|
$(5,6)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {0, 0, 0, 1, -1}, {1, 1, 1, 0, -3}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 1, 4, 6, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}}
Primitive collections: {{4, 5}, {3, 6}, {0, 1, 2, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,6},{1,1,6},{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: {{1,2,4,8,10,20,20,40,35,41,56,70,62,112,74,113,122,188,188,292},{0,1,0,4,0,0,10,20,0,20,0,35,41,56,35,74,56,122,84,188},{0,0,1,2,4,10,8,20,20,20,35,40,30,70,41,62,74,113,122,188},{0,0,0,1,0,0,4,10,0,10,0,20,20,35,20,41,35,74,56,122},{0,0,0,0,1,4,2,8,10,8,20,20,12,40,20,30,41,62,74,113},{0,0,0,0,0,1,0,2,4,2,10,8,3,20,8,12,20,30,41,62},{0,0,0,0,0,0,1,4,0,4,0,10,8,20,10,20,20,41,35,74},{0,0,0,0,0,0,0,1,0,1,0,4,2,10,4,8,10,20,20,41},{T^3,2*T^3,0,0,0,0,0,0,1,T^3,4,2,2*T^3,8,2,3,8,12,20,30},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{4*T^3,8*T^3,T^3,2*T^3,0,0,0,0,0,4*T^3,1,0,8*T^3,2,T^3,2*T^3,2,3,8,12},{0,T^3,0,0,0,0,0,0,0,0,0,1,T^3,4,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,4*T^3,0,T^3,0,0,0,0,0,0,0,0,4*T^3,1,0,T^3,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
|
|
$(5,7)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 0 & 3 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 9 & 8 & 7 & 6 & 6 & 5 & 6 & 4 & 5 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, -1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{1,1,3}},{{2,3,4},{0,2,4},{0,1,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,0,0},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,9},{1,2,8},{1,2,7},{1,2,6},{1,1,6},{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: {{1,4,10,20,21,35,22,56,39,43,66,104,76,124,155,126,221,190,198,277,297,428},{0,1,4,10,10,20,10,35,21,22,39,66,43,76,104,76,155,124,126,190,198,297},{0,0,1,4,4,10,4,20,10,10,21,39,22,43,66,43,104,76,76,124,126,198},{0,0,0,1,1,4,1,10,4,4,10,21,10,22,39,22,66,43,43,76,76,126},{0,0,0,0,1,0,1,0,4,4,10,20,10,20,35,22,56,35,43,56,76,124},{T^3,0,0,0,T^3,1,2*T^3,4,1,1,4,10,4,10,21,10+2*T^3,39,22,22,43,43,76},{0,0,0,0,0,0,1,0,0,4,0,0,10,20,0,21,0,35,39,56,66,104},{4*T^3,T^3,0,0,4*T^3,0,8*T^3,1,T^3,2*T^3,1,4,1,4,10,4+8*T^3,21,10,10+2*T^3,22,22,43},{0,0,0,0,0,0,0,0,1,1,4,10,4,10,20,10,35,20,22,35,43,76},{0,0,0,0,0,0,0,0,0,1,0,0,4,10,0,10,0,20,21,35,39,66},{0,0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,10,20,22,43},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,10,20,21,39},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,10,21},{0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,1,2*T^3,4,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,4*T^3,0,4*T^3,0,T^3,T^3,0,0,0,0,0,8*T^3,1,0,2*T^3,1,1,4},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,T^3,0,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{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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|
$(5,11)$ |
3 |
16 |
|
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8: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, -1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
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},{0,1,3},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,1,3},{0,1,3},{1,0,3},{1,1,2},{0,0,3},{1,0,2},{0,1,2},{0,0,2},{1,1,1},{1,0,1},{0,1,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,5,9,15,25,35,55,36,70,57,75,105,114,126,141,182,207,245,349},{0,1,1,5,5,15,15,35,15,35,36,36,70,75,70,75,126,141,141,245},{0,0,1,2,5,9,15,25,15,35,25,36,55,57,70,75,105,114,141,207},{0,0,0,1,1,5,5,15,5,15,15,15,35,36,35,36,70,75,75,141},{0,0,0,0,1,2,5,9,5,15,9,15,25,25,35,36,55,57,75,114},{0,0,0,0,0,1,1,5,1,5,5,5,15,15,15,15,35,36,36,75},{0,0,0,0,0,0,1,2,1,5,2,5,9,9,15,15,25,25,36,57},{0,0,0,0,0,0,0,1,0,1,1,1,5,5,5,5,15,15,15,36},{0,0,0,0,0,0,0,0,1,0,2,5,0,9,0,15,0,25,35,55},{0,T^3,0,0,0,0,0,0,0,1,T^3,1,2,2,5,5,9,9,15,25},{0,0,0,0,0,0,0,0,0,0,1,1,0,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,5,0,9,15,25},{T^4,0,0,0,0,0,0,0,T^4,0,0,0,1,1,1,1,5,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{T^4,3*T^3,0,T^3,0,0,0,0,T^4,0,3*T^3,0,0,T^3,1,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{5*T^4,T^4,T^4,0,0,0,0,0,5*T^4,0,T^4,T^4,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{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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$(5,15)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -2 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 3 & 5 & 2 & 4 & 1 & 3 & 3 & 0 & 5 & 2 & -1 & 2 & 4 & 1 & 1 & 3 & 3 & 0 & 2 & 2 & -1 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, -1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}}
Primitive collections: {{2, 3, 5}, {4, 6}, {3, 5, 6}, {0, 1, 2, 7}, {0, 1, 4, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-2},{0,0,1},{0,1,3},{-1,1,3}},{{0,3,4},{0,2,3},{0,1,4},{3,4,5},{1,4,5},{0,1,2}},{6,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-2},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,0,3},{1,1,5},{2,0,2},{1,1,4},{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: {{1,1,4,4,10,10,12,20,12,20,35,28,28,35,55,55,58,96,96,108,154,154,184,292},{0,1,1,4,4,10,10,10,12,20,20,22,28,35,43,55,55,76,96,99,124,154,166,262},{0,0,1,1,4,4,4,10,4,10,20,12,12,20,28,28,28,55,55,58,96,96,108,184},{0,0,0,1,1,4,4,4,4,10,10,10,12,20,22,28,28,43,55,55,76,96,99,166},{0,0,0,0,1,1,1,4,1,4,10,4,4,10,12,12,12,28,28,28,55,55,58,108},{0,0,0,0,0,1,1,1,1,4,4,4,4,10,10,12,12,22,28,28,43,55,55,99},{0,0,0,0,0,0,1,0,1,0,0,4,4,0,10,10,12,20,20,28,35,35,55,96},{0,0,0,0,0,0,0,1,0,1,4,1,1,4,4,4,4,12,12,12,28,28,28,58},{0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10,10,10,20,22,20,35,43,76},{T^3,0,0,0,0,0,2*T^3,0,0,1,1,1,1,4,4,4,4+3*T^3,10,12,12,22,28,28,55},{T^3,T^3,0,0,0,0,2*T^3,0,2*T^3,0,1,0,0,1,1,1,1+3*T^3,4,4,4,12,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,4,4,10,10,12,20,20,28,55},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,4,4,10,10,10,20,22,43},{4*T^3,T^3,T^3,0,0,0,8*T^3,0,2*T^3,0,0,2*T^3,0,1,1,1,1+12*T^3,4,4,4+3*T^3,10,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,10,10,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,10,10,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,12},{0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,2*T^3,0,1,1,1,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,T^3,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,1,1,4},{0,0,0,0,0,0,4*T^3,0,T^3,0,0,T^3,0,0,0,0,8*T^3,0,0,2*T^3,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{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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$(5,16)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & -1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
