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,5,5,6,7,15,15,21,25,35,27,35,55,65,70,70,120,76,140,175,231,266,351,637},{0,1,1,5,1,6,5,15,6,21,15,22,35,21,55,35,70,55,61,120,141,120,231,286,526},{0,0,1,1,1,1,5,5,6,7,15,7,15,21,25,35,35,55,27,65,76,120,140,175,351},{0,0,0,1,0,1,1,5,1,6,5,6,15,6,21,15,35,21,22,55,61,55,120,141,286},{0,0,0,0,1,1,0,0,5,5,0,7,0,15,15,0,0,35,25,35,65,70,70,140,266},{0,0,0,0,0,1,0,0,1,5,0,6,0,5,15,0,0,15,21,35,55,35,70,120,231},{0,0,0,0,0,0,1,1,1,1,5,1,5,6,7,15,15,21,7,25,27,55,65,76,175},{0,0,0,0,0,0,0,1,0,1,1,1,5,1,6,5,15,6,6,21,22,21,55,61,141},{0,0,0,0,0,0,0,0,1,1,0,1,0,5,5,0,0,15,7,15,25,35,35,65,140},{0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,0,0,5,6,15,21,15,35,55,120},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,5,6,1,7,7,21,25,27,76},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,5,0,15,0,0,35,70},{0,0,0,0,T^4,0,0,0,0,0,0,T^4,1,0,1,1,5,1,1,6,6,6,21,22,61},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,5,1,5,7,15,15,25,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,5,6,5,15,21,55},{0,0,0,0,T^4,0,0,0,0,0,0,T^4,0,0,0,1,1,1,0,1,1,6,7,7,27},{T^4,0,0,0,6*T^4,T^4,0,0,T^4,0,0,6*T^4,0,0,0,0,1,0,T^4,1,1,1,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7536)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}4 & 4 & 3 & 4 & 3 & 4 & 2 & 4 & 3 & 2 & 3 & 1 & 3 & 2 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 2, 3, 4, 5}, {2, 3, 4, 5, 7}, {1, 6, 7}, {0, 8}, {1, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{0,2,5},{1,3,4},{0,1,4},{3,4,5}},{2,1,1})
Cox degrees: {{1,-1,0},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (23): {{4,2,2},{4,1,2},{3,2,2},{4,1,1},{3,1,2},{4,0,1},{2,2,2},{4,0,0},{3,1,1},{2,1,2},{3,0,1},{1,2,2},{3,0,0},{2,1,1},{1,1,2},{2,0,1},{0,2,2},{2,0,0},{1,1,1},{1,0,1},{0,1,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,5,3,5,3,15,6,15,15,15,35,30,45,35,45,70,90,105,105,210,210,420},{0,1,1,1,5,3,5,3,7,15,15,15,18,25,35,45,35,60,65,105,140,150,315},{0,0,1,0,1,0,5,0,3,5,3,15,6,15,15,15,35,30,45,45,105,90,210},{0,0,0,1,0,1,0,3,5,0,5,0,15,15,0,15,0,45,35,35,70,105,210},{0,0,0,0,1,0,1,0,1,5,3,5,3,7,15,15,15,18,25,45,65,60,150},{0,0,0,0,0,1,0,1,1,0,5,0,7,5,0,15,0,25,15,35,35,65,140},{0,0,0,0,0,0,1,0,0,1,0,5,0,3,5,3,15,6,15,15,45,30,90},{0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,0,15,0,0,0,35,70},{0,0,0,0,0,0,0,0,1,0,1,0,3,5,0,5,0,15,15,15,35,45,105},{0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,3,5,3,7,15,25,18,60},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,5,0,7,5,15,15,25,65},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,0,3,3,15,6,30},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,5,5,15,15,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,3,7,3,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,3,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7537)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & -1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 4 & 2 & 3 & 1 & 4 & 3 & 1 & 2 & 0 & 3 & 2 & 0 & 1 & -1 & 2 & 1 & -1 & 0 & 1 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 0, 0, 0, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 2, 3, 4, 6}, {1, 5, 7}, {2, 3, 4, 6, 7}, {0, 8}, {1, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{0,2,4},{0,1,3},{2,4,5},{3,4,5}},{2,1,2})
Cox degrees: {{1,-1,0},{-1,1,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,1,2},{2,2,2},{4,0,1},{2,1,2},{3,1,1},{1,2,2},{4,0,0},{3,0,1},{1,1,2},{2,1,1},{0,2,2},{3,0,0},{2,0,1},{0,1,2},{1,1,1},{-1,2,2},{2,0,0},{1,0,1},{-1,1,2},{0,1,1},{1,0,0},{0,0,1},{-1,1,1},{0,0,0}}
Ext matrix: {{1,1,2,5,3,5,5,11,15,15,15,26,35,35,45,35,80,85,70,105,190,175,210,385},{0,1,0,1,2,5,3,2,5,11,15,17,11,15,35,35,56,35,35,85,140,85,175,295},{0,0,1,0,1,0,3,5,0,5,0,15,15,0,15,0,45,35,0,35,105,70,70,210},{0,0,0,1,0,1,0,2,5,3,5,5,11,15,15,15,26,35,35,45,80,85,105,190},{0,0,0,0,1,0,2,1,0,5,0,11,5,0,15,0,35,15,0,35,85,35,70,175},{0,0,0,0,0,1,0,0,1,2,5,3,2,5,11,15,17,11,15,35,56,35,85,140},{0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,0,15,0,0,0,35,0,0,70},{0,0,0,0,0,0,0,1,0,1,0,3,5,0,5,0,15,15,0,15,45,35,35,105},{0,0,0,0,0,0,0,0,1,0,1,0,2,5,3,5,5,11,15,15,26,35,45,80},{0,0,0,0,0,0,0,0,0,1,0,2,1,0,5,0,11,5,0,15,35,15,35,85},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,5,3,2,5,11,17,11,35,56},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,15,0,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,5,0,5,15,15,15,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,5,3,5,11,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,5,11,5,15,35},{0,0,T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,1,0,0,1,2,3,2,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,5,15},{0,0,T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,5,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3},{0,0,T^4,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7538)$ |
3 |
24 |
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9: $\begin{pmatrix}-2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}3 & 2 & 1 & 0 & 3 & 2 & -1 & 3 & 1 & 2 & 1 & 0 & -1 & 0 & 3 & 2 & 3 & -1 & 1 & 2 & 1 & 0 & -1 & 3 & 0 & -1 & 2 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {-2, 1, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 4}, {5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,1}},{{0,2,4},{0,1,4},{1,3,4},{2,3,4}},{1,1,3})
Cox degrees: {{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{3,2,3},{2,2,3},{1,2,3},{0,2,3},{3,2,2},{2,2,2},{-1,2,3},{3,1,2},{1,2,2},{2,1,2},{1,1,2},{0,2,2},{-1,2,2},{0,1,2},{3,1,1},{2,1,1},{3,0,1},{-1,1,2},{1,1,1},{2,0,1},{1,0,1},{0,1,1},{-1,1,1},{3,0,0},{0,0,1},{-1,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,10,20,11,24,35,13,45,32,65,76,119,116,68,128,71,189,219,140,249,348,522,255,408,627,432,687,1036},{0,1,4,10,4,11,20,4,24,13,32,45,76,65,32,68,32,116,128,71,140,219,348,140,249,408,255,432,687},{0,0,1,4,1,4,10,1,11,4,13,24,45,32,13,32,13,65,68,32,71,128,219,71,140,249,140,255,432},{0,0,0,1,0,1,4,0,4,1,4,11,24,13,4,13,4,32,32,13,32,68,128,32,71,140,71,140,255},{0,0,0,0,1,4,0,1,10,4,10,20,35,20,13,32,13,35,65,32,65,116,189,71,116,189,140,249,408},{0,0,0,0,0,1,0,0,4,1,4,10,20,10,4,13,4,20,32,13,32,65,116,32,65,116,71,140,249},{T^3,0,0,0,T^3,0,1,3*T^3,1,0,1,4,11,4,1+3*T^3,4,1+6*T^3,13,13,4,13,32,68,13+6*T^3,32,71,32,71,140},{0,0,0,0,0,0,0,1,0,4,10,0,0,20,11,24,13,35,45,32,65,76,119,68,116,189,128,219,348},{0,0,0,0,0,0,0,0,1,0,1,4,10,4,1,4,1,10,13,4,13,32,65,13,32,65,32,71,140},{0,0,0,0,0,0,0,0,0,1,4,0,0,10,4,11,4,20,24,13,32,45,76,32,65,116,68,128,219},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,4,1,10,11,4,13,24,45,13,32,65,32,68,128},{0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,1,0,4,4,1,4,13,32,4,13,32,13,32,71},{0,0,0,0,T^3,0,0,T^3,0,0,0,0,1,0,3*T^3,0,3*T^3,1,1,0,1,4,13,1+6*T^3,4,13,4,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,1,4,11,24,4,13,32,13,32,68},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,10,4,10,20,35,13,20,35,32,65,116},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,4,10,20,4,10,20,13,32,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,0,11,20,35,24,45,76},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,3*T^3,1,1,0,1,4,11,1+3*T^3,4,13,4,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,10,1,4,10,4,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,4,10,20,11,24,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,10,4,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,4,1,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,1,3*T^3,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7539)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ -1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 4 & 3 & 2 & 2 & 1 & 3 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 5 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 3 & 4 & 4 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {-2, 1, 1, 1, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 4, 5}, {4, 5, 7}, {1, 2, 3, 6, 7}, {0, 8}, {1, 2, 3, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{2,0,1},{0,1,1},{1,1,1},{1,1,2}},{{6,7,8},{3,6,8},{4,5,7,8},{3,4,8},{1,3,4},{0,5,7},{0,2,7},{0,1,5},{2,6,7},{1,4,5}},{2,1,1})
Cox degrees: {{1,-1,0},{0,1,1},{0,1,1},{0,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{2,5,5},{2,4,5},{1,5,5},{2,4,4},{1,4,5},{2,3,4},{1,4,4},{2,3,3},{2,2,3},{1,3,4},{0,4,4},{1,3,3},{2,2,2},{1,2,3},{2,1,2},{0,3,3},{2,1,1},{1,2,2},{2,0,1},{1,1,2},{0,2,2},{1,1,1},{1,0,1},{0,1,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,2,5,2,5,11,15,15,11,17,35,35,35,35,56,70,85,70,85,140,175,175,295,322,553},{0,1,1,1,2,5,6,5,15,11,12,21,15,35,35,41,35,55,70,85,106,120,175,230,231,442},{0,0,1,0,1,0,5,0,0,5,11,15,0,15,0,35,0,35,0,35,85,70,70,175,126,322},{0,0,0,1,0,1,2,5,5,2,3,11,15,11,15,17,35,35,35,35,56,85,85,140,175,295},{0,0,0,0,1,0,1,0,0,5,6,5,0,15,0,21,0,15,0,35,55,35,70,120,70,231},{0,0,0,0,0,1,1,1,5,2,2,6,5,11,15,12,15,21,35,35,41,55,85,106,120,230},{0,0,0,0,0,0,1,0,0,1,2,5,0,5,0,11,0,15,0,15,35,35,35,85,70,175},{0,0,0,0,0,0,0,1,1,0,0,2,5,2,5,3,15,11,15,11,17,35,35,56,85,140},{0,0,0,0,0,0,0,0,1,0,0,1,1,2,5,2,5,6,15,11,12,21,35,41,55,106},{0,0,0,0,0,0,0,0,0,1,1,1,0,5,0,6,0,5,0,15,21,15,35,55,35,120},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,0,0,15,0,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,0,5,0,5,11,15,15,35,35,85},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,2,5,2,3,11,11,17,35,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,5,6,5,15,21,15,55},{0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,1,0,1,1,5,2,2,6,11,12,21,41},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,35},{0,0,T^4,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,1,0,1,0,0,2,2,3,11,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,5,5,11,15,35},{T^4,0,6*T^4,0,T^4,0,T^4,0,0,0,6*T^4,0,0,0,0,T^4,0,0,1,0,0,1,2,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,6,5,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,5,11},{0,0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,T^4,0,T^4,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7540)$ |
3 |
25 |
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9: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ -2 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\ -1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}3 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 3 & 2 & 2 & 1 & 3 & 1 & 0 & 2 & 2 & 0 & 1 & -1 & 3 & 1 & 0 & 2 & 2 & 0 & 1 & -1 & 3 & 1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 3 & 3 & 2 & 2 & 3 & 1 & 1 & 3 & 2 & 0 & 2 & 0 & 3 & 1 & 1 & 3 & 2 & 0 & 2 & 0 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-2, 1, 1, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 3, 4, 5}, {3, 4, 5, 7}, {1, 2, 6, 7}, {0, 8}, {1, 2, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-2,-1},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{0,1,5},{3,4,5},{0,1,2},{2,3,4},{0,2,4}},{4,1,1})
Cox degrees: {{1,-2,-1},{0,1,1},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (28): {{3,3,3},{3,2,3},{3,2,2},{3,1,2},{2,3,3},{3,1,1},{3,0,1},{2,2,3},{2,2,2},{3,0,0},{2,1,2},{3,-1,0},{1,3,3},{2,1,1},{2,0,1},{1,2,3},{1,2,2},{2,0,0},{1,1,2},{2,-1,0},{0,3,3},{1,1,1},{1,0,1},{0,2,2},{1,0,0},{1,-1,0},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,4,4,7,10,10,7,22,20,22,20,28,50,50,28,74,95,74,95,84,155,155,195,281,281,381,662},{0,1,1,4,4,4,10,7,13,10,22,20,22,32,50,28,56,65,74,95,74,119,155,165,221,281,321,562},{0,0,1,1,1,4,4,1,7,10,7,10,7,22,22,7,28,50,28,50,28,74,74,84,155,155,195,381},{0,0,0,1,1,1,4,1,4,4,7,10,7,13,22,7,22,32,28,50,28,56,74,74,119,155,165,321},{0,0,0,0,1,0,0,1,4,0,4,0,7,10,10,7,22,20,22,20,28,50,50,74,95,95,155,281},{0,0,0,0,0,1,1,0,1,4,1,4,1,7,7,1,7,22,7,22,7,28,28,28,74,74,84,195},{0,0,0,0,0,0,1,0,1,1,1,4,1,4,7,1,7,13,7,22,7,22,28,28,56,74,74,165},{0,0,0,0,0,0,0,1,1,0,4,0,4,4,10,7,13,10,22,20,22,32,50,56,65,95,119,221},{0,0,0,0,0,0,0,0,1,0,1,0,1,4,4,1,7,10,7,10,7,22,22,28,50,50,74,155},{0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,7,1,7,1,7,7,7,28,28,28,84},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,4,4,7,10,7,13,22,22,32,50,56,119},{T^3,0,0,0,3*T^3,0,0,0,0,0,0,1,6*T^3,1,1,0,1,4,1,7,1+10*T^3,7,7,7,22,28,28,74},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,0,7,10,10,22,20,20,50,95},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,1,4,1,7,7,7,22,22,28,74},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,4,1,4,7,7,13,22,22,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,0,4,4,10,13,10,20,32,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,4,4,7,10,10,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,4,10,13,32},{0,0,0,0,T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,1,6*T^3,1,1,1,4,7,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7541)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ -3 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ -2 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 4 & 3 & 3 & 2 & 2 & 1 & 4 & 1 & 0 & 3 & 3 & 0 & 2 & -1 & 2 & -1 & 1 & -2 & 4 & 1 & 0 & 3 & 0 & -1 & 2 & -1 & -2 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 2 & 4 & 1 & 1 & 4 & 3 & 0 & 3 & 0 & 2 & -1 & 2 & -1 & 4 & 1 & 1 & 3 & 0 & 0 & 2 & -1 & -1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {-3, 1, 1, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 4, 5}, {4, 5, 7}, {1, 2, 3, 6, 7}, {0, 8}, {1, 2, 3, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-3,-2},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{0,1,5},{2,3,4},{3,4,5},{0,1,2},{0,2,4}},{6,1,1})