28: $\begin{pmatrix}-1 & 0 & -2 & 1 & -1 & 0 & -2 & 1 & -1 & -2 & 0 & 1 & -1 & 0 & -1 & -2 & 0 & 1 & -1 & 1 & 0 & 1 & 0 & -1 & 0 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 4 & 5 & 3 & 4 & 4 & 3 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, -1, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {2, 3, 4, 5, 7}}
Primitive collections: {{1, 2, 4}, {4, 6}, {3, 5, 6}, {0, 1, 2, 7}, {0, 3, 5, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,3},{-1,1,3}},{{2,4,5},{1,4,5},{0,1,4},{1,3,5},{0,2,4},{2,3,5}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{-1,0,1},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (28): {{-1,1,6},{0,1,5},{-2,1,6},{1,1,4},{-1,1,5},{0,1,4},{-2,1,5},{1,1,3},{-1,1,4},{-2,1,4},{0,1,3},{1,1,2},{-1,1,3},{0,0,3},{-1,0,3},{-2,1,3},{0,1,2},{1,0,2},{-1,1,2},{1,1,1},{0,0,2},{1,0,1},{0,1,1},{-1,0,2},{0,0,1},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,3,6,10,10,14,20,30,30,40,50,31,52,70,70,42,105,90,76,100,140,115,160,226,205,302},{0,1,0,2,2,6,3,10,10,14,20,30,30,20,30,40,50,31,70,70,52,76,105,73,115,154,160,226},{0,0,1,0,2,3,6,4+T^2,10,20,14,18+2*T^2,30,14,31,50,40,18,70,50+3*T^2,42,53,90,76,100,160,124,205},{0,0,4*T^2,1,0,2,5*T^2,6,3,4+6*T^2,10,20,14,10,14,18+7*T^2,30,20,40,50,30,52,70,40,73,94,115,154},{0,0,0,0,1,2,2,3,6,10,10,14,20,10,20,30,30,14,50,40,31,42,70,52,76,115,100,160},{0,0,0,0,0,1,0,2,2,3,6,10,10,6,10,14,20,10,30,30,20,31,50,30,52,73,76,115},{0,0,0,T^3,0,0,1,0,2,6,3,4+T^2,10,3,10,20,14,4,30,18+2*T^2,14,18,40,31,42,76,53,100},{0,0,3*T^2,0,0,0,4*T^2,1,0,5*T^2,2,6,3,2,3,4+6*T^2,10,6,14,20,10,20,30,14,30,40,52,73},{0,0,0,0,0,0,0,0,1,2,2,3,6,2,6,10,10,3,20,14,10,14,30,20,31,52,42,76},{0,0,0,2*T^3,0,0,0,T^3,0,1,0,0,2,0,2,6,3,0,10,4+T^2,3,4,14,10,14,31,18,42},{0,0,0,0,0,0,0,0,0,0,1,2,2,1,2,3,6,2,10,10,6,10,20,10,20,30,31,52},{T^3,0,2*T^2+2*T^3,0,0,0,3*T^2,0,0,4*T^2,0,1,0,T^3,2*T^3,5*T^2,2,1,3,6,2,6,10,3,10,14,20,30},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,0,6,3,2,3,10,6,10,20,14,31},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,2,0,0,6,10,0,10,20,30,30,50},{0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,1,0,0,0,0,3*T^2,2,3,0,6,10,20,14,30},{0,T^3,0,5*T^3,0,0,0,2*T^3,0,0,0,T^3,0,0,0,1,0,T^3,2,0,0,0,3,2,3,10,4,14},{0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,1,0,2,2,1,2,6,2,6,10,10,20},{0,0,2*T^2,0,0,0,3*T^2,0,0,4*T^2,0,0,0,0,0,5*T^2,0,1,0,0,2,6,0,3,10,14,20,30},{T^4,0,0,T^3,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,1,0,0,0,2,1,2,6,3,10},{2*T^3,0,T^2+6*T^3,0,T^3,0,2*T^2+2*T^3,0,0,3*T^2,0,0,0,2*T^3,6*T^3,4*T^2,0,0,0,1,T^3,1,2,2*T^3,2,3,6,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,2,6,10,10,20},{0,0,T^2,0,0,0,2*T^2,0,0,3*T^2,0,0,0,0,0,4*T^2,0,0,0,0,0,1,0,0,2,3,6,10},{2*T^4,T^4,2*T^3,0,0,0,T^3,0,0,0,0,0,0,2*T^4,2*T^3,0,0,T^4,0,0,0,0,1,T^3,1,2,2,6},{0,0,0,T^3,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,0,1,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,2*T^3,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,17)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 3 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,1,6},{0,1,6},{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,1,3},{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: {{1,2,4,8,10,20,20,35,40,21,70,39,56,42,78,66,112,132,104,208},{0,1,0,4,0,10,0,0,20,0,35,0,0,21,39,0,56,66,0,104},{0,0,1,2,4,8,10,20,20,10,40,21,35,20,42,39,70,78,66,132},{0,0,0,1,0,4,0,0,10,0,20,0,0,10,21,0,35,39,0,66},{0,0,0,0,1,2,4,10,8,4,20,10,20,8,20,21,40,42,39,78},{0,0,0,0,0,1,0,0,4,0,10,0,0,4,10,0,20,21,0,39},{0,0,0,0,0,0,1,4,2,1,8,4,10,2,8,10,20,20,21,42},{T^3,2*T^3,0,0,0,0,0,1,0,T^3,2,1,4,2*T^3,2,4,8,8,10,20},{0,0,0,0,0,0,0,0,1,0,4,0,0,1,4,0,10,10,0,21},{0,0,0,0,0,0,0,0,0,1,0,4,0,2,8,10,0,20,20,40},{0,T^3,0,0,0,0,0,0,0,0,1,0,0,T^3,1,0,4,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{4*T^3,8*T^3,T^3,2*T^3,0,0,0,0,0,4*T^3,0,T^3,1,8*T^3,2*T^3,1,2,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,4*T^3,0,T^3,0,0,0,0,0,0,0,0,0,4*T^3,T^3,0,1,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,18)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 3 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 3 & 2 & 3 & 4 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -3}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}}
Primitive collections: {{3, 5}, {4, 6}, {0, 1, 2, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,3},{-1,1,3}},{{0,2,3},{0,1,3},{2,3,4},{1,3,4}},{2,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,0,0},{-1,1,3},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,1,6},{1,1,5},{0,1,6},{1,1,4},{0,1,5},{1,1,3},{1,1,2},{1,0,3},{0,1,4},{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: {{1,4,2,10,8,20,35,22,20,40,43,56,70,43,76,82,124,112,142,228},{0,1,0,4,2,10,20,10,8,20,22,35,40,20,43,43,76,70,82,142},{0,0,1,0,4,0,0,1,10,20,4,0,35,22,10,43,20,56,76,124},{0,0,0,1,0,4,10,4,2,8,10,20,20,8,22,20,43,40,43,82},{0,0,0,0,1,0,0,0,4,10,1,0,20,10,4,22,10,35,43,76},{0,0,0,0,0,1,4,1,0,2,4,10,8,2,10,8,22,20,20,43},{T^3,0,2*T^3,0,0,0,1,2*T^3,0,0,1,4,2,3*T^3,4,2,10,8,8,20},{0,0,0,0,0,0,0,1,0,0,4,0,0,2,10,8,20,0,20,40},{0,0,0,0,0,0,0,0,1,4,0,0,10,4,1,10,4,20,22,43},{0,0,0,0,0,0,0,0,0,1,0,0,4,1,0,4,1,10,10,22},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,2,10,0,8,20},{4*T^3,T^3,8*T^3,0,2*T^3,0,0,8*T^3,0,0,2*T^3,1,0,12*T^3,1,3*T^3,4,2,2,8},{0,0,T^3,0,0,0,0,T^3,0,0,0,0,1,2*T^3,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2},{0,0,4*T^3,0,T^3,0,0,4*T^3,0,0,T^3,0,0,8*T^3,0,2*T^3,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,25)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 5 & 3 & 2 & 4 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {0, 0, 0, 1, -1}, {1, 1, 1, -1, -2}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 1, 4, 6, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}}