Cox degrees: {{1,-3,-2},{0,1,1},{0,1,1},{0,1,1},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (29): {{2,4,4},{2,3,4},{2,3,3},{2,2,3},{2,2,2},{2,1,2},{1,4,4},{2,1,1},{2,0,1},{1,3,4},{1,3,3},{2,0,0},{1,2,3},{2,-1,0},{1,2,2},{2,-1,-1},{1,1,2},{2,-2,-1},{0,4,4},{1,1,1},{1,0,1},{0,3,3},{1,0,0},{1,-1,0},{0,2,2},{1,-1,-1},{1,-2,-1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,15,17,35,35,17,45,70,45,70,100,126,100,126,103,196,196,211,350,350,395,582,582,687,1125},{0,1,1,5,5,15,15,15,35,17,37,35,45,70,80,70,100,126,100,156,196,199,280,350,365,470,582,627,1020},{0,0,1,1,5,5,5,15,15,5,17,35,17,35,45,70,45,70,45,100,100,103,196,196,211,350,350,395,687},{0,0,0,1,1,5,5,5,15,5,15,15,17,35,37,35,45,70,45,80,100,100,156,196,199,280,350,365,627},{0,0,0,0,1,1,1,5,5,1,5,15,5,15,17,35,17,35,17,45,45,45,100,100,103,196,196,211,395},{0,0,0,0,0,1,1,1,5,1,5,5,5,15,15,15,17,35,17,37,45,45,80,100,100,156,196,199,365},{0,0,0,0,0,0,1,0,0,1,5,0,5,0,15,0,15,0,17,35,35,45,70,70,100,126,126,196,350},{0,0,0,0,0,0,0,1,1,0,1,5,1,5,5,15,5,15,5,17,17,17,45,45,45,100,100,103,211},{0,0,0,0,0,0,0,0,1,0,1,1,1,5,5,5,5,15,5,15,17,17,37,45,45,80,100,100,199},{0,0,0,0,0,0,0,0,0,1,1,0,5,0,5,0,15,0,15,15,35,37,35,70,80,70,126,156,280},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,5,15,15,17,35,35,45,70,70,100,196},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,1,5,1,5,5,5,17,17,17,45,45,45,103},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,0,5,5,15,15,15,35,37,35,70,80,156},{T^4,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,1,1,1,5,1+3*T^4,5,5,5,15,17,17,37,45,45,100},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,5,15,15,17,35,35,45,100},{T^4,T^4,0,0,0,0,2*T^4,0,0,2*T^4,0,0,0,0,0,1,0,1,3*T^4,1,1,1,5,5,5,17,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,5,5,5,15,15,15,35,37,80},{5*T^4,T^4,T^4,0,0,0,10*T^4,0,0,2*T^4,2*T^4,0,0,0,0,0,0,1,15*T^4,1,1,1+3*T^4,5,5,5,15,17,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,17},{0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,1,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,T^4,0,0,T^4,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,5*T^4,0,0,T^4,T^4,0,0,0,0,0,0,0,10*T^4,0,0,2*T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7542)$ |
3 |
23 |
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9: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ -2 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ -1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 4 & 3 & 3 & 2 & 4 & 2 & 3 & 1 & 1 & 3 & 2 & 0 & 2 & 4 & 0 & -1 & 1 & 3 & 1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 4 & 4 & 3 & 3 & 4 & 2 & 4 & 2 & 1 & 3 & 3 & 1 & 2 & 4 & 0 & 0 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-2, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (23): {{0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 1, 2}, {1, 2, 7}, {3, 4, 5, 6, 7}, {0, 8}, {3, 4, 5, 6, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-2,-1},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{2,3,4},{0,1,5},{3,4,5},{0,1,2},{0,2,4}},{4,1,1})
Cox degrees: {{1,-2,-1},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (25): {{2,4,4},{2,3,4},{2,3,3},{2,2,3},{1,4,4},{2,2,2},{1,3,4},{2,1,2},{2,1,1},{1,3,3},{1,2,3},{2,0,1},{1,2,2},{0,4,4},{2,0,0},{2,-1,0},{1,1,2},{0,3,3},{1,1,1},{1,0,1},{0,2,2},{1,0,0},{1,-1,0},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,5,5,7,15,7,15,35,25,25,35,65,28,70,70,65,80,140,140,185,266,266,371,672},{0,1,1,5,5,5,7,15,15,17,25,35,45,25,35,70,65,68,100,140,155,196,266,311,567},{0,0,1,1,1,5,1,5,15,7,7,15,25,7,35,35,25,28,65,65,80,140,140,185,371},{0,0,0,1,1,1,1,5,5,5,7,15,17,7,15,35,25,25,45,65,68,100,140,155,311},{0,0,0,0,1,0,1,0,0,5,5,0,15,7,0,0,15,25,35,35,65,70,70,140,266},{0,0,0,0,0,1,0,1,5,1,1,5,7,1,15,15,7,7,25,25,28,65,65,80,185},{0,0,0,0,0,0,1,0,0,1,5,0,5,5,0,0,15,17,15,35,45,35,70,100,196},{0,0,0,0,0,0,0,1,1,1,1,5,5,1,5,15,7,7,17,25,25,45,65,68,155},{0,0,0,0,0,0,0,0,1,0,0,1,1,0,5,5,1,1,7,7,7,25,25,28,80},{0,0,0,0,0,0,0,0,0,1,1,0,5,1,0,0,5,7,15,15,25,35,35,65,140},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,5,5,5,15,17,15,35,45,100},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,5,1,1,5,7,7,17,25,25,68},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,5,7,15,15,25,65},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,7,7,7,28},{T^4,0,0,0,2*T^4,0,0,0,0,0,0,0,0,3*T^4,0,1,0,0,1,1,1,5,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,17,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,T^4,0,0,0,0,0,0,0,0,2*T^4,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7543)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 2 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 7}, {1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,3,5},{2,2,5},{2,3,4},{2,2,4},{2,3,3},{1,2,4},{2,3,2},{2,2,3},{1,1,4},{2,2,2},{1,2,3},{1,1,3},{1,2,2},{0,1,3},{1,2,1},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,10,20,20,16,40,28,46,60,49,110,100,70,185,112,164,215,320,368,554},{0,1,0,4,0,4,0,10,10,20,10,28,20,28,35,60,49,110,60,112,110,215,182,368},{0,0,1,2,4,2,10,8,3,20,10,16,28,16,60,46,22,100,49,70,112,164,215,320},{0,0,0,1,0,1,0,4,2,10,4,10,10,10,20,28,16,60,28,49,60,112,110,215},{0,0,0,0,1,0,4,2,0,8,2,3,10,3,28,16,4,46,16,22,49,70,112,164},{0,0,0,0,0,1,0,0,2,0,4,8,10,10,20,20,16,40,28,46,60,100,110,185},{0,0,0,0,0,0,1,0,0,2,0,0,2,0,10,3,0,16,3,4,16,22,49,70},{0,0,0,0,0,0,0,1,0,4,1,2,4,2,10,10,3,28,10,16,28,49,60,112},{0,0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,10,20,10,28,20,60,35,110},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,2,0,10,2,3,10,16,28,49},{0,0,0,0,0,0,0,0,0,0,1,2,4,2,10,8,3,20,10,16,28,46,60,100},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,10,10,28,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,0,8,2,3,10,16,28,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,2,3,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,2,4,10,10,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7544)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 1 & 0 & 3 & 2 & 1 & 2 & 0 & 3 & 0 & 2 & 3 & 1 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 1, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3, 5}, {4, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{1,3,4},{0,1,3},{2,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,2,3},{2,2,3},{3,2,2},{1,2,3},{2,2,2},{3,1,2},{1,2,2},{0,2,3},{3,1,1},{2,1,2},{1,1,2},{2,1,1},{0,2,2},{3,0,1},{0,1,2},{2,0,1},{3,0,0},{1,1,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,2,10,8,7,20,20,13,22,50,40,40,28,95,74,49,90,170,126,155,281,260,467},{0,1,0,4,2,1,8,10,2,7,22,13,20,7,50,28,13,40,90,49,74,155,126,260},{0,0,1,0,4,1,10,0,7,4,10,22,20,7,20,22,28,50,95,74,50,95,155,281},{0,0,0,1,0,0,2,4,0,1,7,2,8,1,22,7,2,13,40,13,28,74,49,126},{0,0,0,0,1,0,4,0,1,1,4,7,10,1,10,7,7,22,50,28,22,50,74,155},{0,0,0,0,0,1,0,0,2,4,10,8,0,7,20,22,13,20,40,40,50,95,90,170},{0,0,0,0,0,0,1,0,0,0,1,1,4,0,4,1,1,7,22,7,7,22,28,74},{0,0,0,0,0,0,0,1,0,0,1,0,2,0,7,1,0,2,13,2,7,28,13,49},{0,0,0,0,0,0,0,0,1,0,0,4,0,1,0,4,7,10,20,22,10,20,50,95},{0,0,0,0,0,0,0,0,0,1,4,2,0,1,10,7,2,8,20,13,22,50,40,90},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,2,8,2,7,22,13,40},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,4,10,7,4,10,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,7,1,1,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,0,0,8,10,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,1,7,2,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,4,10,8,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,1,4,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7545)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3}, {4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{1,3,4},{0,1,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,5,6},{2,5,5},{2,4,5},{1,4,5},{2,4,4},{2,3,4},{1,4,4},{1,3,4},{2,3,3},{1,3,3},{0,3,4},{2,2,3},{0,3,3},{1,2,3},{2,2,2},{1,2,2},{0,2,3},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,2,5,7,9,15,13,25,25,43,28,35,49,65,55,105,80,132,140,185,215,290,371,557},{0,1,1,1,5,5,7,7,15,25,7,15,28,25,35,65,28,80,65,80,140,185,185,371},{0,0,1,1,2,5,2,7,9,13,7,15,13,25,25,43,28,49,65,80,105,132,185,290},{0,0,0,1,0,0,2,5,0,9,7,0,13,15,0,25,25,43,35,65,55,105,140,215},{0,0,0,0,1,1,1,1,5,7,1,5,7,7,15,25,7,28,25,28,65,80,80,185},{0,0,0,0,0,1,0,1,2,2,1,5,2,7,9,13,7,13,25,28,43,49,80,132},{0,0,0,0,0,0,1,1,0,5,1,0,7,5,0,15,7,25,15,25,35,65,65,140},{0,0,0,0,0,0,0,1,0,2,1,0,2,5,0,9,7,13,15,25,25,43,65,105},{0,0,0,0,0,0,0,0,1,1,0,1,1,1,5,7,1,7,7,7,25,28,28,80},{0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,5,1,7,5,7,15,25,25,65},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,5,9,0,15,0,25,35,55},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,1,2,7,7,13,13,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,2,5,7,9,13,25,43},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7546)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}}
Primitive collections: {{1, 2, 3}, {4, 5, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,3,4},{1,3,4},{2,3,3},{0,3,4},{2,2,3},{1,3,3},{1,2,3},{2,2,2},{0,3,3},{1,2,2},{0,2,3},{2,1,2},{0,2,2},{2,1,1},{1,1,2},{0,1,2},{1,1,1},{2,0,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,2,6,5,6,15,9,12,27,30,15,54,25,45,90,75,35,150,55,105,210,165,330},{0,1,0,3,0,2,5,0,6,9,15,0,27,0,15,45,25,0,75,0,35,105,55,165},{0,0,1,0,1,3,3,5,6,15,6,5,30,15,15,30,45,15,90,35,45,90,105,210},{0,0,0,1,0,0,0,0,2,0,5,0,9,0,0,15,0,0,25,0,0,35,0,55},{0,0,0,0,1,0,3,2,0,6,6,5,12,9,15,30,27,15,54,25,45,90,75,150},{0,0,0,0,0,1,1,0,3,5,3,0,15,0,5,15,15,0,45,0,15,45,35,105},{0,0,0,0,0,0,1,0,0,2,3,0,6,0,5,15,9,0,27,0,15,45,25,75},{0,0,0,0,0,0,0,1,0,3,0,1,6,5,3,6,15,5,30,15,15,30,45,90},{0,0,0,0,0,0,0,0,1,0,1,0,5,0,0,5,0,0,15,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,3,5,0,15,0,5,15,15,45},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,5,0,0,9,0,0,15,0,25},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,5,12,9,15,30,27,54},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,5,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,6,5,3,6,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,0,6,0,5,15,9,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,5,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,3,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7547)$ |
3 |
24 |
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9: $\begin{pmatrix}-1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 1 & 3 & 2 & 0 & 3 & 2 & 1 & 3 & 0 & 1 & 0 & 2 & 3 & 2 & 1 & 3 & 1 & 0 & 0 & 2 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {-1, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {1, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{0,1,4},{1,3,4},{2,3,4}},{1,1,2})
Cox degrees: {{-1,0,1},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,2,3},{2,2,3},{1,2,3},{3,2,2},{2,2,2},{0,2,3},{3,1,2},{2,1,2},{1,2,2},{3,1,1},{0,2,2},{1,1,2},{0,1,2},{2,1,1},{3,0,1},{2,0,1},{1,1,1},{3,0,0},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,10,5,14,20,7,22,30,25,55,50,95,62,28,74,125,80,155,221,281,179,341,582},{0,1,4,1,5,10,1,7,14,7,30,22,50,25,7,28,62,28,74,125,155,80,179,341},{0,0,1,0,1,4,0,1,5,1,14,7,22,7,1,7,25,7,28,62,74,28,80,179},{0,0,0,1,4,0,1,4,10,7,20,10,20,22,7,22,50,28,50,95,95,74,155,281},{0,0,0,0,1,0,0,1,4,1,10,4,10,7,1,7,22,7,22,50,50,28,74,155},{0,0,0,0,0,1,0,0,1,0,5,1,7,1,0,1,7,1,7,25,28,7,28,80},{0,0,0,0,0,0,1,4,0,5,0,10,20,14,7,22,30,25,50,55,95,62,125,221},{0,0,0,0,0,0,0,1,0,1,0,4,10,5,1,7,14,7,22,30,50,25,62,125},{0,0,0,0,0,0,0,0,1,0,4,1,4,1,0,1,7,1,7,22,22,7,28,74},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,4,10,7,10,20,20,22,50,95},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,7,7,1,7,28},{0,0,0,0,0,0,0,0,0,0,0,1,4,1,0,1,5,1,7,14,22,7,25,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,5,7,1,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,4,10,10,7,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,5,10,0,20,14,30,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,10,5,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,1,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7548)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 1 & 0 & 3 & 2 & 1 & 2 & 0 & 3 & 0 & 2 & 3 & 1 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {1, 6, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,2,3},{2,2,3},{3,2,2},{1,2,3},{2,2,2},{3,1,2},{1,2,2},{0,2,3},{3,1,1},{2,1,2},{1,1,2},{2,1,1},{0,2,2},{3,0,1},{0,1,2},{2,0,1},{3,0,0},{1,1,1},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,2,10,8,4,20,20,7,16,40,28,40,10,80,40,16,70,140,64,100,200,160,320},{0,1,0,4,2,0,8,10,0,4,16,7,20,0,40,10,0,28,70,16,40,100,64,160},{0,0,1,0,4,1,10,0,4,4,10,16,20,4,20,16,10,40,80,40,40,80,100,200},{0,0,0,1,0,0,2,4,0,0,4,0,8,0,16,0,0,7,28,0,10,40,16,64},{0,0,0,0,1,0,4,0,0,1,4,4,10,0,10,4,0,16,40,10,16,40,40,100},{0,0,0,0,0,1,0,0,2,4,10,8,0,4,20,16,7,20,40,28,40,80,70,140},{0,0,0,0,0,0,1,0,0,0,1,0,4,0,4,0,0,4,16,0,4,16,10,40},{0,0,0,0,0,0,0,1,0,0,0,0,2,0,4,0,0,0,7,0,0,10,0,16},{0,0,0,0,0,0,0,0,1,0,0,4,0,1,0,4,4,10,20,16,10,20,40,80},{0,0,0,0,0,0,0,0,0,1,4,2,0,0,10,4,0,8,20,7,16,40,28,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,2,8,0,4,16,7,28},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,10,4,4,10,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,4,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,0,0,8,10,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,4,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,4,10,8,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7549)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}2 & 1 & 2 & 3 & 0 & 1 & 3 & 2 & 0 & -1 & 1 & 2 & 3 & 2 & 0 & 3 & 1 & -1 & -1 & 2 & 1 & 0 & -1 & 1 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 3 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 2 & 2 & 0 & 1 & 1 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, 0, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {1, 5, 7}, {0, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{2,3,4},{0,1,3},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{-1,1,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (26): {{2,2,3},{1,2,3},{2,2,2},{3,1,2},{0,2,3},{1,2,2},{3,1,1},{2,1,2},{0,2,2},{-1,2,3},{1,1,2},{2,1,1},{3,0,1},{2,0,1},{0,1,2},{3,0,0},{1,1,1},{-1,2,2},{-1,1,2},{2,0,0},{1,0,1},{0,1,1},{-1,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,2,2,10,8,4,10,20,20,28,19,16,49,60,30,52,40,110,88,112,110,200,196,215,370},{0,1,0,0,4,2,0,2,8,10,10,4,3,16,28,6,19,20,60,30,49,52,110,88,112,196},{0,0,1,0,0,4,2,1,10,0,4,10,2,10,10,16,28,20,20,49,28,60,110,112,60,215},{0,0,0,1,0,0,2,4,0,0,10,8,10,28,20,19,20,0,35,52,60,40,70,110,110,200},{0,0,0,0,1,0,0,0,2,4,2,0,0,3,10,0,4,8,28,6,16,19,52,30,49,88},{0,0,0,0,0,1,0,0,4,0,1,2,0,2,4,3,10,10,10,16,10,28,60,49,28,112},{0,0,0,0,0,0,1,0,0,0,0,4,1,4,0,10,10,0,0,28,10,20,35,60,20,110},{0,0,0,0,0,0,0,1,0,0,4,2,2,10,10,4,8,0,20,19,28,20,40,52,60,110},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,2,4,4,3,2,10,28,16,10,49},{0,0,0,2*T^3,0,0,3*T^3,0,0,1,0,0,3*T^3,0,2,4*T^3,0,2,10,0,3,4,19,6,16,30},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,2,0,10,4,10,8,20,19,28,52},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,4,0,0,10,4,10,20,28,10,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,2,0,0,0,8,10,0,0,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,4,0,0,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,2,2,8,4,10,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,4,10,10,4,28},{0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,2*T^3,0,0,3*T^3,0,1,1,0,0,2,10,3,2,16},{0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,2*T^3,0,0,3*T^3,0,0,1,0,0,0,2,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,1,10},{0,0,0,0,0,0,T^3,0,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7550)$ |
3 |
25 |
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9: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}3 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 0 & 1 & 2 & 3 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0 \\ 3 & 2 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 0 & 1 & 3 & 2 & 1 & 0 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 1 & 2 & 3 & 2 & 1 & 0 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {1, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {-1, 1, 1, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, -1}}
Cones (25): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 8}, {2, 3, 4, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}}
Primitive collections: {{0, 3, 4, 5}, {3, 4, 5, 7}, {1, 2, 6, 7}, {0, 8}, {1, 2, 6, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{0,1,4},{0,2,5},{3,4,5},{1,3,4}},{2,1,1})
Cox degrees: {{1,-1,0},{0,1,1},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (25): {{3,3,3},{3,2,3},{2,3,3},{3,2,2},{2,2,3},{3,1,2},{1,3,3},{2,2,2},{3,1,1},{1,2,3},{3,0,1},{2,1,2},{0,3,3},{1,2,2},{2,1,1},{3,0,0},{1,1,2},{2,0,1},{0,2,2},{1,1,1},{2,0,0},{1,0,1},{0,1,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,4,4,4,4,10,16,10,10,10,16,20,40,40,20,40,40,80,100,80,100,200,200,400},{0,1,1,1,4,4,4,7,4,10,10,16,10,22,22,10,40,40,50,64,50,100,140,140,300},{0,0,1,0,1,0,4,4,0,4,0,4,10,16,10,0,16,10,40,40,20,40,100,80,200},{0,0,0,1,0,1,0,4,4,0,4,4,0,10,16,10,10,16,20,40,40,40,80,100,200},{0,0,0,0,1,0,1,1,0,4,0,4,4,7,4,0,16,10,22,22,10,40,64,50,140},{0,0,0,0,0,1,0,1,1,0,4,4,0,4,7,4,10,16,10,22,22,40,50,64,140},{0,0,0,0,0,0,1,0,0,1,0,0,4,4,0,0,4,0,16,10,0,10,40,20,80},{0,0,0,0,0,0,0,1,0,0,0,1,0,4,4,0,4,4,10,16,10,16,40,40,100},{0,0,0,0,0,0,0,0,1,0,1,0,0,0,4,4,0,4,0,10,16,10,20,40,80},{0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,4,0,7,4,0,10,22,10,50},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,4,0,4,7,10,10,22,50},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,4,4,4,7,4,16,22,22,64},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,0,4,16,10,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,4,10,16,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,4,7,4,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7553)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 7 & 7 & 6 & 6 & 5 & 5 & 4 & 3 & 4 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -3}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,1,7},{0,1,7},{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{1,1,3},{1,0,4},{0,1,4},{0,0,4},{0,1,3},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,30,35,70,36,70,72,140,75,126,252,150,141,210,282,245,420,490,400,800},{0,1,0,5,0,15,0,0,0,35,36,70,0,0,126,75,0,0,141,0,210,245,0,400},{0,0,1,2,5,10,15,35,15,30,30,70,36,70,140,72,75,126,150,141,252,282,245,490},{0,0,0,1,0,5,0,0,0,15,15,35,0,0,70,36,0,0,75,0,126,141,0,245},{0,0,0,0,1,2,5,15,5,10,10,30,15,35,70,30,36,70,72,75,140,150,141,282},{0,0,0,0,0,1,0,0,0,5,5,15,0,0,35,15,0,0,36,0,70,75,0,141},{0,0,0,0,0,0,1,5,1,2,2,10,5,15,30,10,15,35,30,36,70,72,75,150},{0,0,0,0,0,0,0,1,0,0,0,2,1,5,10,2,5,15,10,15,30,30,36,72},{0,0,0,0,0,0,0,0,1,0,2,0,5,0,0,10,15,0,30,35,0,70,70,140},{0,0,0,0,0,0,0,0,0,1,1,5,0,0,15,5,0,0,15,0,35,36,0,75},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,0,5,0,15,15,0,36},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,10,15,0,30,35,70},{T^4,2*T^4,0,0,0,0,0,0,T^4,0,2*T^4,0,0,1,2,0,1,5,2,5,10,10,15,30},{0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,0,0,1,0,5,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,10,15,30},{5*T^4,10*T^4,T^4,2*T^4,0,0,0,0,5*T^4,0,10*T^4,0,T^4,0,0,2*T^4,0,1,0,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,10},{0,5*T^4,0,T^4,0,0,0,0,0,0,5*T^4,0,0,0,0,T^4,0,0,0,0,1,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7554)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 7 & 6 & 7 & 5 & 6 & 4 & 3 & 5 & 4 & 2 & 3 & 4 & 4 & 3 & 2 & 1 & 3 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 0, -3}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{4, 6}, {5, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{-1,1,3}},{{0,2,3},{2,3,4},{0,1,3},{1,3,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,1,7},{1,1,6},{0,1,7},{1,1,5},{0,1,6},{1,1,4},{1,1,3},{0,1,5},{1,0,4},{1,1,2},{1,0,3},{0,1,4},{0,0,4},{0,1,3},{1,0,2},{1,1,1},{0,0,3},{1,0,1},{0,1,2},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,2,15,10,35,70,30,37,126,80,70,73,140,156,210,155,280,252,297,470,420,525,870},{0,1,0,5,2,15,35,10,15,70,37,30,30,70,80,126,73,156,140,155,280,252,297,525},{0,0,1,0,5,0,0,15,1,0,5,35,37,70,15,0,80,35,126,156,70,210,280,470},{0,0,0,1,0,5,15,2,5,35,15,10,10,30,37,70,30,80,70,73,156,140,155,297},{0,0,0,0,1,0,0,5,0,0,1,15,15,35,5,0,37,15,70,80,35,126,156,280},{0,0,0,0,0,1,5,0,1,15,5,2,2,10,15,35,10,37,30,30,80,70,73,155},{0,0,0,0,0,0,1,0,0,5,1,0,0,2,5,15,2,15,10,10,37,30,30,73},{0,0,0,0,0,0,0,1,0,0,0,5,5,15,1,0,15,5,35,37,15,70,80,156},{0,0,0,0,0,0,0,0,1,0,5,0,2,0,15,0,10,35,0,30,70,0,70,140},{T^4,0,2*T^4,0,0,0,0,0,2*T^4,1,0,0,3*T^4,0,1,5,0,5,2,2,15,10,10,30},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,2,15,0,10,35,0,30,70},{0,0,0,0,0,0,0,0,0,0,0,1,1,5,0,0,5,1,15,15,5,35,37,80},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,5,1,15,15,37},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,2,15,0,10,30},{5*T^4,T^4,10*T^4,0,2*T^4,0,0,0,10*T^4,0,2*T^4,0,15*T^4,0,0,1,3*T^4,1,0,0,5,2,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,2,10},{0,0,T^4,0,0,0,0,0,T^4,0,0,0,2*T^4,0,0,0,0,0,1,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,5*T^4,0,T^4,0,0,0,5*T^4,0,T^4,0,10*T^4,0,0,0,2*T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7556)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 4 & 5 & 4 & 3 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -2}}
Cones (20): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}}
Primitive collections: {{4, 5}, {6, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,2},{2,1,2}},{{2,3,4},{0,1,5},{0,3,5},{3,4,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (23): {{1,1,7},{1,1,6},{0,1,6},{1,1,5},{1,0,5},{1,1,4},{0,1,5},{0,1,4},{1,1,3},{1,0,4},{0,1,3},{0,0,4},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,15,16,35,20,50,70,40,105,56,85,126,196,125,161,210,246,280,336,441,736},{0,1,1,5,5,15,6,20,35,16,50,21,40,70,105,56,85,126,125,161,196,246,441},{0,0,1,0,0,0,5,15,0,0,35,16,0,0,70,40,0,0,85,0,126,161,280},{0,0,0,1,1,5,1,6,15,5,20,6,16,35,50,21,40,70,56,85,105,125,246},{0,0,0,0,1,0,0,0,0,5,0,6,15,0,0,20,35,0,50,70,0,105,196},{0,0,0,0,0,1,0,1,5,1,6,1,5,15,20,6,16,35,21,40,50,56,125},{0,0,0,0,0,0,1,5,0,0,15,5,0,0,35,16,0,0,40,0,70,85,161},{0,0,0,0,0,0,0,1,0,0,5,1,0,0,15,5,0,0,16,0,35,40,85},{0,0,0,0,0,0,0,0,1,0,1,0,1,5,6,1,5,15,6,16,20,21,56},{0,0,0,0,0,0,0,0,0,1,0,1,5,0,0,6,15,0,20,35,0,50,105},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,1,0,0,5,0,15,16,40},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,15,0,20,50},{T^4,0,T^4,0,T^4,0,0,0,0,0,0,T^4,0,1,1,0,1,5,1,5,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,6,20},{5*T^4,T^4,6*T^4,0,5*T^4,0,T^4,0,0,T^4,0,6*T^4,0,0,0,T^4,0,1,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,T^4,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7557)$ |
3 |
20 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 5 & 6 & 4 & 4 & 3 & 5 & 4 & 2 & 3 & 3 & 4 & 2 & 1 & 2 & 3 & 1 & 0 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, -1, -2}}
Cones (20): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}}
Primitive collections: {{4, 6}, {5, 7}, {0, 1, 2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{1,0,-1},{0,0,1},{0,1,1},{0,1,2},{-1,1,2}},{{0,4,6},{5,6,7},{0,2,5,6},{4,6,7},{1,2,3},{1,5,7},{0,2,3},{1,2,5}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,0,1},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,1,5},{0,1,6},{1,1,4},{1,0,4},{1,1,3},{0,1,5},{0,1,4},{1,1,2},{1,0,3},{0,1,3},{0,0,4},{1,0,2},{1,1,1},{0,1,2},{0,0,3},{1,0,1},{1,1,0},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,5,6,15,6,20,35,21,50,26,55,70,105,71,120,126,160,231,196,316,567},{0,1,0,1,0,5,15,0,5,35,21,15,0,70,55,35,0,120,70,126,231,406},{0,0,1,1,5,1,6,15,6,20,7,21,35,50,26,55,70,71,120,105,160,316},{0,0,0,1,0,0,0,0,5,0,6,15,0,0,20,35,0,50,70,0,105,196},{0,0,0,0,1,0,1,5,1,6,1,6,15,20,7,21,35,26,55,50,71,160},{0,0,0,0,0,1,5,0,1,15,6,5,0,35,21,15,0,55,35,70,120,231},{0,0,0,0,0,0,1,0,0,5,1,1,0,15,6,5,0,21,15,35,55,120},{0,0,0,0,0,0,0,1,0,1,0,1,5,6,1,6,15,7,21,20,26,71},{0,0,0,0,0,0,0,0,1,0,1,5,0,0,6,15,0,20,35,0,50,105},{0,0,0,0,0,0,0,0,0,1,0,0,0,5,1,1,0,6,5,15,21,55},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,15,0,20,50},{0,T^4,0,T^4,0,0,0,0,0,0,T^4,0,1,1,0,1,5,1,6,6,7,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,6,20},{T^4,6*T^4,0,6*T^4,0,T^4,0,0,T^4,0,6*T^4,0,0,0,T^4,0,1,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,T^4,0,T^4,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7559)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 5 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,2}},{{1,2,3},{0,1,3},{0,2,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,0},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,3,5},{1,2,5},{1,3,4},{1,1,5},{1,2,4},{1,3,3},{1,1,4},{1,3,2},{1,2,3},{0,2,3},{1,1,3},{1,3,1},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,24,20,30,31,60,35,60,63,64,105,120,106,132,210,115,224,188,240,410,396,680},{0,1,0,3,4,0,12,0,10,10,30,0,20,31,20,35,60,63,64,105,35,132,56,115,240,188,396},{0,0,1,0,3,4,6,10,12,12,24,20,30,24,31,60,60,40,63,120,64,106,115,132,224,240,410},{0,0,0,1,0,0,4,0,0,0,10,0,0,10,0,0,20,31,20,35,0,64,0,35,115,56,188},{0,0,0,0,1,0,3,0,4,4,12,0,10,12,10,20,30,24,31,60,20,63,35,64,132,115,240},{0,0,0,0,0,1,0,4,3,3,6,10,12,6,12,30,24,10,24,60,31,40,64,63,106,132,224},{0,0,0,0,0,0,1,0,0,0,4,0,0,4,0,0,10,12,10,20,0,31,0,20,64,35,115},{0,0,0,0,0,0,0,1,0,0,0,4,3,0,3,12,6,0,6,24,12,10,31,24,40,63,106},{0,0,0,0,0,0,0,0,1,1,3,0,4,3,4,10,12,6,12,30,10,24,20,31,63,64,132},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,6,12,0,10,24,20,30,60,60,120},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,4,3,4,10,0,12,0,10,31,20,64},{T^3,3*T^3,0,6*T^3,0,0,0,0,0,T^3,0,1,0,3*T^3,0,3,0,6*T^3,0,6,3,0,12,6,10,24,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,3,0,3,12,4,6,10,12,24,31,63},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,12,24,30,60},{0,T^3,0,3*T^3,0,0,0,0,0,0,0,0,0,T^3,0,1,0,3*T^3,0,3,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,3,0,4,12,10,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,12,10,30},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7562)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