Primitive collections: {{4, 5}, {3, 6}, {0, 1, 2, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,3,0},{0,1,-1},{0,0,1},{1,1,2}},{{1,4,5},{0,4,5},{1,2,5},{1,2,3},{0,2,5},{0,2,3}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{0,1,-1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,5},{1,2,4},{1,1,5},{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: {{1,4,5,10,20,14,30,35,31,56,55,59,91,70,140,101,125,160,205,315},{0,1,1,4,10,5,14,20,14,35,30,31,55,35,91,59,70,101,125,205},{0,0,1,0,0,4,10,0,10,0,20,20,35,31,56,35,59,56,101,160},{0,0,0,1,4,1,5,10,5,20,14,14,30,15,55,31,35,59,70,125},{0,0,0,0,1,0,1,4,1,10,5,5,14,5,30,14,15,31,35,70},{0,0,0,0,0,1,4,0,4,0,10,10,20,14,35,20,31,35,59,101},{0,0,0,0,0,0,1,0,1,0,4,4,10,5,20,10,14,20,31,59},{T^3,0,T^3,0,0,0,0,1,T^3,4,1,1,5,1+T^3,14,5,5,14,15,35},{0,0,0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,30,55},{4*T^3,T^3,5*T^3,0,0,T^3,0,0,4*T^3,1,0,T^3,1,5*T^3,5,1,1+T^3,5,5,15},{0,0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,14,31},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,14,30},{0,0,T^3,0,0,0,0,0,0,0,0,0,1,T^3,4,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,4*T^3,0,0,T^3,0,0,0,0,0,0,0,4*T^3,1,0,T^3,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,27)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 0 & 2 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 6 & 5 & 5 & 4 & 5 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, -1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,3},{2,3,6}},{{2,3,4},{0,1,5},{3,4,5},{1,3,5},{0,2,4},{0,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,1,3},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (21): {{1,2,8},{1,2,7},{1,2,6},{1,1,6},{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: {{1,4,10,11,20,24,35,25,56,45,76,49,86,119,91,176,139,153,211,241,360},{0,1,4,4,10,11,20,11,35,24,45,25,49,76,50,119,86,91,139,153,241},{0,0,1,1,4,4,10,4,20,11,24,11,25,45,25,76,49,50,86,91,153},{0,0,0,1,0,4,0,4,0,10,20,10,20,35,25,56,35,49,56,86,139},{0,0,0,0,1,1,4,1,10,4,11,4,11,24,11,45,25,25,49,50,91},{0,0,0,0,0,1,0,1,0,4,10,4,10,20,11,35,20,25,35,49,86},{T^3,0,0,T^3,0,0,1,T^3,4,1,4,1,4,11,4+T^3,24,11,11,25,25,50},{0,0,0,0,0,0,0,1,0,0,0,4,10,0,11,0,20,24,35,45,76},{4*T^3,T^3,0,4*T^3,0,T^3,0,5*T^3,1,0,1,T^3,1,4,1+5*T^3,11,4,4+T^3,11,11,25},{0,0,0,0,0,0,0,0,0,1,4,1,4,10,4,20,10,11,20,25,49},{0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,10,4,4,10,11,25},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,4,0,10,11,20,24,45},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,11,24},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,1,T^3,4,1,1,4,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,4*T^3,0,T^3,0,T^3,0,0,0,0,0,0,5*T^3,1,0,T^3,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,11},{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,T^3,0,0,0,0,0,0,T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{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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$(5,32)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 5 & 6 & 4 & 5 & 3 & 5 & 3 & 4 & 4 & 2 & 3 & 2 & 3 & 1 & 3 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, -1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{3, 4}, {2, 5, 6}, {4, 5, 6}, {0, 1, 2, 7}, {0, 1, 3, 7}}
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},{2,3,4},{0,2,4},{0,1,2},{1,5,6},{0,1,5}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,2},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,1,5},{0,2,6},{1,1,4},{0,2,5},{1,1,3},{0,1,5},{1,0,3},{0,2,4},{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: {{1,1,4,4,10,5,12,10,15,20,20,28,34,35,36,55,65,74,96,111,135,225},{0,1,1,4,4,4,4,10,12,10,20,12,28,20,28,28,55,58,55,96,108,184},{0,0,1,1,4,1,4,4,5,10,10,12,15,20,15,28,34,36,55,65,74,135},{0,0,0,1,1,1,1,4,4,4,10,4,12,10,12,12,28,28,28,55,58,108},{0,0,0,0,1,0,1,1,1,4,4,4,5,10,5,12,15,15,28,34,36,74},{0,0,0,0,0,1,1,0,4,0,0,4,10,0,12,10,20,28,20,35,55,96},{0,0,0,0,0,0,1,0,1,0,0,4,4,0,5,10,10,15,20,20,34,65},{0,0,0,0,0,0,0,1,1,1,4,1,4,4,4,4,12,12,12,28,28,58},{0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,4,10,12,10,20,28,55},{0,0,0,0,0,T^3,0,0,0,1,1,1,1,4,1+T^3,4,5,5,12,15,15,36},{T^3,0,0,0,0,2*T^3,2*T^3,0,0,0,1,0,1,1,1+3*T^3,1,4,4,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,4,5,10,10,15,34},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,4,10,12,28},{T^3,T^3,0,0,0,5*T^3,2*T^3,0,T^3,0,0,0,0,1,6*T^3,1,1,1+T^3,4,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,12},{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,T^3,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,1,5},{0,0,0,0,0,T^3,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{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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$(5,37)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & -1 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 3 & 1 & 3 & 4 & 2 & 2 & 0 & 3 & 1 & 3 & -1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & -1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, -1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}}
Primitive collections: {{2, 3, 5}, {4, 6}, {3, 5, 6}, {0, 1, 2, 7}, {0, 1, 4, 7}}
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},{6,7,8},{0,4,5},{1,2,3},{0,2,6,7},{5,7,8},{0,2,3},{0,3,4},{1,6,8},{1,2,6}},{4,1,2})
Cox degrees: {{0,0,1},{0,0,1},{1,-1,-1},{1,0,-1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (21): {{2,0,2},{1,1,3},{2,0,1},{1,0,3},{0,1,4},{1,1,2},{1,0,2},{2,0,0},{0,1,3},{1,1,1},{0,0,3},{2,0,-1},{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: {{1,1,4,2,2,4,9,10,9,10,14,20,24,24,20,39,50,50,84,90,155},{0,1,1,1,2,4,5,4,9,10,10,10,15,24,20,29,34,50,65,65,124},{0,0,1,0,0,1,2,4,2,4,3,10,9,9,10,14,24,24,39,50,84},{0,0,0,1,1,0,4,0,4,0,9,0,10,10,0,24,20,20,50,35,90},{0,0,0,0,1,0,1,0,4,0,5,0,4,10,0,15,10,20,34,20,65},{0,0,0,0,0,1,1,1,2,4,2,4,5,9,10,10,15,24,29,34,65},{0,0,0,0,0,0,1,0,1,0,2,0,4,4,0,9,10,10,24,20,50},{0,0,0,0,0,0,0,1,0,1,0,4,2,2,4,3,9,9,14,24,39},{0,0,0,0,0,0,0,0,1,0,1,0,1,4,0,5,4,10,15,10,34},{0,0,0,T^3,0,0,0,0,0,1,T^3,1,1,2,4,2,5,9,10,15,29},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,10,0,20},{0,0,0,T^3,T^3,0,0,0,0,0,T^3,1,0,0,1,0,2,2,3,9,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,4,4,9,10,24},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,5,4,15},{T^3,0,0,5*T^3,T^3,0,T^3,0,0,0,5*T^3,0,0,0,1,T^3,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,4,9},{0,0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,T^3,T^3,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,42)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & -1 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}-2 & -1 & -2 & 0 & -2 & -1 & 0 & -1 & -2 & -2 & -1 & 0 & -1 & 0 & -2 & 0 & -1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 5 & 4 & 5 & 4 & 3 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, -1, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (20): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 6}, {0, 1, 4, 6, 7}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 6}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{1, 2, 4}, {3, 4, 6}, {3, 5, 6}, {0, 1, 2, 7}, {0, 5, 7}}
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},{0,4,5},{0,1,4},{1,3,6},{0,2,5},{4,5,6},{1,4,6},{2,3,6}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{-1,0,1},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{-2,2,6},{-1,2,5},{-2,2,5},{0,2,4},{-2,1,5},{-1,2,4},{0,2,3},{-1,1,4},{-2,2,4},{-2,1,4},{-1,2,3},{0,1,3},{-1,1,3},{0,2,2},{-2,1,3},{0,1,2},{-1,0,3},{0,0,2},{-1,1,2},{-1,0,2},{0,1,1},{0,0,1},{-1,0,1},{0,0,0}}
Ext matrix: {{1,2,4,3,5,7,10,10,10,15,16,15,27,22,34,39,30,45,56,68,78,99,130,183},{0,1,1,2,1,4,7,5,4,5,10,10,15,16,15,27,16,30,34,39,56,68,80,130},{0,0,1,0,1,2,3,2,4,5,7,3,10,10,15,15,10,15,27,30,39,45,68,99},{0,0,0,1,0,1,4,1,1,1,4,5,5,10,5,15,5,16,15,16,34,39,39,80},{0,0,0,T^2,1,0,2*T^2,2,0,4,0,3,7,3*T^2,10,10,10,15,16,27,22,39,56,78},{0,0,0,0,0,1,2,1,1,1,4,2,5,7,5,10,5,10,15,16,27,30,39,68},{0,0,0,0,T^3,0,1,0,0,0,1,1,1,4,1,5,1+T^3,5,5,5,15,16,16,39},{0,0,0,0,0,0,0,1,0,1,0,2,4,0,4,7,5,10,10,15,16,27,34,56},{0,0,0,0,0,0,0,0,1,1,2,0,2,3,5,3,2,3,10,10,15,15,30,45},{0,0,0,0,0,0,T^2,0,0,1,0,0,2,2*T^2,4,3,2,3,7,10,10,15,27,39},{0,0,0,0,T^3,0,0,0,0,0,1,0,1,2,1,2,1+T^3,2,5,5,10,10,16,30},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,1,5,4,5,10,15,15,34},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,1,2,4,5,7,10,15,27},{T^3,0,0,0,5*T^3,0,0,T^3,0,T^3,0,0,0,1,0,1,5*T^3,1+T^3,1,1+T^3,5,5,5,16},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^2,1,0,0,0,2,2,3,3,10,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,4,5,5,15},{0,0,0,T^2,0,0,2*T^2,0,0,0,0,0,0,3*T^2,0,0,1,2,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,5,10},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,0,2,4,7},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,T^3,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,43)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 2 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
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},{0,1,5},{3,4,5}},{1,1,1})
Cox degrees: {{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 (19): {{1,1,6},{1,1,5},{0,1,5},{1,1,4},{1,0,4},{0,1,4},{1,1,3},{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: {{1,4,5,10,11,14,20,30,35,24,35,55,56,45,69,76,91,121,195},{0,1,1,4,4,5,10,14,20,11,15,30,35,24,35,45,55,69,121},{0,0,1,0,0,4,0,10,0,0,11,20,0,0,24,0,35,45,76},{0,0,0,1,1,1,4,5,10,4,5,14,20,11,15,24,30,35,69},{0,0,0,0,1,0,0,0,0,4,5,0,0,10,14,20,0,30,55},{0,0,0,0,0,1,0,4,0,0,4,10,0,0,11,0,20,24,45},{0,0,0,0,0,0,1,1,4,1,1,5,10,4,5,11,14,15,35},{0,0,0,0,0,0,0,1,0,0,1,4,0,0,4,0,10,11,24},{T^3,0,T^3,0,T^3,0,0,0,1,0,T^3,1,4,1,1,4,5,5,15},{0,0,0,0,0,0,0,0,0,1,1,0,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,11},{4*T^3,T^3,5*T^3,0,4*T^3,T^3,0,0,0,T^3,5*T^3,0,1,0,T^3,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,45)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & -1 & 0 & 2 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 5 & 3 & 2 & 4 & 1 & 2 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,-1,-1},{0,0,1},{1,0,1},{0,1,2}},{{3,4,5},{2,3,4},{0,1,5},{0,1,2},{0,2,4},{0,4,5}},{3,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,0,1},{1,-1,-1},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (19): {{1,1,5},{1,1,4},{1,0,4},{1,1,3},{0,1,5},{1,0,3},{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: {{1,4,4,10,5,11,20,15,35,24,34,45,35,76,65,70,111,125,205},{0,1,1,4,1,4,10,5,20,11,15,24,15,45,34,35,65,70,125},{0,0,1,0,1,4,0,4,0,10,10,20,15,35,20,34,35,65,111},{0,0,0,1,0,1,4,1,10,4,5,11,5,24,15,15,34,35,70},{0,0,0,0,1,0,0,4,0,0,10,0,11,0,20,24,35,45,76},{0,0,0,0,0,1,0,1,0,4,4,10,5,20,10,15,20,34,65},{0,0,T^3,0,T^3,0,1,0,4,1,1,4,1+T^3,11,5,5,15,15,35},{0,0,0,0,0,0,0,1,0,0,4,0,4,0,10,11,20,24,45},{T^3,0,4*T^3,0,5*T^3,T^3,0,T^3,1,0,0,1,5*T^3,4,1,1+T^3,5,5,15},{0,0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,15,34},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10,11,24},{0,0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,T^3,0,T^3,0,0,0,0,0,0,0,T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,4,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,46)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -1 & 2 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 5 & 3 & 3 & 4 & 2 & 3 & 1 & 2 & 3 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}}
Primitive collections: {{3, 5}, {4, 6}, {0, 1, 2, 7}}
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},{4,6,7},{0,2,3},{0,2,5,6},{1,2,3},{5,6,7},{1,2,5},{1,5,7}},{2,1,1})