29: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 9 & 8 & 7 & 7 & 6 & 7 & 5 & 6 & 6 & 5 & 5 & 4 & 5 & 4 & 5 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{0,1,4},{1,3,4},{0,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (29): {{1,3,9},{1,3,8},{1,3,7},{1,2,7},{1,3,6},{0,2,7},{1,3,5},{1,2,6},{0,2,6},{1,2,5},{0,2,5},{1,2,4},{1,1,5},{0,2,4},{0,1,5},{1,1,4},{1,2,3},{0,2,3},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{0,0,3},{1,1,1},{0,1,2},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,10,12,20,13,35,28,32,55,65,96,58,116,70,108,154,189,136,184,239,292,246,438,388,416,592,662,1000},{0,1,4,4,10,4,20,12,13,28,32,55,28,65,32,58,96,116,70,108,136,184,136,292,239,246,388,416,662},{0,0,1,1,4,1,10,4,4,12,13,28,12,32,13,28,55,65,32,58,70,108,70,184,136,136,239,246,416},{0,0,0,1,0,1,0,4,4,10,10,20,12,20,13,28,35,35,32,55,65,96,70,154,116,136,189,239,388},{0,0,0,0,1,0,4,1,1,4,4,12,4,13,4,12,28,32,13,28,32,58,32,108,70,70,136,136,246},{0,0,0,0,0,1,0,0,4,0,10,0,0,20,12,0,0,35,28,0,55,0,58,0,96,108,154,184,292},{T^3,0,0,2*T^3,0,3*T^3,1,0,0,1,1,4,1+3*T^3,4,1+5*T^3,4,12,13,4,12,13,28,13+7*T^3,58,32,32,70,70,136},{0,0,0,0,0,0,0,1,1,4,4,10,4,10,4,12,20,20,13,28,32,55,32,96,65,70,116,136,239},{0,0,0,0,0,0,0,0,1,0,4,0,0,10,4,0,0,20,12,0,28,0,28,0,55,58,96,108,184},{0,0,0,0,0,0,0,0,0,1,1,4,1,4,1,4,10,10,4,12,13,28,13,55,32,32,65,70,136},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,0,10,4,0,12,0,12,0,28,28,55,58,108},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,4,4,1,4,4,12,4,28,13,13,32,32,70},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,10,10,20,13,35,20,32,35,65,116},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,4,0,4,0,12,12,28,28,58},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,12,0,20,28,35,55,96},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,4,10,4,20,10,13,20,32,65},{0,0,0,T^3,0,T^3,0,0,0,0,0,0,2*T^3,0,3*T^3,0,1,1,0,1,1,4,1+5*T^3,12,4,4,13,13,32},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,1,0,0,1,0,1+3*T^3,0,4,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,4,0,10,12,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,4,10,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,3*T^3,1,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7563)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 7 & 7 & 6 & 5 & 6 & 5 & 4 & 5 & 5 & 4 & 3 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (28): {{1,2,7},{0,2,7},{1,2,6},{1,2,5},{0,2,6},{0,2,5},{1,2,4},{1,1,5},{0,1,5},{1,1,4},{1,2,3},{0,2,4},{0,2,3},{1,1,3},{0,1,4},{1,1,2},{0,1,3},{1,0,3},{0,1,2},{1,0,2},{1,1,1},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,10,8,20,20,12,24,28,35,40,70,55,56,96,110,58,192,108,154,116,216,184,308,368,292,584},{0,1,0,0,4,10,0,0,12,0,0,20,35,0,28,0,55,0,96,0,0,58,108,0,154,184,0,292},{0,0,1,4,2,8,10,4,8,12,20,20,40,28,24,55,56,28,110,58,96,56,116,108,192,216,184,368},{0,0,0,1,0,2,4,1,2,4,10,8,20,12,8,28,24,12,56,28,55,24,56,58,110,116,108,216},{0,0,0,0,1,4,0,0,4,0,0,10,20,0,12,0,28,0,55,0,0,28,58,0,96,108,0,184},{0,0,0,0,0,1,0,0,1,0,0,4,10,0,4,0,12,0,28,0,0,12,28,0,55,58,0,108},{0,0,0,0,0,0,1,0,0,1,4,2,8,4,2,12,8,4,24,12,28,8,24,28,56,56,58,116},{0,0,0,0,0,0,0,1,2,4,0,0,0,10,8,20,20,12,40,28,35,24,56,55,70,110,96,192},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,10,0,20,0,0,12,28,0,35,55,0,96},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,10,8,4,20,12,20,8,24,28,40,56,55,110},{T^3,2*T^3,0,0,0,0,0,2*T^3,4*T^3,0,1,0,2,1,0,4,2,1+3*T^3,8,4,12,2+6*T^3,8,12,24,24,28,56},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,0,4,0,12,0,0,4,12,0,28,28,0,58},{0,T^3,0,0,0,0,0,0,2*T^3,0,0,0,1,0,0,0,1,0,4,0,0,1+3*T^3,4,0,12,12,0,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,2,1,8,4,10,2,8,12,20,24,28,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10,0,0,4,12,0,20,28,0,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,4,0,2,4,8,8,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,1,4,0,10,12,0,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,4,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,0,0,T^3,2*T^3,0,0,0,0,0,0,0,0,2*T^3,0,0,1,4*T^3,0,1,2,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,1,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7564)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 0 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, -1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{1,3,4},{0,1,4},{2,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,1,5},{1,1,5},{0,1,5},{2,1,4},{1,1,4},{2,1,3},{0,1,4},{1,1,3},{2,0,3},{1,0,3},{2,1,2},{0,1,3},{0,0,3},{2,0,2},{1,1,2},{2,1,1},{0,1,2},{1,0,2},{1,1,1},{0,0,2},{2,0,1},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,6,15,21,28,46,22,49,56,81,87,62,111,126,186,126,231,214,147,277,371,452,308,545,858},{0,1,3,1,6,6,15,21,6,22,21,46,49,22,56,56,111,62,126,126,62,147,231,277,147,308,545},{0,0,1,0,1,1,6,6,1,6,6,21,22,6,21,21,56,22,56,62,22,62,126,147,62,147,308},{0,0,0,1,3,6,6,15,6,15,21,28,28,22,46,56,81,49,111,87,62,126,186,214,147,277,452},{0,0,0,0,1,1,3,6,1,6,6,15,15,6,21,21,46,22,56,49,22,62,111,126,62,147,277},{0,0,0,0,0,1,0,3,1,3,6,6,6,6,15,21,28,15,46,28,22,49,81,87,62,126,214},{0,0,0,0,0,0,1,1,0,1,1,6,6,1,6,6,21,6,21,22,6,22,56,62,22,62,147},{0,0,0,0,0,0,0,1,0,1,1,3,3,1,6,6,15,6,21,15,6,22,46,49,22,62,126},{0,0,0,0,0,0,0,0,1,3,0,0,6,6,0,0,0,15,0,28,21,46,0,81,56,111,186},{0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,0,0,6,0,15,6,21,0,46,21,56,111},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,6,6,3,15,6,6,15,28,28,22,49,87},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,6,1,6,6,1,6,21,22,6,22,62},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,6,1,6,0,21,6,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,6,15,0,28,21,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,6,3,1,6,15,15,6,22,49},{0,T^3,3*T^3,0,0,0,0,0,0,T^3,0,0,3*T^3,0,0,1,0,0,3,0,1,3,6,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,6,6,1,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,6,0,15,6,21,46},{0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,1,3,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,6,15},{T^5,0,0,0,0,0,0,0,T^5,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7565)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 0 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 5 & 4 & 3 & 3 & 2 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 3 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{3, 4, 5}, {6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,1,5},{1,1,5},{2,1,4},{0,1,5},{1,1,4},{2,1,3},{1,1,3},{2,1,2},{2,0,3},{0,1,4},{1,0,3},{2,0,2},{0,1,3},{2,1,1},{1,1,2},{0,1,2},{1,1,1},{2,0,1},{0,0,3},{1,0,2},{0,1,1},{0,0,2},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,30,20,11,24,33,24,60,35,60,120,105,45,66,72,210,144,76,135,270,228,456},{0,1,0,3,4,0,10,0,0,12,11,0,30,0,20,60,35,0,33,24,105,72,0,45,135,76,228},{0,0,1,0,3,4,12,10,4,6,12,11,24,20,30,60,60,24,24,33,120,66,45,72,144,135,270},{0,0,0,1,0,0,0,0,0,4,0,0,10,0,0,20,0,0,11,0,35,24,0,0,45,0,76},{0,0,0,0,1,0,4,0,0,3,4,0,12,0,10,30,20,0,12,11,60,33,0,24,72,45,135},{0,0,0,0,0,1,3,4,1,0,3,4,6,10,12,24,30,11,6,12,60,24,24,33,66,72,144},{0,0,0,0,0,0,1,0,0,0,1,0,3,0,4,12,10,0,3,4,30,12,0,11,33,24,72},{0,0,0,0,0,0,0,1,0,0,0,1,0,4,3,6,12,4,0,3,24,6,11,12,24,33,66},{0,0,0,0,0,0,0,0,1,0,3,4,0,0,0,0,0,10,6,12,0,24,20,30,60,60,120},{0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,0,4,0,20,11,0,0,24,0,45},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,3,4,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,4,0,3,0,6,10,12,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,1,0,10,4,0,0,11,0,24},{T^3,3*T^3,0,6*T^3,0,0,0,0,T^3,0,3*T^3,0,0,1,0,0,3,1,6*T^3,0,6,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,0,0,1,12,3,0,4,12,11,33},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,1,0,0,4,0,11},{0,T^3,0,3*T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,3*T^3,0,3,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,12,10,30},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7566)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 0 & 2 & -1 & 1 & 0 & 2 & 1 & -1 & 2 & 1 & 2 & 0 & 0 & -1 & 2 & 1 & 2 & 0 & 1 & -1 & 0 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 5 & 4 & 4 & 3 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2},{-1,1,2}},{{0,2,4},{2,3,5},{2,4,5},{1,4,5},{1,3,5},{0,1,4}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{1,1,5},{0,1,5},{2,1,4},{-1,1,5},{1,1,4},{0,1,4},{2,1,3},{1,1,3},{-1,1,4},{2,0,3},{1,0,3},{2,1,2},{0,1,3},{0,0,3},{-1,1,3},{2,0,2},{1,1,2},{2,1,1},{0,1,2},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{1,0,1},{0,1,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,1,6,6,15,6,21,28,7,24,21,46,52,81,27,56,56,111,71,186,139,126,77,172,231,182,312,363,620},{0,1,0,3,1,6,1,6,15,1,7,6,21,24,46,7,21,21,56,27,111,71,56,27,77,126,77,172,182,363},{0,0,1,0,3,6,6,15,10,6,15,21,28,28,45,24,46,56,81,52,126,91,111,71,139,186,172,231,312,497},{0,0,3*T^2,1,0,1,6*T^2,1,6,6*T^2,1,1+10*T^2,6,7,21,1+10*T^2,6,6+15*T^2,21,7,56,27,21,7+15*T^2,27,56,27+21*T^2,77,77,182},{0,0,0,0,1,3,1,6,6,1,6,6,15,15,28,7,21,21,46,24,81,52,56,27,71,111,77,139,172,312},{0,0,0,0,0,1,0,1,3,0,1,1,6,6,15,1,6,6,21,7,46,24,21,7,27,56,27,71,77,172},{0,0,0,0,0,0,1,3,0,1,3,6,6,6,10,6,15,21,28,15,45,28,46,24,52,81,71,91,139,231},{0,0,0,0,0,0,0,1,0,0,1,1,3,3,6,1,6,6,15,6,28,15,21,7,24,46,27,52,71,139},{0,0,T^2,0,0,0,3*T^2,0,1,3*T^2,0,6*T^2,1,1,6,6*T^2,1,1+10*T^2,6,1,21,7,6,1+10*T^2,7,21,7+15*T^2,27,27,77},{0,0,0,0,0,0,0,0,0,1,3,0,0,6,0,6,0,0,0,15,0,28,0,21,46,0,56,81,111,186},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,0,0,0,6,0,15,0,6,21,0,21,46,56,111},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,6,6,3,10,6,15,6,15,28,24,28,52,91},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,1,1,6,1,15,6,6,1,7,21,7,24,27,71},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,6,0,1,6,0,6,21,21,56},{0,0,0,0,0,0,T^2,0,0,T^2,0,3*T^2,0,0,1,3*T^2,0,6*T^2,1,0,6,1,1,6*T^2,1,6,1+10*T^2,7,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6,0,6,15,0,21,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,6,3,6,1,6,15,7,15,24,52},{T^3,3*T^3,0,6*T^3,0,0,0,0,0,T^3,3*T^3,0,0,6*T^3,0,0,0,1,0,0,0,0,3,1,3,6,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,0,1,6,1,6,7,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,6,0,6,15,21,46},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,3*T^2,0,0,1,0,0,3*T^2,0,1,6*T^2,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6,6,21},{0,T^3,0,3*T^3,0,0,0,0,0,0,T^3,0,0,3*T^3,0,0,0,0,0,0,0,0,1,0,1,3,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,15},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7567)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 2 & 0 & 1 & 0 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 3 & 5 & 3 & 4 & 2 & 1 & 3 & 2 & 3 & 1 & 1 & 2 & 3 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4, 6}, {5, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{1,3,4},{2,3,4},{0,1,3}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,1,5},{2,1,4},{1,1,5},{2,1,3},{1,1,4},{2,1,2},{2,0,3},{0,1,5},{1,1,3},{0,1,4},{2,0,2},{2,1,1},{1,0,3},{1,1,2},{0,1,3},{2,0,1},{1,1,1},{1,0,2},{0,0,3},{0,1,2},{2,0,0},{1,0,1},{0,0,2},{0,1,1},{1,0,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,3,10,12,20,13,6,30,24,32,35,36,60,60,65,105,84,70,120,116,165,160,210,288,310,536},{0,1,0,4,3,10,4,0,12,6,13,20,12,30,24,32,60,36,24,60,65,84,70,120,165,160,310},{0,0,1,0,4,0,1,3,10,12,4,0,13,20,30,10,35,32,36,60,20,65,84,105,116,165,288},{0,0,0,1,0,4,1,0,3,0,4,10,3,12,6,13,30,12,6,24,32,36,24,60,84,70,160},{0,0,0,0,1,0,0,0,4,3,1,0,4,10,12,4,20,13,12,30,10,32,36,60,65,84,165},{0,0,0,0,0,1,0,0,0,0,1,4,0,3,0,4,12,3,0,6,13,12,6,24,36,24,70},{0,0,0,0,0,0,1,0,0,0,4,0,3,0,0,10,0,12,6,0,20,30,24,0,60,60,120},{0,0,0,0,0,0,0,1,0,4,0,0,1,0,10,0,0,4,13,20,0,10,32,35,20,65,116},{0,0,0,0,0,0,0,0,1,0,0,0,1,4,3,1,10,4,3,12,4,13,12,30,32,36,84},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,1,4,10,0,4,13,20,10,32,65},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,3,0,0,10,12,6,0,30,24,60},{T^3,0,3*T^3,0,0,0,3*T^3,6*T^3,0,0,0,1,6*T^3,0,0,1,3,0,10*T^3,0,4,3,0,6,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,10,12,0,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,3,1,4,3,12,13,12,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,1,4,10,4,13,32},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,12,6,24},{0,0,T^3,0,0,0,T^3,3*T^3,0,0,0,0,3*T^3,0,0,0,1,0,6*T^3,0,0,1,0,3,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,3,0,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,T^3,0,0,0,0,T^3,0,0,0,0,0,3*T^3,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7568)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -1 & 2 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