Cox degrees: {{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 (18): {{1,1,4},{0,1,5},{1,1,3},{1,0,3},{0,1,4},{1,1,2},{0,1,3},{1,1,1},{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: {{1,1,4,5,5,10,14,20,15,19,30,35,34,45,65,55,89,156},{0,1,0,1,4,0,10,0,4,15,20,0,10,34,20,35,65,111},{0,0,1,1,1,4,5,10,5,6,14,20,15,19,34,30,45,89},{0,0,0,1,0,0,0,0,4,5,0,0,10,14,20,0,30,55},{0,0,0,0,1,0,4,0,1,5,10,0,4,15,10,20,34,65},{0,0,0,0,0,1,1,4,1,1,5,10,5,6,15,14,19,45},{0,0,0,0,0,0,1,0,0,1,4,0,1,5,4,10,15,34},{0,T^3,0,T^3,0,0,0,1,0,T^3,1,4,1,1,5,5,6,19},{0,0,0,0,0,0,0,0,1,1,0,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,4,5,15},{T^3,5*T^3,0,5*T^3,T^3,0,0,0,T^3,5*T^3,0,1,0,T^3,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,T^3,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,47)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}-1 & 0 & -1 & 0 & -1 & 0 & -1 & -1 & 0 & -1 & 0 & 0 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 6}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{2, 4}, {3, 4, 6}, {3, 5, 6}, {0, 1, 2, 7}, {0, 1, 5, 7}}
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},{2,3,6},{0,1,4},{0,4,5},{4,5,6},{1,3,6},{1,4,6}},{1,1,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{0,1,1},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{-1,2,6},{0,2,5},{-1,2,5},{0,2,4},{-1,1,5},{0,1,4},{-1,2,4},{-1,1,4},{0,2,3},{-1,2,3},{0,1,3},{0,2,2},{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: {{1,1,4,4,5,6,10,15,10,20,18,20,20,34,40,65,49,75,99,176},{0,1,1,4,1,5,4,5,10,10,15,20,16,15,34,34,39,65,80,145},{0,0,1,1,1,1,4,5,4,10,6,10,6,15,18,34,20,40,49,99},{0,0,0,1,0,1,1,1,4,4,5,10,5,5,15,15,16,34,39,80},{0,0,0,0,1,1,0,4,0,0,4,0,6,10,10,20,18,20,40,75},{0,0,0,0,0,1,0,1,0,0,4,0,5,4,10,10,15,20,34,65},{0,0,0,0,0,0,1,1,1,4,1,4,1,5,6,15,6,18,20,49},{0,0,0,0,0,0,0,1,0,0,1,0,1,4,4,10,6,10,18,40},{0,0,0,0,T^3,0,0,0,1,1,1,4,1+T^3,1,5,5,5,15,16,39},{0,0,0,0,T^3,0,0,0,0,1,0,1,T^3,1,1,5,1,6,6,20},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,5,10,15,34},{T^3,0,0,0,5*T^3,T^3,0,T^3,0,0,0,1,5*T^3,0,1,1,1+T^3,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,1,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,50)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 4 & 3 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}, {0, 0, 1, 1, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {0, 1, 6}, {2, 3, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (23): {{1,4,4},{1,3,4},{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: {{1,3,3,6,6,9,18,18,30,30,36,37,60,60,63,100,63,96,96,109,168,168,261},{0,1,0,3,0,3,9,6,18,10,18,18,30,36,37,60,30,63,45,63,109,96,168},{0,0,1,0,3,3,6,9,10,18,18,18,36,30,30,60,37,45,63,63,96,109,168},{0,0,0,1,0,0,3,0,9,0,6,6,10,18,18,30,10,37,15,30,63,45,96},{0,0,0,0,1,0,0,3,0,9,6,6,18,10,10,30,18,15,37,30,45,63,96},{0,0,0,0,0,1,3,3,6,6,9,9,18,18,18,36,18,30,30,37,63,63,109},{0,0,0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,10,18,37,30,63},{0,0,0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,18,18,30,37,63},{0,0,T^2,0,3*T^2,0,0,0,1,0,0,0,0,3,3,6,T^2,9,3*T^2,6,18,10,30},{0,T^2,0,3*T^2,0,0,0,0,0,1,0,0,3,0,T^2,6,3,3*T^2,9,6,10,18,30},{0,0,0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,9,18,18,37},{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,T^2,0,0,0,0,0,0,0,0,1,0,0,3,1,T^2,3,3,6,9,18},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,1,1,3,0,3,T^2,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,1,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,93)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 2 & 2 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {0, 0, 1, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4, 5}, {2, 6}, {0, 1, 7}}
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},{1,1,2},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (22): {{2,3,6},{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: {{1,2,3,6,6,12,10,14,20,22,26,42,42,69,62,72,103,102,112,162,162,238},{0,1,0,3,0,6,0,6,10,14,10,26,15,42,21,42,62,72,62,112,86,162},{0,0,1,2,3,6,6,6,12,9,14,22,26,42,42,42,69,58,72,102,112,162},{0,0,0,1,0,3,0,3,6,6,6,14,10,26,15,26,42,42,42,72,62,112},{0,0,0,0,1,2,3,2,6,3,6,9,14,22,26,22,42,30,42,58,72,102},{0,0,0,0,0,1,0,1,3,2,3,6,6,14,10,14,26,22,26,42,42,72},{T^2,2*T^2,0,0,0,0,1,2*T^2,2,4*T^2,2,3,6,9,14,9+3*T^2,22,12+6*T^2,22,30,42,58},{0,0,0,0,0,0,0,1,0,2,3,6,6,12,10,14,20,22,26,42,42,69},{0,T^2,0,0,0,0,0,0,1,2*T^2,1,2,3,6,6,6,14,9+3*T^2,14,22,26,42},{0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,6,10,14,10,26,15,42},{0,0,0,0,0,0,0,0,0,0,1,2,3,6,6,6,12,9,14,22,26,42},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,6,14,10,26},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,2,6,3,6,9,14,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,6,6,14},{0,0,0,0,0,0,0,T^2,0,2*T^2,0,0,0,0,1,2*T^2,2,4*T^2,2,3,6,9},{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,T^2,0,0,0,0,0,0,1,2*T^2,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{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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$(5,121)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 6 & 5 & 6 & 4 & 5 & 3 & 4 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{2, 4}, {3, 5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{0,1,3},{2,3,4},{1,3,4}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{-1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,6},{1,2,5},{0,2,6},{1,2,4},{0,2,5},{1,2,3},{1,1,4},{0,2,4},{1,1,3},{0,1,4},{0,2,3},{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: {{1,3,2,6,6,10,9,12,19,17,20,33,35,51,39,60,69,69,92,109,119,185},{0,1,0,3,2,6,3,6,9,6,12,19,17,33,19,35,39,35,60,69,69,119},{0,0,1,0,3,0,1,6,3,9,10,6,19,10,9,33,19,39,51,33,69,109},{0,0,0,1,0,3,1,2,3,2,6,9,6,19,9,17,19,17,35,39,35,69},{0,0,0,0,1,0,0,3,1,3,6,3,9,6,3,19,9,19,33,19,39,69},{T^2,0,2*T^2,0,0,1,3*T^2,0,1,5*T^2,2,3,2,9,3+6*T^2,6,9,6+9*T^2,17,19,17,35},{0,0,0,0,0,0,1,0,3,2,0,6,6,10,9,12,19,17,20,33,35,60},{0,0,0,0,0,0,0,1,0,1,3,1,3,3,1,9,3,9,19,9,19,39},{0,0,0,0,0,0,0,0,1,0,0,3,2,6,3,6,9,6,12,19,17,35},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,1,6,3,9,10,6,19,33},{0,0,T^2,0,0,0,T^2,0,0,3*T^2,1,0,1,1,3*T^2,3,1,3+6*T^2,9,3,9,19},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,3,2,6,9,6,17},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,3,6,3,9,19},{0,0,0,0,0,0,T^2,0,0,2*T^2,0,0,0,1,3*T^2,0,1,5*T^2,2,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,T^2,0,0,3*T^2,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,122)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 