34: $\begin{pmatrix}1 & 0 & 2 & 1 & 0 & 2 & 0 & 1 & -1 & 0 & 1 & 2 & 0 & 1 & 2 & 1 & -1 & 0 & -1 & 1 & 0 & 1 & -1 & 0 & 0 & -1 & -1 & 1 & 0 & -1 & 0 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 2 & 2 & 1 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 5 & 6 & 3 & 4 & 5 & 2 & 5 & 3 & 6 & 4 & 3 & 1 & 4 & 2 & 0 & 2 & 5 & 3 & 5 & 1 & 3 & 1 & 4 & 3 & 2 & 4 & 3 & 0 & 2 & 3 & 1 & 1 & 2 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 0, 1}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, 0, -2}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}}
Primitive collections: {{2, 4, 6}, {3, 5, 7}, {4, 6, 7}, {0, 1, 2, 8}, {0, 1, 3, 5, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{0,1,2},{-1,1,2}},{{0,3,4},{0,1,2},{1,4,5},{0,1,4},{0,2,3},{3,4,5}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-1},{-1,1,2},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (34): {{1,1,5},{0,2,6},{2,0,3},{1,1,4},{0,2,5},{2,0,2},{0,1,5},{1,1,3},{-1,2,6},{0,2,4},{1,0,3},{2,0,1},{0,1,4},{1,1,2},{2,0,0},{1,0,2},{-1,2,5},{0,2,3},{-1,1,5},{1,1,1},{0,1,3},{1,0,1},{-1,2,4},{0,0,3},{0,1,2},{-1,1,4},{-1,2,3},{1,0,0},{0,0,2},{-1,1,3},{0,1,1},{0,0,1},{-1,1,2},{0,0,0}}
Ext matrix: {{1,1,2,5,5,9,7,15,7,15,19,25,25,35,55,53,25,35,28,70,65,120,65,71,140,80,140,236,167,185,266,341,371,627},{0,1,0,2,5,3,5,9,7,15,9,13,19,25,35,31,25,35,25,55,53,81,65,53,120,71,140,175,129,167,236,275,341,525},{0,0,1,1,1,5,1,5,1,5,7,15,7,15,35,25,7,15,7,35,25,65,25,28,65,28,65,140,80,80,140,185,185,371},{0,0,0,1,1,2,1,5,1,5,5,9,7,15,25,19,7,15,7,35,25,53,25,25,65,28,65,120,71,80,140,167,185,341},{0,0,0,0,1,0,1,2,1,5,2,3,5,9,13,9,7,15,7,25,19,31,25,19,53,25,65,81,53,71,120,129,167,275},{0,0,0,0,0,1,0,1,0,1,1,5,1,5,15,7,1,5,1,15,7,25,7,7,25,7,25,65,28,28,65,80,80,185},{0,0,0,0,0,0,1,0,1,0,2,0,5,0,0,9,5,0,7,0,15,25,15,19,35,25,35,55,53,65,70,120,140,236},{0,0,0,0,0,0,0,1,0,1,1,2,1,5,9,5,1,5,1,15,7,19,7,7,25,7,25,53,25,28,65,71,80,167},{0,0,6*T^2,0,0,10*T^2,0,0,1,0,0,15*T^2,2,0,21*T^2,3,5,0,5,0,9,13,15,9,25,19,35,35,31,53,55,81,120,175},{0,0,0,0,0,0,0,0,0,1,0,0,1,2,3,2,1,5,1,9,5,9,7,5,19,7,25,31,19,25,53,53,71,129},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,1,0,1,0,5,15,5,7,15,7,15,35,25,25,35,65,65,140},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,1,0,1,0,5,1,7,1,1,7,1,7,25,7,7,25,28,28,80},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,1,0,5,9,5,5,15,7,15,25,19,25,35,53,65,120},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,0,1,0,5,1,5,1,1,7,1,7,19,7,7,25,25,28,71},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,1,7,1,1,7,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,5,1,1,5,1,5,15,7,7,15,25,25,65},{0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,10*T^2,0,0,15*T^2,0,1,0,1,0,2,3,5,2,9,5,15,13,9,19,25,31,53,81},{T^3,0,2*T^3,0,0,0,2*T^3,0,0,0,4*T^3,0,0,0,0,0,0,1,3*T^3,2,1,2,1,1+6*T^3,5,1,7,9,5,7,19,19,25,53},{0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,10*T^2,0,0,15*T^2,0,0,0,1,0,0,0,0,2,0,5,0,0,9,15,0,25,35,55},{0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,1,0,1,0,3*T^3,1,0,1,5,1,1,7,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,1,5,1,5,9,5,7,15,19,25,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,5,1,1,5,7,7,25},{0,0,T^2,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,10*T^2,0,0,0,0,0,0,0,1,0,2,1,5,3,2,5,9,9,19,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,5,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,1,1,5,5,7,19},{0,0,T^2,0,0,3*T^2,0,0,0,0,0,6*T^2,0,0,10*T^2,0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,9,15,25},{0,0,0,0,0,T^2,T^3,0,0,0,2*T^3,3*T^2,0,0,6*T^2,0,0,0,2*T^3,0,0,0,0,4*T^3,0,0,1,0,0,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5,5,15},{0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,6*T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7570)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 1 & 4 & 3 & 2 & 0 & 2 & 1 & 3 & 1 & 2 & 0 & 3 & 2 & 1 & 0 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 1, 1, -1}, {1, 1, 1, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {3, 4, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{1,2,5},{0,2,3},{0,2,5},{1,2,3},{0,4,5}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,0},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,3,4},{1,3,3},{1,2,4},{1,3,2},{1,2,3},{1,3,1},{1,1,4},{0,2,3},{1,2,2},{1,3,0},{0,2,2},{1,2,1},{1,1,3},{0,2,1},{1,1,2},{1,2,0},{0,1,3},{0,1,2},{1,1,1},{0,2,0},{0,0,3},{1,1,0},{0,1,1},{0,0,2},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,6,10,18,20,21,19,40,35,44,75,52,85,105,126,58,123,186,146,142,301,226,278,376,486,782},{0,1,1,4,6,10,6,6,18,20,19,40,21,44,52,75,22,58,105,85,62,186,123,142,226,278,486},{0,0,1,0,4,0,6,4,10,0,10,20,18,20,40,35,19,44,75,35,58,126,85,123,146,226,376},{0,0,0,1,1,4,1,1,6,10,6,18,6,19,21,40,6,22,52,44,22,105,58,62,123,142,278},{0,0,0,0,1,0,1,1,4,0,4,10,6,10,18,20,6,19,40,20,22,75,44,58,85,123,226},{0,0,0,0,0,1,0,0,1,4,1,6,1,6,6,18,1,6,21,19,6,52,22,22,58,62,142},{0,0,0,0,0,0,1,0,0,0,0,0,4,0,10,0,4,10,20,0,19,35,20,44,35,85,146},{0,0,0,0,0,0,0,1,0,0,4,0,0,10,0,0,6,18,0,20,21,0,40,52,75,105,186},{0,0,0,0,0,0,0,0,1,0,1,4,1,4,6,10,1,6,18,10,6,40,19,22,44,58,123},{T^3,0,2*T^3,0,0,0,3*T^3,T^3,0,1,0,1,0,1,1,6,2*T^3,1,6,6,1+3*T^3,21,6,6,22,22,62},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,1,6,0,10,6,0,18,21,40,52,105},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,0,1,6,4,1,18,6,6,19,22,58},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,1,4,10,0,6,20,10,19,20,44,85},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,1,0,6,6,18,21,52},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,1,10,4,6,10,19,44},{0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,0,1,T^3,0,1,1,2*T^3,6,1,1,6,6,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,6,0,10,18,20,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,6,10,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,4,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,T^3,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7572)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 2 & 3 & 4 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, -1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,3,5},{1,2,5},{1,3,4},{1,2,4},{1,3,3},{0,2,4},{1,1,4},{1,3,2},{1,2,3},{0,1,4},{0,2,3},{1,2,2},{1,1,3},{0,2,2},{0,1,3},{1,1,2},{1,2,1},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,4,9,10,10,14,20,24,16,28,50,39,60,48,84,90,68,108,155,110,158,205,308,348,534},{0,1,0,4,0,4,9,0,10,10,10,20,24,20,28,50,35,48,60,90,35,108,110,205,182,348},{0,0,1,2,4,2,3,10,9,3,10,24,14,28,16,39,50,22,48,84,60,68,108,158,205,308},{0,0,0,1,0,1,2,0,4,2,4,10,9,10,10,24,20,16,28,50,20,48,60,108,110,205},{0,0,0,0,1,0,0,4,2,0,2,9,3,10,3,14,24,4,16,39,28,22,48,68,108,158},{0,0,0,0,0,1,0,0,0,2,4,0,0,10,9,0,0,14,24,0,20,39,50,84,90,155},{0,0,0,0,0,0,1,0,0,1,0,0,4,0,4,10,0,10,10,20,0,28,20,60,35,110},{0,T^3,0,0,0,0,T^3,1,0,2*T^3,0,2,0,2,0,3,9,2*T^3,3,14,10,4,16,22,48,68},{0,0,0,0,0,0,0,0,1,0,1,4,2,4,2,9,10,3,10,24,10,16,28,48,60,108},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,9,10,0,0,24,20,50,35,90},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,0,3,9,0,10,14,24,39,50,84},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,4,0,2,9,4,3,10,16,28,48},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,2,4,10,0,10,10,28,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,4,3,9,14,24,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,0,9,10,24,20,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,2,4,10,10,28},{0,T^3,0,0,0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,1,2*T^3,0,2,1,0,2,3,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,9,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,4,10},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,1,0,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7573)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 1 & 3 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}}
Primitive collections: {{3, 4}, {5, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,2,4},{0,2,4},{1,1,4},{1,2,3},{0,2,3},{0,1,4},{1,2,2},{1,1,3},{0,1,3},{0,2,2},{1,1,2},{1,2,1},{1,0,3},{0,2,1},{0,0,3},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,0,1},{1,1,0},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,4,8,4,10,9,18,20,24,20,14,40,28,48,39,50,100,78,84,90,168,155,180,310},{0,1,0,0,4,2,0,0,9,10,0,0,0,20,14,24,0,0,50,39,0,0,84,0,90,155},{0,0,1,0,0,2,0,4,8,0,10,0,9,0,18,20,24,20,40,48,50,35,100,90,70,180},{0,0,0,1,2,0,4,2,4,8,9,10,3,20,6,18,14,24,48,28,39,50,78,84,100,168},{0,0,0,0,1,0,0,0,2,4,0,0,0,10,3,9,0,0,24,14,0,0,39,0,50,84},{0,0,0,0,0,1,0,0,4,0,0,0,0,0,9,10,0,0,20,24,0,0,50,0,35,90},{0,0,0,0,0,0,1,0,0,2,2,4,0,8,0,4,3,9,18,6,14,24,28,39,48,78},{0,0,0,0,0,0,0,1,2,0,4,0,2,0,4,8,9,10,20,18,24,20,48,50,40,100},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,4,0,0,10,9,0,0,24,0,20,50},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,2,0,0,9,3,0,0,14,0,24,39},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,4,8,4,9,10,18,24,20,48},{0,0,T^3,0,0,2*T^3,0,0,0,0,0,1,T^3,2,2*T^3,0,0,2,4,0,3,9,6,14,18,28},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,4,0,0,8,10,0,20,20,0,40},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,T^3,0,0,0,2,0,0,0,3,0,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,0,0,9,0,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,2,4,4,9,8,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,0,8},{0,0,T^3,0,0,2*T^3,0,0,0,0,0,0,T^3,0,2*T^3,0,0,0,0,0,0,1,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7574)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 4 & 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{2,3,4},{1,4,5},{0,1,5},{0,3,5},{3,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,1},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,2,6},{1,2,5},{1,1,5},{0,2,5},{1,2,4},{0,2,4},{1,2,3},{1,1,4},{0,1,4},{0,2,3},{1,1,3},{1,2,2},{1,0,4},{1,0,3},{0,2,2},{0,1,3},{1,1,2},{0,1,2},{0,0,3},{1,1,1},{1,0,2},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,4,6,5,10,14,20,18,24,30,40,35,21,52,55,58,75,115,73,126,105,157,186,201,291,487},{0,1,1,1,4,5,10,6,7,14,18,20,6,21,30,24,40,58,27,75,52,73,105,115,157,291},{0,0,1,0,0,0,0,4,5,0,10,0,6,18,0,14,20,30,24,35,40,58,75,55,115,201},{0,0,0,1,0,4,0,0,6,10,0,0,0,0,20,18,0,40,21,0,0,52,0,75,105,186},{0,0,0,0,1,1,4,1,1,5,6,10,1,6,14,7,18,24,7,40,21,27,52,58,73,157},{0,0,0,0,0,1,0,0,1,4,0,0,0,0,10,6,0,18,6,0,0,21,0,40,52,105},{0,0,0,0,0,0,1,0,0,1,1,4,0,1,5,1,6,7,1,18,6,7,21,24,27,73},{0,0,0,0,0,0,0,1,1,0,4,0,1,6,0,5,10,14,7,20,18,24,40,30,58,115},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,10,6,0,0,18,0,20,40,75},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,1,0,6,1,0,0,6,0,18,21,52},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,4,5,1,10,6,7,18,14,24,58},{T^3,0,2*T^3,T^3,0,0,0,0,2*T^3,0,0,1,3*T^3,0,1,0,1,1,3*T^3,6,1,1,6,7,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,0,5,0,10,14,20,0,30,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,0,0,6,0,10,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,1,1,6,5,7,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,T^3,0,0,0,0,0,T^3,0,0,0,2*T^3,0,0,0,0,0,2*T^3,1,0,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7575)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 0 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 5 & 4 & 5 & 4 & 3 & 4 & 4 & 3 & 2 & 3 & 2 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}}
Primitive collections: {{4, 5}, {3, 6, 7}, {0, 1, 2, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{3,4,5},{1,3,4},{0,1,4},{0,4,5},{0,2,5}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (26): {{1,2,5},{1,1,5},{1,2,4},{0,2,5},{1,1,4},{1,2,3},{1,0,4},{0,2,4},{1,1,3},{1,2,2},{0,2,3},{1,1,2},{1,0,3},{0,1,4},{0,1,3},{0,2,2},{1,0,2},{1,1,1},{0,1,2},{0,0,3},{1,0,1},{0,0,2},{1,0,0},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,1,4,2,6,10,6,10,18,20,28,40,21,12,39,60,52,75,92,42,105,108,186,180,226,412},{0,1,0,1,4,0,6,4,10,0,10,20,18,10,28,20,40,35,60,39,75,92,126,110,180,312},{0,0,1,0,1,4,1,2,6,10,10,18,6,2,12,28,21,40,39,12,52,42,105,92,108,226},{0,0,0,1,0,0,0,4,0,0,10,0,0,6,18,20,0,0,40,21,0,52,0,75,105,186},{0,0,0,0,1,0,1,1,4,0,4,10,6,2,10,10,18,20,28,12,40,39,75,60,92,180},{0,0,0,0,0,1,0,0,1,4,2,6,1,0,2,10,6,18,12,2,21,12,52,39,42,108},{0,0,0,0,0,0,1,0,0,0,0,0,4,1,4,0,10,0,10,10,20,28,35,20,60,110},{0,0,0,0,0,0,0,1,0,0,4,0,0,1,6,10,0,0,18,6,0,21,0,40,52,105},{0,0,0,0,0,0,0,0,1,0,1,4,1,0,2,4,6,10,10,2,18,12,40,28,39,92},{0,2*T^3,0,2*T^3,0,0,3*T^3,0,0,1,0,1,0,3*T^3,0,2,1,6,2,4*T^3,6,2,21,12,12,42},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,0,6,1,0,6,0,18,21,52},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,4,2,0,6,2,18,10,12,39},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,0,4,2,10,10,20,10,28,60},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,0,10,6,0,18,0,20,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,6,0,10,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,10,28},{0,T^3,0,T^3,0,0,2*T^3,0,0,0,0,0,0,2*T^3,0,0,0,1,0,3*T^3,1,0,6,2,2,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,2*T^3,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7576)$ |
3 |
28 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 0 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 1 & 0 & 2 & 2 & 0 & 1 & 1 & 1 & 2 & 0 & 0 & 0 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 3 & 3 & 2 & 2 & 1 & 2 & 3 & 2 & 3 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 0, 1, 1}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 1, 0, -1, -1}}
Cones (28): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 6}, {4, 5, 7}, {3, 4, 6, 7}, {0, 1, 2, 8}, {0, 1, 5, 8}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{0,2,4},{0,1,3},{2,4,5},{3,4,5}},{2,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,0},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (30): {{2,1,3},{2,0,3},{1,2,3},{2,1,2},{1,1,3},{1,0,3},{0,2,3},{1,2,2},{2,0,2},{2,1,1},{1,1,2},{0,1,3},{0,2,2},{0,0,3},{1,0,2},{2,0,1},{1,2,1},{2,1,0},{0,1,2},{1,1,1},{1,0,1},{0,0,2},{2,0,0},{0,2,1},{1,1,0},{0,1,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,1,4,4,7,4,4,10,10,16,10,16,16,31,28,10,20,40,40,82,68,60,40,80,100,176,170,200,360},{0,1,0,0,1,4,1,0,4,0,4,4,4,10,16,10,0,0,16,10,40,40,20,10,20,40,100,80,80,200},{0,0,1,1,2,3,4,4,2,4,10,7,16,10,16,10,10,10,31,28,49,46,28,40,60,82,128,112,170,276},{0,0,0,1,0,0,0,1,2,4,4,0,4,0,7,10,4,10,10,16,31,16,28,16,40,40,68,82,100,176},{0,0,0,0,1,2,1,0,1,0,4,4,4,7,10,4,0,0,16,10,28,31,10,10,20,40,82,60,80,170},{0,0,0,0,0,1,0,0,0,0,0,1,0,4,4,0,0,0,4,0,10,16,0,0,0,10,40,20,20,80},{0,0,0,0,0,0,1,0,0,0,1,2,4,3,2,1,0,0,10,4,10,16,4,10,10,28,49,28,60,112},{0,0,0,0,0,0,0,1,0,1,2,0,4,0,3,2,4,4,7,10,16,10,10,16,28,31,46,49,82,128},{0,0,0,0,0,0,0,0,1,0,1,0,1,0,4,4,0,0,4,4,16,10,10,4,10,16,40,40,40,100},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,1,4,0,4,7,0,10,4,16,10,16,31,40,68},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,2,1,0,0,4,4,10,7,4,4,10,16,31,28,40,82},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,0,4,0,4,10,0,0,0,10,28,10,20,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,1,2,3,1,4,4,10,16,10,28,49},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,10,0,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,4,0,0,0,4,16,10,10,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,4,0,4,1,4,4,10,16,16,40},{0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,4*T^3,0,0,1,1,0,2,3,0,2,4,10,7,10,16,31,46},{0,2*T^3,0,0,0,3*T^3,0,0,0,0,0,0,0,4*T^3,0,0,0,1,0,0,0,0,2,0,4,0,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,0,0,0,4,10,4,10,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,1,4,4,7,10,16,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,4,4,10},{0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,1,1,2,3,2,10,16},{0,T^3,0,0,0,2*T^3,0,0,0,0,0,0,0,3*T^3,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7580)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}, {0, 0, 1, 1, 0, -1}}
Cones (27): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 7}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{4, 5, 6}, {0, 1, 7}, {2, 3, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{1,1,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,4,4},{2,3,4},{2,4,3},{2,2,4},{2,4,2},{2,3,3},{1,3,3},{2,3,2},{2,2,3},{1,2,3},{2,2,2},{1,3,2},{1,1,3},{1,3,1},{1,2,2},{0,2,2},{1,2,1},{1,1,2},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,6,6,9,11,18,18,24,36,24,42,42,54,57,96,96,105,172,105,168,168,199,324,324,533},{0,1,0,3,0,3,3,6,9,11,18,6,24,10,24,24,42,54,57,96,42,105,65,105,199,168,324},{0,0,1,0,3,3,3,9,6,6,18,11,10,24,24,24,54,42,42,96,57,65,105,105,168,199,324},{0,0,0,1,0,0,0,0,3,3,6,0,11,0,6,6,10,24,24,42,10,57,15,42,105,65,168},{0,0,0,0,1,0,0,3,0,0,6,3,0,11,6,6,24,10,10,42,24,15,57,42,65,105,168},{0,0,0,0,0,1,1,3,3,3,9,3,6,6,11,11,24,24,24,54,24,42,42,57,105,105,199},{0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,11,18,18,24,36,24,42,42,54,96,96,172},{0,0,0,0,0,0,0,1,0,0,3,1,0,3,3,3,11,6,6,24,11,10,24,24,42,57,105},{0,0,0,0,0,0,0,0,1,1,3,0,3,0,3,3,6,11,11,24,6,24,10,24,57,42,105},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,3,6,9,11,18,6,24,10,24,54,42,96},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,3,3,3,11,3,6,6,11,24,24,57},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,3,9,6,6,18,11,10,24,24,42,54,96},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,6,0,11,0,6,24,10,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6,3,0,11,6,10,24,42},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,11,24,24,54},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,3,6,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,3,0,3,11,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7582)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 1 & 2 & 0 & 0 & 0 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3, 5}, {4, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{2,3,4},{1,3,4},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,2,4},{1,2,4},{2,2,3},{1,2,3},{0,2,4},{2,1,3},{2,2,2},{1,2,2},{1,1,3},{2,1,2},{0,2,3},{0,2,2},{0,1,3},{2,0,2},{2,1,1},{1,1,2},{2,0,1},{1,0,2},{1,1,1},{0,1,2},{0,1,1},{0,0,2},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,9,6,7,6,18,18,18,18,36,34,28,34,45,64,64,84,84,156,115,115,141,249,249,436},{0,1,0,3,3,1,0,6,7,3,9,18,18,7,6,18,18,28,34,45,84,64,34,64,141,115,249},{0,0,1,3,0,1,3,9,3,7,6,18,6,7,18,18,28,18,45,34,84,34,64,64,115,141,249},{0,0,0,1,0,0,0,3,1,1,3,9,3,1,3,7,7,7,18,18,45,18,18,28,64,64,141},{0,0,0,0,1,0,0,0,1,0,3,6,7,1,0,3,3,7,6,18,34,28,6,18,64,34,115},{0,0,0,0,0,1,0,0,3,3,0,0,6,7,6,9,18,18,18,18,36,34,34,45,84,84,156},{0,0,0,0,0,0,1,3,0,1,0,6,0,1,7,3,7,3,18,6,34,6,28,18,34,64,115},{0,0,0,0,0,0,0,1,0,0,0,3,0,0,1,1,1,1,7,3,18,3,7,7,18,28,64},{0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,3,3,7,6,9,18,18,6,18,45,34,84},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,7,3,9,6,18,6,18,18,34,45,84},{0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,1,1,1,3,7,18,7,3,7,28,18,64},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,7,1,1,1,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,3,6,7,0,3,18,6,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,0,0,6,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,0,6,0,7,3,6,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,9,3,3,7,18,18,45},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,1,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,1,7,3,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7588)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, -1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{1,3,4},{0,2,4},{0,1,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,4,6},{1,4,5},{1,3,5},{1,4,4},{0,3,5},{1,3,4},{0,3,4},{1,3,3},{1,2,4},{1,2,3},{0,2,4},{0,3,3},{0,2,3},{1,1,3},{1,2,2},{0,2,2},{0,1,3},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,6,6,7,15,18,28,21,46,27,34,61,56,81,109,77,111,157,186,182,267,342,557},{0,1,1,3,1,6,7,15,6,21,7,18,27,21,46,61,27,56,77,111,77,157,182,342},{0,0,1,0,1,3,3,6,6,15,7,6,18,21,28,34,27,46,61,81,77,109,157,267},{0,0,0,1,0,1,1,6,1,6,1,7,7,6,21,27,7,21,27,56,27,77,77,182},{0,0,0,0,1,0,3,0,0,0,6,6,15,0,0,28,21,0,46,0,56,81,111,186},{0,0,0,0,0,1,1,3,1,6,1,3,7,6,15,18,7,21,27,46,27,61,77,157},{0,0,0,0,0,0,1,0,0,0,1,3,6,0,0,15,6,0,21,0,21,46,56,111},{0,0,0,0,0,0,0,1,0,1,0,1,1,1,6,7,1,6,7,21,7,27,27,77},{0,0,0,0,0,0,0,0,1,3,1,0,3,6,6,6,7,15,18,28,27,34,61,109},{0,0,0,0,0,0,0,0,0,1,0,0,1,1,3,3,1,6,7,15,7,18,27,61},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,6,6,0,15,0,21,28,46,81},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,6,1,0,6,0,6,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,6,0,6,15,21,46},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,3,6,7,6,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,6,1,7,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7589)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{2, 3}, {4, 5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,3,5},{0,3,5},{1,3,4},{0,3,4},{1,3,3},{1,2,4},{0,3,3},{0,2,4},{1,2,3},{1,1,3},{1,2,2},{0,2,3},{0,1,3},{1,1,2},{0,2,2},{0,1,2},{1,0,2},{1,1,1},{0,1,1},{0,0,2},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,6,6,6,12,12,15,21,28,30,42,46,56,92,56,81,162,112,111,222,186,372},{0,1,0,3,0,0,6,6,0,0,0,15,21,0,28,46,0,0,81,56,0,111,0,186},{0,0,1,2,3,1,6,2,6,6,15,12,12,21,30,42,21,46,92,42,56,112,111,222},{0,0,0,1,0,0,3,1,0,0,0,6,6,0,15,21,0,0,46,21,0,56,0,111},{0,0,0,0,1,0,2,0,1,1,6,2,2,6,12,12,6,21,42,12,21,42,56,112},{0,0,0,0,0,1,0,2,3,6,6,6,12,15,12,30,21,28,56,42,46,92,81,162},{0,0,0,0,0,0,1,0,0,0,0,1,1,0,6,6,0,0,21,6,0,21,0,56},{0,0,0,0,0,0,0,1,0,0,0,3,6,0,6,15,0,0,28,21,0,46,0,81},{0,0,0,0,0,0,0,0,1,1,3,2,2,6,6,12,6,15,30,12,21,42,46,92},{0,0,0,0,0,0,0,0,0,1,0,0,2,3,0,6,6,6,12,12,15,30,28,56},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,1,6,12,2,6,12,21,42},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,6,0,0,15,6,0,21,0,46},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,6,6,0,15,0,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,3,6,2,6,12,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,6,1,0,6,0,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,6,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7590)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 2 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 0, -1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (27): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}}