4 & 0 & 2 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 10 & 9 & 8 & 8 & 7 & 7 & 6 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, -2, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4}, {2, 5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,2,4}},{{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},{1,2,4},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (27): {{1,4,10},{1,4,9},{1,4,8},{1,3,8},{1,4,7},{1,3,7},{1,3,6},{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: {{1,3,6,8,10,16,27,30,41,31,50,53,76,80,108,82,118,120,88,136,170,197,230,205,271,295,406},{0,1,3,3,6,8,16,16,27,16,30,31,50,50,76,53,82,80,53,88,120,136,170,136,197,205,295},{0,0,1,1,3,3,8,8,16,8,16,16,30,30,50,31,53,50,31,53,80,88,120,88,136,136,205},{0,0,0,1,0,3,6,8,10,8,16,16,27,30,41,27,41,50,31,53,76,82,108,88,118,136,197},{T^2,0,0,2*T^2,1,1,3,3+3*T^2,8,3+4*T^2,8,8,16,16+4*T^2,30,16,31,30,16+6*T^2,31,50,53,80,53+8*T^2,88,88,136},{0,0,0,0,0,1,3,3,6,3,8,8,16,16,27,16,27,30,16,31,50,53,76,53,82,88,136},{0,0,0,0,0,0,1,1,3,1,3,3,8,8,16,8,16,16,8,16,30,31,50,31,53,53,88},{0,0,0,0,0,0,0,1,0,1,3,3,6,8,10,6,10,16,8,16,27,27,41,31,41,53,82},{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+4*T^2,8,16,16,30,16+6*T^2,31,31,53},{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},{0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,8,3,8,16,16,27,16,27,31,53},{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},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,1,3,8,8,16,8,16,16,31},{0,0,T^2,0,3*T^2,0,0,0,0,0,0,0,0,1,0,T^2,3*T^2,3,1,3,6,6,10,8,10,16,27},{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+4*T^2,8,8,16},{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,T^2,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3+3*T^2,8,8,16},{T^4,0,0,0,T^2,0,0,0,0,T^4,0,0,0,0,0,0,T^2,1,0,1,3,3,6,3,6,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,8,10,16,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,8,16},{3*T^4,T^4,0,0,0,0,0,0,0,3*T^4,0,T^4,0,0,0,0,0,0,0,0,1,1,3,1,3,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,8},{6*T^4,3*T^4,T^4,0,0,0,0,0,0,6*T^4,0,3*T^4,0,T^2,0,T^4,0,0,T^2,0,0,0,1,2*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,137)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & 0 & 2 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, -1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{1,1,2}},{{2,3,4},{0,2,4},{0,1,4},{1,3,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,2},{1,1,2},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (23): {{2,3,8},{2,3,7},{2,3,6},{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: {{1,3,6,7,10,9,13,19,21,33,31,36,51,39,60,69,91,109,129,115,159,177,255},{0,1,3,3,6,3,7,9,13,19,21,19,33,19,36,39,60,69,91,69,109,115,177},{0,0,1,1,3,1,3,3,7,9,13,9,19,9,19,19,36,39,60,39,69,69,115},{0,0,0,1,0,1,3,3,6,6,10,9,10,9,19,19,33,33,51,39,51,69,109},{T^2,0,0,T^2,1,3*T^2,1,1,3,3,7,3+3*T^2,9,3+6*T^2,9,9,19,19,36,19+6*T^2,39,39,69},{0,0,0,0,0,1,0,3,0,6,0,7,10,9,13,19,21,33,31,36,51,60,91},{0,0,0,0,0,0,1,1,3,3,6,3,6,3,9,9,19,19,33,19,33,39,69},{0,0,0,0,0,0,0,1,0,3,0,3,6,3,7,9,13,19,21,19,33,36,60},{0,0,0,0,0,0,0,0,1,1,3,1,3,1,3,3,9,9,19,9,19,19,39},{0,0,0,0,0,0,0,0,0,1,0,1,3,1,3,3,7,9,13,9,19,19,36},{0,0,0,T^2,0,T^2,0,0,0,0,1,3*T^2,1,3*T^2,1,1,3,3,9,3+6*T^2,9,9,19},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,6,10,9,10,19,33},{0,0,0,0,0,T^2,0,0,0,0,0,T^2,1,3*T^2,1,1,3,3,7,3+3*T^2,9,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,0,7,10,13,21},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,6,3,6,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,7,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,9},{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,T^2,0,T^2,0,0,0,0,1,3*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,140)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 0 & 2 & 1 & 3 & 2 & 0 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 2 & 1 & 0 & 0 & 2 & 1 & 0 \\ 4 & 4 & 3 & 4 & 4 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {0, -1, 1, 1, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {2, 3, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,-1,1},{1,1,2},{1,0,3}},{{1,2,4},{0,3,5},{0,4,5},{0,1,4},{2,3,5},{2,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{0,-1,1},{0,1,0},{0,1,0},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (25): {{1,3,4},{1,2,4},{1,3,3},{1,1,4},{1,0,4},{1,2,3},{1,1,3},{1,3,2},{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: {{1,3,5,6,10,12,22,15,31,35,32,35,53,56,65,81,87,105,70,117,155,177,135,216,318},{0,1,1,3,6,5,12,5,15,22,15,15,31,32,35,53,56,65,36,70,105,117,75,135,216},{0,0,1,0,0,3,6,5,12,10,12,15,22,22,31,35,35,53,32,56,81,87,70,117,177},{0,0,0,1,3,1,5,1,5,12,5,5,15,15,15,31,32,35,15,36,65,70,36,75,135},{T^2,0,2*T^2,0,1,0,1,3*T^2,1,5,1+T^2,1+4*T^2,5,5,5,15,15,15,5+2*T^2,15,35,36,15+3*T^2,36,75},{0,0,0,0,0,1,3,1,5,6,5,5,12,12,15,22,22,31,15,32,53,56,36,70,117},{0,0,0,0,0,0,1,0,1,3,1,1,5,5,5,12,12,15,5,15,31,32,15,36,70},{0,0,0,0,0,0,0,1,3,0,3,5,6,6,12,10,10,22,12,22,35,35,32,56,87},{0,0,0,0,0,0,0,0,1,0,1,1,3,3,5,6,6,12,5,12,22,22,15,32,56},{0,0,T^2,0,0,0,0,2*T^2,0,1,0,3*T^2,1,1,1,5,5,5,1+T^2,5,15,15,5+2*T^2,15,36},{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,T^2,0,3*T^2,6*T^2,0,0,0,0,0,0,1,0,T^2,3,0,3*T^2,6,3,6,10,10,12,22,35},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,5,1,5,12,12,5,15,32},{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,T^2,3*T^2,0,0,0,0,0,0,0,0,0,1,0,T^2,3,1,3,6,6,5,12,22},{0,0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,1,1,1,0,1,5,5,1+T^2,5,15},{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},{T^4,0,0,0,T^2,0,0,0,0,0,T^4,0,0,0,0,0,0,1,0,1,3,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,5,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,5,12},{3*T^4,T^4,0,0,0,0,0,0,0,0,3*T^4,T^2,0,T^4,0,0,0,0,0,0,1,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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}}