Primitive collections: {{3, 4, 5}, {2, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,1,4},{0,2,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,4,6},{2,4,5},{2,3,5},{2,4,4},{1,3,5},{2,3,4},{1,3,4},{2,2,4},{2,3,3},{1,2,4},{1,3,3},{2,2,3},{0,2,4},{2,2,2},{1,2,3},{0,2,3},{1,1,3},{1,2,2},{0,1,3},{0,2,2},{1,1,2},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,3,5,6,7,12,18,15,22,25,34,31,28,53,55,64,65,97,80,115,127,163,211,185,277,343,554},{0,1,1,3,1,5,7,5,12,7,18,15,7,31,25,28,25,55,28,64,65,80,127,80,163,185,343},{0,0,1,0,1,3,3,5,6,7,6,12,7,22,18,18,25,34,28,34,55,64,97,80,115,163,277},{0,0,0,1,0,1,1,1,5,1,7,5,1,15,7,7,7,25,7,28,25,28,65,28,80,80,185},{0,0,0,0,1,0,3,0,0,5,6,0,7,0,12,18,15,22,25,34,31,55,53,65,97,127,211},{0,0,0,0,0,1,1,1,3,1,3,5,1,12,7,7,7,18,7,18,25,28,55,28,64,80,163},{0,0,0,0,0,0,1,0,0,1,3,0,1,0,5,7,5,12,7,18,15,25,31,25,55,65,127},{0,0,0,0,0,0,0,1,0,1,0,3,1,6,3,3,7,6,7,6,18,18,34,28,34,64,115},{0,0,0,0,0,0,0,0,1,0,1,1,0,5,1,1,1,7,1,7,7,7,25,7,28,28,80},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,3,5,6,7,6,12,18,22,25,34,55,97},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,5,1,7,5,7,15,7,25,25,65},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,1,3,1,3,7,7,18,7,18,28,64},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,0,5,6,0,12,0,15,22,31,53},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,1,7,1,7,7,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,1,3,5,7,12,7,18,25,55},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,5,0,5,12,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,7,6,18,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,1,7,7,25},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,7,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7591)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 3 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 3 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}, {0, 0, 1, 1, 1, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{5, 6}, {0, 1, 7}, {2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,1,1}},{{1,2,3},{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,3,4},{1,2,4},{1,3,3},{1,1,4},{1,2,3},{1,3,2},{0,2,3},{1,1,3},{1,3,1},{1,2,2},{0,1,3},{0,2,2},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,6,12,10,13,24,20,30,27,34,60,60,46,72,120,70,124,125,150,260,270,470},{0,1,0,3,4,0,4,12,0,10,13,10,20,30,27,34,60,20,72,35,70,150,125,270},{0,0,1,0,3,4,3,6,10,12,6,13,30,24,10,27,60,34,46,70,72,124,150,260},{0,0,0,1,0,0,0,4,0,0,4,0,0,10,13,10,20,0,34,0,20,70,35,125},{0,0,0,0,1,0,1,3,0,4,3,4,10,12,6,13,30,10,27,20,34,72,70,150},{0,0,0,0,0,1,0,0,4,3,0,3,12,6,0,6,24,13,10,34,27,46,72,124},{0,0,0,0,0,0,1,0,0,0,3,4,0,0,6,12,0,10,24,20,30,60,60,120},{0,0,0,0,0,0,0,1,0,0,1,0,0,4,3,4,10,0,13,0,10,34,20,70},{0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,6,3,0,13,6,10,27,46},{0,0,0,0,0,0,0,0,0,1,0,1,4,3,0,3,12,4,6,10,13,27,34,72},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,12,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,6,10,12,24,30,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,0,4,3,6,13,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,3,0,4,13,10,34},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,4,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7592)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 3 & 1 & 0 & 2 & 3 & 3 & 2 & 1 & 1 & 3 & 0 & 2 & 0 & 2 & 1 & 0 & 3 & 1 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, -1, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{0,1,4},{2,3,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,1,3},{2,1,3},{3,1,2},{1,1,3},{0,1,3},{2,1,2},{3,0,2},{3,1,1},{2,0,2},{1,1,2},{1,0,2},{3,0,1},{0,1,2},{2,1,1},{0,0,2},{2,0,1},{1,1,1},{0,1,1},{3,0,0},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,6,10,20,18,7,21,22,40,50,27,75,52,95,70,105,186,77,145,261,173,331,567},{0,1,1,4,10,6,1,6,7,18,22,7,40,21,50,27,52,105,27,70,145,77,173,331},{0,0,1,0,0,4,1,6,4,10,10,7,20,18,20,22,40,75,27,50,95,70,145,261},{0,0,0,1,4,1,0,1,1,6,7,1,18,6,22,7,21,52,7,27,70,27,77,173},{0,0,0,0,1,0,0,0,0,1,1,0,6,1,7,1,6,21,1,7,27,7,27,77},{0,0,0,0,0,1,0,1,1,4,4,1,10,6,10,7,18,40,7,22,50,27,70,145},{0,0,0,0,0,0,1,0,4,0,10,6,0,0,20,18,0,0,21,40,75,52,105,186},{0,0,0,0,0,0,0,1,0,0,0,1,0,4,0,4,10,20,7,10,20,22,50,95},{0,0,0,0,0,0,0,0,1,0,4,1,0,0,10,6,0,0,6,18,40,21,52,105},{0,0,0,0,0,0,0,0,0,1,1,0,4,1,4,1,6,18,1,7,22,7,27,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,1,0,0,1,6,18,6,21,52},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,6,10,20,18,40,75},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,6,0,1,7,1,7,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,10,1,4,10,7,22,50},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,6,1,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,10,6,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,4,1,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,1,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7593)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 3 & 1 & 0 & 2 & 3 & 2 & 1 & 0 & 2 & 1 & 3 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}}
Primitive collections: {{2, 3, 4, 5}, {6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,1,3},{2,1,3},{3,1,2},{1,1,3},{2,1,2},{3,0,2},{3,1,1},{1,1,2},{0,1,3},{2,1,1},{3,0,1},{2,0,2},{1,0,2},{0,1,2},{2,0,1},{1,1,1},{3,0,0},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,3,10,12,4,6,30,20,24,9,16,40,60,36,60,16,80,120,64,90,180,160,320},{0,1,0,4,3,0,0,12,10,6,0,4,16,30,9,24,0,40,60,16,36,90,64,160},{0,0,1,0,4,1,3,10,0,12,4,4,10,20,16,30,9,20,60,36,40,80,90,180},{0,0,0,1,0,0,0,3,4,0,0,0,4,12,0,6,0,16,24,0,9,36,16,64},{0,0,0,0,1,0,0,4,0,3,0,1,4,10,4,12,0,10,30,9,16,40,36,90},{0,0,0,0,0,1,0,0,0,0,3,4,10,0,12,0,6,20,0,24,30,60,60,120},{0,0,0,0,0,0,1,0,0,4,1,0,0,0,4,10,4,0,20,16,10,20,40,80},{0,0,0,0,0,0,0,1,0,0,0,0,1,4,0,3,0,4,12,0,4,16,9,36},{0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,4,6,0,0,9,0,16},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,0,0,10,4,4,10,16,40},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,0,0,12,10,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,3,0,0,10,0,6,12,30,24,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,3,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,0,4,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,4,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,1,4,4,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7594)$ |
3 |
24 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 3 & 1 & 0 & 2 & 3 & 2 & 1 & 0 & 2 & 1 & 3 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, 1}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (24): {{0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4, 6}, {5, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,2,3},{0,1,3},{1,3,4},{2,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{3,1,3},{2,1,3},{3,1,2},{1,1,3},{2,1,2},{3,0,2},{3,1,1},{1,1,2},{0,1,3},{2,1,1},{3,0,1},{2,0,2},{1,0,2},{0,1,2},{2,0,1},{1,1,1},{3,0,0},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,4,3,10,12,7,6,30,20,24,18,22,50,60,54,60,34,95,120,100,120,225,220,410},{0,1,0,4,3,1,0,12,10,6,3,7,22,30,18,24,6,50,60,34,54,120,100,220},{0,0,1,0,4,1,3,10,0,12,7,4,10,20,22,30,18,20,60,54,50,95,120,225},{0,0,0,1,0,0,0,3,4,0,0,1,7,12,3,6,0,22,24,6,18,54,34,100},{0,0,0,0,1,0,0,4,0,3,1,1,4,10,7,12,3,10,30,18,22,50,54,120},{0,0,0,0,0,1,0,0,0,0,3,4,10,0,12,0,6,20,0,24,30,60,60,120},{0,0,0,0,0,0,1,0,0,4,1,0,0,0,4,10,7,0,20,22,10,20,50,95},{0,0,0,0,0,0,0,1,0,0,0,0,1,4,1,3,0,4,12,3,7,22,18,54},{0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,0,0,7,6,0,3,18,6,34},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,4,1,0,10,7,4,10,22,50},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,3,0,0,12,10,20,30,60},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,3,0,0,10,0,6,12,30,24,60},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,3,12,6,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,1,7,3,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,4,10,12,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,1,4,7,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7595)$ |
3 |
27 |
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9: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 1 & 2 & 0 & 0 & 0 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {1, 1, 0, 0, 0, -1}}
Cones (27): {{0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{2, 3, 4}, {5, 6, 7}, {0, 1, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,2,4},{1,2,4},{2,2,3},{1,2,3},{0,2,4},{2,1,3},{2,2,2},{1,2,2},{1,1,3},{2,1,2},{0,2,3},{0,2,2},{0,1,3},{2,0,2},{2,1,1},{1,1,2},{2,0,1},{1,0,2},{1,1,1},{0,1,2},{0,1,1},{0,0,2},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,9,6,5,6,18,15,12,18,36,30,15,22,36,31,45,66,72,132,90,53,93,186,159,318},{0,1,0,3,3,0,0,6,5,0,9,18,15,0,0,12,0,15,22,36,66,45,0,31,93,53,159},{0,0,1,3,0,1,3,9,3,5,6,18,6,5,12,15,15,15,36,30,72,30,31,45,90,93,186},{0,0,0,1,0,0,0,3,1,0,3,9,3,0,0,5,0,5,12,15,36,15,0,15,45,31,93},{0,0,0,0,1,0,0,0,0,0,3,6,5,0,0,0,0,0,0,12,22,15,0,0,31,0,53},{0,0,0,0,0,1,0,0,3,3,0,0,6,5,6,9,12,15,18,18,36,30,22,36,72,66,132},{0,0,0,0,0,0,1,3,0,1,0,6,0,1,5,3,5,3,15,6,30,6,15,15,30,45,90},{0,0,0,0,0,0,0,1,0,0,0,3,0,0,0,1,0,1,5,3,15,3,0,5,15,15,45},{0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,3,0,5,6,9,18,15,0,12,36,22,66},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,5,3,9,6,18,6,12,15,30,36,72},{0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,0,0,0,0,5,12,5,0,0,15,0,31},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,5,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,6,5,0,0,12,0,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,0,0,6,6,9,18,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,0,6,0,5,3,6,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,9,3,0,5,15,12,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,0,1,3,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,0,0,5,0,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7602)$ |
3 |
20 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -2, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (20): {{0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (22): {{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,1,3},{1,0,4},{0,1,3},{0,0,4},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,30,35,16,70,32,40,70,140,80,85,126,170,161,252,322,280,560},{0,1,0,5,0,15,0,0,35,16,0,0,70,40,0,0,85,0,126,161,0,280},{0,0,1,2,5,10,15,5,30,10,16,35,70,32,40,70,80,85,140,170,161,322},{0,0,0,1,0,5,0,0,15,5,0,0,35,16,0,0,40,0,70,85,0,161},{0,0,0,0,1,2,5,1,10,2,5,15,30,10,16,35,32,40,70,80,85,170},{0,0,0,0,0,1,0,0,5,1,0,0,15,5,0,0,16,0,35,40,0,85},{0,0,0,0,0,0,1,0,2,0,1,5,10,2,5,15,10,16,30,32,40,80},{0,0,0,0,0,0,0,1,0,2,5,0,0,10,15,0,30,35,0,70,70,140},{0,0,0,0,0,0,0,0,1,0,0,0,5,1,0,0,5,0,15,16,0,40},{0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,0,70},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,5,0,10,15,0,30,35,70},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,5,2,5,10,10,16,32},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5,5,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,10,15,30},{T^4,2*T^4,0,0,0,0,0,T^4,0,2*T^4,0,0,0,0,0,1,0,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,10},{0,T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7603)$ |
3 |
20 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$
21: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (20): {{0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,3,5},{0,1,5},{3,4,5},{1,4,5}},{1,1,1})
Cox degrees: {{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (21): {{1,1,6},{1,1,5},{1,0,5},{0,1,5},{1,1,4},{1,0,4},{0,1,4},{1,1,3},{0,0,4},{0,1,3},{1,0,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,6,6,15,20,20,35,26,50,50,70,105,70,105,126,155,196,196,301,532},{0,1,1,1,5,6,6,15,7,20,20,35,50,26,50,70,70,105,105,155,301},{0,0,1,0,0,5,0,0,6,0,15,0,0,20,35,0,50,70,0,105,196},{0,0,0,1,0,0,5,0,6,15,0,0,35,20,0,0,50,0,70,105,196},{0,0,0,0,1,1,1,5,1,6,6,15,20,7,20,35,26,50,50,70,155},{0,0,0,0,0,1,0,0,1,0,5,0,0,6,15,0,20,35,0,50,105},{0,0,0,0,0,0,1,0,1,5,0,0,15,6,0,0,20,0,35,50,105},{0,0,0,0,0,0,0,1,0,1,1,5,6,1,6,15,7,20,20,26,70},{0,0,0,0,0,0,0,0,1,0,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,0,6,0,15,20,50},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,0,6,15,0,20,50},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,5,1,6,6,7,26},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,5,6,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,0,6,20},{T^4,0,T^4,T^4,0,0,0,0,T^4,0,0,0,0,0,0,1,0,1,1,1,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7604)$ |
3 |
20 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 1 & 2 & 2 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, -1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (20): {{0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (20): {{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,1,3},{1,0,4},{0,0,4},{0,1,3},{1,0,3},{1,1,2},{1,1,1},{0,1,2},{1,0,2},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,10,15,6,12,30,20,35,70,70,50,40,100,105,140,210,196,392},{0,1,0,5,0,0,6,15,0,0,0,35,0,20,50,0,70,105,0,196},{0,0,1,2,5,1,2,10,6,15,35,30,20,12,40,50,70,100,105,210},{0,0,0,1,0,0,1,5,0,0,0,15,0,6,20,0,35,50,0,105},{0,0,0,0,1,0,0,2,1,5,15,10,6,2,12,20,30,40,50,100},{0,0,0,0,0,1,2,0,5,0,0,0,15,10,30,35,0,70,70,140},{0,0,0,0,0,0,1,0,0,0,0,0,0,5,15,0,0,35,0,70},{0,0,0,0,0,0,0,1,0,0,0,5,0,1,6,0,15,20,0,50},{0,0,0,0,0,0,0,0,1,0,0,0,5,2,10,15,0,30,35,70},{0,0,0,0,0,0,0,0,0,1,5,2,1,0,2,6,10,12,20,40},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,2,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5,6,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,10,15,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,0,15,0,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7605)$ |
3 |
20 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 4 & 2 & 3 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (20): {{0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1}},{{0,1,2}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (20): {{1,1,4},{1,0,4},{0,1,4},{1,1,3},{1,0,3},{0,1,3},{0,0,4},{1,1,2},{0,0,3},{0,1,2},{1,0,2},{1,1,1},{0,0,2},{1,1,0},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,5,10,10,4,15,20,30,30,35,60,70,70,70,140,140,140,280},{0,1,0,0,5,0,2,0,10,0,15,0,30,0,35,0,70,70,0,140},{0,0,1,0,0,5,2,0,10,15,0,0,30,0,0,35,70,0,70,140},{0,0,0,1,2,2,0,5,4,10,10,15,20,35,30,30,60,70,70,140},{0,0,0,0,1,0,0,0,2,0,5,0,10,0,15,0,30,35,0,70},{0,0,0,0,0,1,0,0,2,5,0,0,10,0,0,15,30,0,35,70},{0,0,0,0,0,0,1,0,5,0,0,0,15,0,0,0,35,0,0,70},{0,0,0,0,0,0,0,1,0,2,2,5,4,15,10,10,20,30,30,60},{0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,0,15,0,0,35},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,5,10,0,15,30},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,5,0,10,15,0,30},{0,0,0,0,0,0,0,0,0,0,0,1,0,5,2,2,4,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7606)$ |
3 |
20 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ -1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 4 & 3 & 4 & 3 & 2 & 4 & 3 & 1 & 2 & 3 & 2 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-2, 0, 1, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (20): {{0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}, {1, 3, 5, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,2},{1,-1,2}},{{1,2,3},{0,3,4},{0,1,3},{2,3,4}},{2,3,2})
Cox degrees: {{1,-1,2},{1,0,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (22): {{1,1,6},{1,1,5},{1,0,6},{1,1,4},{1,0,5},{0,1,4},{1,1,3},{1,0,4},{0,1,3},{1,1,2},{0,0,4},{1,0,3},{1,1,1},{0,1,2},{0,0,3},{1,0,2},{0,1,1},{0,0,2},{1,0,1},{0,1,0},{0,0,1},{0,0,0}}
Ext matrix: {{1,5,2,15,10,17,35,30,45,70,33,70,126,100,85,140,196,185,252,350,357,630},{0,1,0,5,2,5,15,10,17,35,10,30,70,45,33,70,100,85,140,196,185,357},{0,0,1,0,5,1,0,15,5,0,17,35,0,15,45,70,35,100,126,70,196,350},{0,0,0,1,0,1,5,2,5,15,2,10,35,17,10,30,45,33,70,100,85,185},{0,0,0,0,1,0,0,5,1,0,5,15,0,5,17,35,15,45,70,35,100,196},{0,0,0,0,0,1,0,0,5,0,2,0,0,15,10,0,35,30,0,70,70,140},{0,0,0,0,0,0,1,0,1,5,0,2,15,5,2,10,17,10,30,45,33,85},{0,0,0,0,0,0,0,1,0,0,1,5,0,1,5,15,5,17,35,15,45,100},{0,0,0,0,0,0,0,0,1,0,0,0,0,5,2,0,15,10,0,35,30,70},{0,0,0,0,0,0,0,0,0,1,0,0,5,1,0,2,5,2,10,17,10,33},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,5,1,5,15,5,17,45},{T^4,0,2*T^4,0,0,2*T^4,0,0,0,0,3*T^4,0,1,0,0,0,1,0,2,5,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,2,0,15,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,1,5,17},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,T^4,0,0,T^4,0,0,0,0,2*T^4,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7607)$ |
3 |
24 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}, {0, 1, 1, 1, 0, -1}}
Cones (24): {{0, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{0, 1}, {5, 6, 7}, {2, 3, 4, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1}},{{0,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{0,0,1},{0,0,1},{0,0,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,2,5},{0,2,5},{1,2,4},{0,2,4},{1,2,3},{1,1,4},{0,1,4},{0,2,3},{1,1,3},{1,2,2},{0,1,3},{1,0,3},{0,2,2},{1,1,2},{0,1,2},{1,0,2},{1,1,1},{0,0,3},{0,0,2},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,8,10,6,12,20,18,20,36,21,40,40,80,52,75,42,104,105,150,210,186,372},{0,1,0,4,0,0,6,10,0,0,18,0,20,0,40,0,0,21,52,0,75,105,0,186},{0,0,1,2,4,1,2,8,6,10,12,6,20,18,36,21,40,12,42,52,80,104,105,210},{0,0,0,1,0,0,1,4,0,0,6,0,10,0,18,0,0,6,21,0,40,52,0,105},{0,0,0,0,1,0,0,2,1,4,2,1,8,6,12,6,18,2,12,21,36,42,52,104},{0,0,0,0,0,1,2,0,4,0,8,6,0,10,20,18,20,12,36,40,40,80,75,150},{0,0,0,0,0,0,1,0,0,0,4,0,0,0,10,0,0,6,18,0,20,40,0,75},{0,0,0,0,0,0,0,1,0,0,1,0,4,0,6,0,0,1,6,0,18,21,0,52},{0,0,0,0,0,0,0,0,1,0,2,1,0,4,8,6,10,2,12,18,20,36,40,80},{0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,1,6,0,2,6,12,12,21,42},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,1,6,0,10,18,0,40},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,6,6,0,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,4,0,2,6,8,12,18,36},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,6,0,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,2,2,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7608)$ |
3 |
24 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 0 & 1 & 0 & 1 & 2 & 0 & 2 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 3 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {-1, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (24): {{0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3, 4}, {5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{1,0,1}},{{1,2,3},{0,1,3}},{1,1,1})
Cox degrees: {{1,0,1},{1,0,0},{0,1,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (24): {{1,2,4},{1,1,4},{1,2,3},{1,0,4},{0,2,3},{1,2,2},{1,1,3},{0,2,2},{0,1,3},{1,1,2},{1,2,1},{1,0,3},{0,0,3},{0,1,2},{1,0,2},{1,1,1},{0,2,1},{0,0,2},{0,2,0},{1,0,1},{0,1,1},{0,0,1},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,4,6,5,10,12,14,15,30,20,24,30,42,60,60,30,84,55,120,90,180,165,330},{0,1,0,3,0,0,4,0,5,10,0,12,15,14,30,20,0,42,0,60,30,90,55,165},{0,0,1,0,1,4,3,5,3,12,10,6,6,15,24,30,14,30,30,60,42,84,90,180},{0,0,0,1,0,0,0,0,0,0,0,4,5,0,10,0,0,14,0,20,0,30,0,55},{0,0,0,0,1,0,0,4,3,0,0,0,6,12,0,0,10,24,20,0,30,60,60,120},{0,0,0,0,0,1,0,1,0,3,4,0,0,3,6,12,5,6,14,24,15,30,42,84},{0,0,0,0,0,0,1,0,1,4,0,3,3,5,12,10,0,15,0,30,14,42,30,90},{0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,4,6,10,0,12,24,30,60},{0,0,0,0,0,0,0,0,1,0,0,0,3,4,0,0,0,12,0,0,10,30,20,60},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,4,0,3,0,12,5,15,14,42},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,1,0,5,6,3,6,15,30},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,0,0,5,0,10,0,14,0,30},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,4,12,10,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,0,5,0,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,3,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,3,6,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7609)$ |
3 |
24 |
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9: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 3 & 2 & 1 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 1, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (24): {{0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 7, 8}, {1, 3, 4, 6, 7, 8}}
Primitive collections: {{0, 1}, {2, 3, 4}, {5, 6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1}},{{0,1,2}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{0,1,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (24): {{1,2,3},{1,1,3},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,0,3},{1,2,1},{1,1,2},{0,0,3},{0,1,2},{0,2,1},{1,1,1},{1,2,0},{1,0,2},{0,1,1},{0,0,2},{0,2,0},{1,0,1},{1,1,0},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,2,4,6,8,6,10,12,12,24,20,30,20,24,60,48,40,60,60,120,120,120,240},{0,1,0,0,2,0,3,0,4,6,8,0,10,0,12,20,24,0,30,20,60,60,40,120},{0,0,1,0,3,4,0,0,0,6,12,10,0,0,0,30,24,20,0,0,60,0,60,120},{0,0,0,1,0,2,0,4,3,0,6,8,12,10,6,24,12,20,24,30,48,60,60,120},{0,0,0,0,1,0,0,0,0,3,4,0,0,0,0,10,12,0,0,0,30,0,20,60},{0,0,0,0,0,1,0,0,0,0,3,4,0,0,0,12,6,10,0,0,24,0,30,60},{0,0,0,0,0,0,1,0,0,2,0,0,0,0,4,0,8,0,10,0,20,20,0,40},{0,0,0,0,0,0,0,1,0,0,0,2,3,4,0,6,0,8,6,12,12,24,24,48},{0,0,0,0,0,0,0,0,1,0,2,0,4,0,3,8,6,0,12,10,24,30,20,60},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,10,0,0,20},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,3,0,0,0,12,0,10,30},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,4,0,0,6,0,12,24},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,0,3,4,6,12,8,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,3,0,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,4,0,8,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,0,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7617)$ |
3 |
27 |
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9: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 2 & 2 & 0 & 0 & 1 & 2 & 2 & 1 & 1 & 0 & 0 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 0 & 0 & 1 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 0 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 0 & 2 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, -1}}
Cones (27): {{0, 1, 3, 4, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 1, 3, 4, 7, 8}, {0, 1, 3, 5, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 1, 4, 5, 6, 7}, {0, 1, 4, 5, 6, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 7, 8}, {0, 2, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 8}, {0, 2, 3, 5, 7, 8}, {0, 2, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 7, 8}, {1, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 7, 8}}
Primitive collections: {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1}},{{0,1,2}},{1,1,1})
Cox degrees: {{1,0,0},{1,0,0},{1,0,0},{0,1,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1}}
Theta-collection (27): {{2,2,2},{2,1,2},{1,2,2},{2,2,1},{0,2,2},{1,1,2},{1,2,1},{2,1,1},{2,2,0},{2,0,2},{0,2,1},{0,1,2},{1,0,2},{2,0,1},{2,1,0},{1,1,1},{1,2,0},{0,0,2},{0,2,0},{0,1,1},{1,1,0},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,3,3,3,6,9,9,9,6,6,18,18,18,18,18,27,18,36,36,54,54,36,54,108,108,108,216},{0,1,0,0,0,3,0,3,0,3,0,6,9,9,6,9,0,18,0,18,18,18,27,54,54,36,108},{0,0,1,0,3,3,3,0,0,0,9,9,6,0,0,9,6,18,18,27,18,0,18,54,36,54,108},{0,0,0,1,0,0,3,3,3,0,6,0,0,6,9,9,9,0,18,18,27,18,18,36,54,54,108},{0,0,0,0,1,0,0,0,0,0,3,3,0,0,0,0,0,6,6,9,0,0,0,18,0,18,36},{0,0,0,0,0,1,0,0,0,0,0,3,3,0,0,3,0,9,0,9,6,0,9,27,18,18,54},{0,0,0,0,0,0,1,0,0,0,3,0,0,0,0,3,3,0,9,9,9,0,6,18,18,27,54},{0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,3,0,0,0,6,9,9,9,18,27,18,54},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,3,0,6,0,9,6,0,0,18,18,36},{0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,0,0,6,0,0,0,6,9,18,18,0,36},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,3,3,0,0,0,6,0,9,18},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,3,0,0,0,9,0,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,3,9,6,0,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,3,3,6,9,0,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,3,0,0,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,3,9,9,9,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,0,0,0,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,0,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(6,7621)$ |
3 |
17 |
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9: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 5 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & -1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}10 & 9 & 9 & 8 & 8 & 7 & 7 & 6 & 6 & 5 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (9): {{-1, -1, -1, -1, 4, -1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}}
Cones (17): {{0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 4, 5, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 5, 7}, {0, 1, 3, 4, 5, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 6, 8}}
Primitive collections: {{0, 1, 2, 3, 4, 5}, {5, 6}, {6, 7}, {0, 1, 2, 3, 4, 8}, {7, 8}}
Chambers: ({{1,0,0},{0,1,0},{5,1,0},{1,0,-1},{5,1,-1},{0,0,1}},{{0,2,4},{1,2,4},{0,2,5},{0,3,4},{1,2,5},{1,3,4}},{2,1,1})
Cox degrees: {{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,-1},{5,1,-1},{0,1,0},{0,0,1}}
Theta-collection (24): {{10,1,-1},{9,1,0},{9,1,-1},{8,1,0},{8,1,-1},{7,1,0},{7,1,-1},{6,1,0},{6,1,-1},{5,1,0},{5,0,0},{5,1,-1},{4,1,0},{4,0,0},{4,1,-1},{3,1,0},{3,0,0},{3,1,-1},{2,1,0},{2,0,0},{2,1,-1},{1,1,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,6,6,21,21,56,56,126,126,127,252,252,258,462,462,483,792,792,848,1287,1287,1413,2254},{0,1,1,6,6,21,21,56,56,126,126,126,252,253,252,462,468,462,792,813,792,1287,1343,2128},{0,0,1,1,6,6,21,21,56,56,56,126,126,127,252,252,258,462,462,483,792,792,848,1413},{0,0,0,1,1,6,6,21,21,56,56,56,126,126,126,252,253,252,462,468,462,792,813,1343},{0,0,0,0,1,1,6,6,21,21,21,56,56,56,126,126,127,252,252,258,462,462,483,848},{0,0,0,0,0,1,1,6,6,21,21,21,56,56,56,126,126,126,252,253,252,462,468,813},{0,0,0,0,0,0,1,1,6,6,6,21,21,21,56,56,56,126,126,127,252,252,258,483},{0,0,0,0,0,0,0,1,1,6,6,6,21,21,21,56,56,56,126,126,126,252,253,468},{0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,56,56,126,126,127,258},{0,0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,56,56,126,126,253},{0,0,0,0,0,0,0,0,0,0,1,0,0,6,0,0,21,0,0,56,0,0,126,252},{0,0,0,0,0,0,0,0,0,0,0,1,1,1,6,6,6,21,21,21,56,56,56,127},{T^5,0,0,0,0,0,0,0,0,0,T^5,0,1,1,1,6,6,6,21,21,21,56,56,126},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,0,0,21,0,0,56,126},{T^5,T^5,0,0,0,0,0,0,0,0,T^5,0,0,0,1,1,1,6,6,6,21,21,21,56},{6*T^5,T^5,T^5,0,0,0,0,0,0,0,6*T^5,0,0,T^5,0,1,1,1,6,6,6,21,21,56},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,0,0,21,56},{6*T^5,6*T^5,T^5,T^5,0,0,0,0,0,0,6*T^5,0,0,T^5,0,0,0,1,1,1,6,6,6,21},{21*T^5,6*T^5,6*T^5,T^5,T^5,0,0,0,0,0,21*T^5,0,0,6*T^5,0,0,T^5,0,1,1,1,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,6,21},{21*T^5,21*T^5,6*T^5,6*T^5,T^5,T^5,0,0,0,0,21*T^5,0,0,6*T^5,0,0,T^5,0,0,0,1,1,1,6},{56*T^5,21*T^5,21*T^5,6*T^5,6*T^5,T^5,T^5,0,0,0,56*T^5,0,0,21*T^5,0,0,6*T^5,0,0,T^5,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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