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$(5,161)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, -1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,6},{0,2,6},{1,2,5},{0,2,5},{1,2,4},{1,1,4},{0,2,4},{0,1,4},{1,2,3},{0,2,3},{1,1,3},{0,1,3},{1,1,2},{1,0,2},{0,1,2},{0,0,2},{1,1,1},{0,1,1},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,4,7,10,12,16,20,20,30,28,44,55,58,82,88,96,137,108,158,184,260},{0,1,1,4,4,4,10,12,10,20,12,28,28,28,55,58,55,96,58,108,108,184},{0,0,1,2,4,4,7,7,10,16,12,20,28,28,44,44,55,82,58,88,108,158},{0,0,0,1,1,1,4,4,4,10,4,12,12,12,28,28,28,55,28,58,58,108},{0,0,0,0,1,1,2,2,4,7,4,7,12,12,20,20,28,44,28,44,58,88},{0,0,0,0,0,1,0,2,0,0,4,7,10,12,16,20,20,30,28,44,55,82},{0,0,0,0,0,0,1,1,1,4,1,4,4,4,12,12,12,28,12,28,28,58},{0,0,0,0,0,0,0,1,0,0,1,4,4,4,10,12,10,20,12,28,28,55},{0,T^2,0,0,0,0,0,2*T^2,1,2,1,2,4,4,7,7+3*T^2,12,20,12,20,28,44},{T^3,0,0,0,0,2*T^3,0,0,0,1,0,1,1,1+3*T^3,4,4,4,12,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,1,2,4,4,7,7,10,16,12,20,28,44},{0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,10,4,12,12,28},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,4,7,4,7,12,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,4,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,1,4,4,12},{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,T^2,0,0,0,0,0,0,0,2*T^2,1,2,1,2,4,7},{0,0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,1,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{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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$(5,188)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & -1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 3 & 1 & 2 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 0, 0, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}}
Primitive collections: {{1, 2, 3, 5}, {4, 6}, {2, 3, 5, 6}, {0, 1, 7}, {0, 4, 7}}
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},{0,1,2},{0,1,4},{3,4,5}},{4,1,2})
Cox degrees: {{0,0,1},{1,-1,-1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (21): {{3,0,2},{2,1,3},{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: {{1,1,3,3,6,6,6,6,15,15,21,28,21,28,46,46,56,81,81,111,186},{0,1,1,3,3,3,6,6,9,15,15,19,21,28,34,46,46,63,81,91,156},{0,0,1,1,1,3,1,3,6,6,6,15,6,15,21,21,21,46,46,56,111},{0,0,0,1,1,1,1,3,3,6,6,9,6,15,15,21,21,34,46,46,91},{0,0,0,0,1,0,1,0,3,3,6,6,6,6,15,15,21,28,28,46,81},{0,0,0,0,0,1,0,1,1,1,1,6,1,6,6,6,6,21,21,21,56},{0,0,0,0,0,0,1,0,1,3,3,3,6,6,9,15,15,19,28,34,63},{T^2,0,0,0,3*T^2,0,0,1,1,1,1+6*T^2,3,1,6,6,6,6+10*T^2,15,21,21,46},{0,0,0,0,0,0,0,0,1,1,1,3,1,3,6,6,6,15,15,21,46},{0,0,0,0,0,0,0,0,0,1,1,1,1,3,3,6,6,9,15,15,34},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,3,6,9,19},{0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,0,1,1,1,1+6*T^2,3,6,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,3*T^2,0,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,189)$ |
3 |
18 |
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8: $\begin{pmatrix}-1 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 2 & 0 & 1 & -1 & 0 & 2 & -1 & 1 & 0 & 2 & 1 & -1 & 0 & 1 & 2 & -1 & 0 & 1 & 2 & 0 & -1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {-1, -1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,1,4},{2,1,3},{0,1,4},{1,1,3},{-1,1,4},{0,1,3},{2,1,2},{-1,1,3},{1,1,2},{0,1,2},{2,1,1},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{-1,0,2},{0,1,1},{1,0,1},{2,0,0},{0,0,1},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,3,7,6,15,11,26,25,45,35,26,71,48,65,37,77,105,72,96,120,181,165,255},{0,1,0,3,0,6,7,10,15,26,25,15,40,26,45,26,40,71,48,72,77,113,120,181},{0,0,1,2,3,7,3,15,11,25,15,11,45,26,35,15,48,65,37,48,72,120,96,165},{0,0,0,1,0,3,2,6,7,15,11,7,26,15,25,11,26,45,26,37,48,77,72,120},{0,T^2,0,0,1,2,T^2,7,3,11,4+T^2,3,25,11,15,4+2*T^2,26,35,15,19+2*T^2,37,72,48,96},{0,0,0,0,0,1,0,3,2,7,3,2,15,7,11,3,15,25,11,15,26,48,37,72},{0,0,0,0,0,0,1,0,3,6,7,3,10,6,15,7,10,26,15,26,26,40,48,77},{0,T^2,0,0,0,0,T^2,1,0,2,T^2,0,7,2,3,2*T^2,7,11,3,4+2*T^2,11,26,15,37},{0,0,0,0,0,0,0,0,1,3,2,1,6,3,7,2,6,15,7,11,15,26,26,48},{0,0,0,0,0,0,0,0,0,1,0,0,3,1,2,0,3,7,2,3,7,15,11,26},{0,0,T^2,0,3*T^2,0,0,0,0,0,1,0,0,T^2,3,1,3*T^2,6,3,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,2,6,0,7,11,15,26,25,45},{0,0,0,0,0,0,T^2,0,0,0,T^2,0,1,0,0,T^2,1,2,0,2*T^2,2,7,3,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,2,3,7,15,11,25},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,T^2,3,1,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,7,6,10,15,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,1,0,0,T^2,2,7,3,11},{T^4,0,0,0,0,0,0,0,0,0,0,T^4,0,0,0,0,0,1,0,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6,7,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,1,0,2},{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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$(5,193)$ |
3 |
20 |
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8: $\begin{pmatrix}1 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ -1 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ -1 & -1 & 2 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
27: $\begin{pmatrix}2 & 1 & 3 & 0 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & -1 & 0 & -1 & 1 & 0 \\ 0 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 0 & 2 & 1 & -1 & 1 & 0 & 2 & 1 & -1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & 1 & -1 & 0 \\ 2 & 3 & 0 & 4 & 1 & -1 & 2 & 2 & 0 & 3 & 3 & 0 & 1 & 1 & 4 & 2 & -1 & 2 & 3 & 0 & 0 & 1 & 3 & 1 & 2 & -1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-1, -1, 1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (20): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{0, 1, 3, 5}, {2, 4, 6}, {3, 5, 6}, {0, 1, 7}, {2, 4, 7}}
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},{0,1,4},{1,4,5}},{4,1,2})
Cox degrees: {{1,-1,-1},{1,-1,-1},{-1,1,2},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (27): {{2,0,2},{1,1,3},{3,-1,0},{0,2,4},{2,0,1},{3,-1,-1},{1,1,2},{1,0,2},{2,0,0},{0,2,3},{0,1,3},{2,-1,0},{1,1,1},{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: {{1,2,2,3,5,8,8,10,14,11,15,18,20,30,20,42,46,45,54,68,74,90,60,105,136,154,207},{0,1,0,2,2,3,5,5,8,8,10,8,14,18,15,30,26,30,42,46,46,68,45,74,105,104,154},{0,0,1,2*T^2,2,5,3,3,8,4+2*T^2,4,10,11,15,5+3*T^2,20,30,20,25+3*T^2,42,45,54,25,60,75,105,136},{0,0,0,1,0,0,2,2,3,5,5,3,8,8,10,18,11,18,30,26,26,46,30,46,74,62,104},{0,0,0,0,1,2,2,2,5,3,3,5,8,10,4,15,18,15,20,30,30,42,20,45,60,74,105},{0,0,0,2*T^2,0,1,0,0,2,2*T^2,0,2,3,3,3*T^2,4,10,4,5+3*T^2,15,15,20,5,20,25,45,60},{0,0,0,0,0,0,1,1,2,2,2,2,5,5,3,10,8,10,15,18,18,30,15,30,45,46,74},{0,0,0,0,0,0,0,1,0,0,2,2,0,5,3,8,8,10,11,14,18,20,15,30,42,46,68},{0,0,0,0,0,0,0,0,1,0,0,1,2,2,0,3,5,3,4,10,10,15,4,15,20,30,45},{T^2,0,2*T^2,0,0,0,0,2*T^2,0,1,1,4*T^2,2,2,2,5,3,5+3*T^2,10,8,8+6*T^2,18,10,18,30,26,46},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,5,3,5,8,8,8,14,10,18,30,26,46},{0,0,0,T^2,0,0,0,0,0,T^2,0,1,0,2,2*T^2,3,5,3,4+2*T^2,8,10,11,4,15,20,30,42},{0,0,T^2,0,0,0,0,0,0,0,0,2*T^2,1,1,0,2,2,2,3,5,5+3*T^2,10,3,10,15,18,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,2,3,5,5,8,3,10,15,18,30},{0,0,T^3,0,0,T^3,0,0,0,0,0,0,0,0,1,2,0,2,5,3,3,8,5,8,18,11,26},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,5,2,5,10,8,18},{0,0,0,T^2,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,1,0,2*T^2,2,2,3,0,3,4,10,15},{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^3,0,0,T^3,0,T^2,0,0,0,2*T^2,0,0,0,0,0,2*T^2,1,0,4*T^2,2,1,2,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,2,3,5,10},{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,T^2,0,0,0,0,0,0,0,0,2*T^2,1,0,1,2,2,5},{0,0,T^3,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,5,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,5},{0,0,T^3,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,194)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {0, 0, 1, 1, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {2, 3, 6}, {0, 1, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (21): {{1,3,4},{1,2,4},{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: {{1,3,3,6,9,6,18,10,18,19,30,36,39,60,33,66,51,69,118,108,186},{0,1,0,3,3,0,9,0,6,6,10,18,19,30,10,39,15,33,69,51,108},{0,0,1,0,3,3,6,6,9,9,18,18,18,36,19,30,33,39,66,69,118},{0,0,0,1,0,0,3,0,0,0,0,6,6,10,0,19,0,10,33,15,51},{0,0,0,0,1,0,3,0,3,3,6,9,9,18,6,18,10,19,39,33,69},{0,0,0,0,0,1,0,3,3,3,9,6,6,18,9,10,19,18,30,39,66},{0,0,0,0,0,0,1,0,0,0,0,3,3,6,0,9,0,6,19,10,33},{T^2,3*T^2,0,6*T^2,0,0,0,1,0,T^2,3,0,3*T^2,6,3,6*T^2,9,6,10,18,30},{0,0,0,0,0,0,0,0,1,1,3,3,3,9,3,6,6,9,18,19,39},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,36},{0,T^2,0,3*T^2,0,0,0,0,0,0,1,0,T^2,3,1,3*T^2,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,3,0,3,9,6,19},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,0,T^2,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,197)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 2 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 6 & 5 & 6 & 5 & 5 & 4 & 4 & 3 & 4 & 3 & 3 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{1,0,0},{0,1,2},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (23): {{1,3,8},{1,3,7},{1,3,6},{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: {{1,3,6,8,10,9,16,19,27,30,41,33,51,50,38,66,76,103,108,110,149,170,246},{0,1,3,3,6,3,8,9,16,16,27,19,33,30,19,38,50,66,76,66,103,110,170},{0,0,1,1,3,1,3,3,8,8,16,9,19,16,9,19,30,38,50,38,66,66,110},{0,0,0,1,0,1,3,3,6,8,10,6,10,16,9,19,27,33,41,38,51,66,103},{T^2,0,0,2*T^2,1,3*T^2,1,1,3,3+3*T^2,8,3,9,8,3+5*T^2,9,16,19,30,19+7*T^2,38,38,66},{0,0,0,0,0,1,0,3,0,0,0,6,10,0,8,16,0,27,0,30,41,50,76},{0,0,0,0,0,0,1,1,3,3,6,3,6,8,3,9,16,19,27,19,33,38,66},{0,0,0,0,0,0,0,1,0,0,0,3,6,0,3,8,0,16,0,16,27,30,50},{0,0,0,0,0,0,0,0,1,1,3,1,3,3,1,3,8,9,16,9,19,19,38},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,1,3,6,6,10,9,10,19,33},{0,0,0,T^2,0,T^2,0,0,0,2*T^2,1,0,1,1,3*T^2,1,3,3,8,3+5*T^2,9,9,19},{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,T^2,0,0,0,0,0,0,1,0,2*T^2,1,0,3,0,3+3*T^2,8,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,3,6,9,19},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,6,0,8,10,16,27},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,3,9},{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,T^2,0,0,0,0,T^2,0,0,0,1,3*T^2,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,198)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 2 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 6 & 6 & 5 & 4 & 5 & 4 & 4 & 3 & 3 & 3 & 4 & 2 & 3 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (22): {{1,2,6},{0,2,6},{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},{1,1,2},{0,1,3},{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: {{1,2,3,6,6,12,8,10,20,16,16,27,32,54,30,41,82,60,50,100,76,152},{0,1,0,0,3,6,0,0,10,0,8,0,16,27,0,0,41,30,0,50,0,76},{0,0,1,3,2,6,3,6,12,8,6,16,16,32,16,27,54,32,30,60,50,100},{0,0,0,1,0,2,1,3,6,3,2,8,6,16,8,16,32,16,16,32,30,60},{0,0,0,0,1,3,0,0,6,0,3,0,8,16,0,0,27,16,0,30,0,50},{0,0,0,0,0,1,0,0,3,0,1,0,3,8,0,0,16,8,0,16,0,30},{0,0,0,0,0,0,1,0,0,3,2,6,6,12,8,10,20,16,16,32,27,54},{T^2,2*T^2,0,0,0,0,2*T^2,1,2,1,4*T^2,3,2,6,3+3*T^2,8,16,6+6*T^2,8,16,16,32},{0,T^2,0,0,0,0,0,0,1,0,2*T^2,0,1,3,0,0,8,3+3*T^2,0,8,0,16},{0,0,0,0,0,0,0,0,0,1,0,3,2,6,3,6,12,6,8,16,16,32},{0,0,0,0,0,0,0,0,0,0,1,0,3,6,0,0,10,8,0,16,0,27},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,3,6,2,3,6,8,16},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,6,3,0,8,0,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,3,0,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,6,12},{0,0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,2*T^2,1,2,4*T^2,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2*T^2,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{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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$(5,199)$ |
3 |
18 |
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|
8: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 2 & 0 & 2 & 1 & 2 & 1 & 0 & 0 & 1 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, -1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{0,2,4},{2,3,4},{0,1,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{1,0,0},{0,1,2},{0,1,0},{0,0,1}}
Theta-collection (21): {{2,1,4},{1,1,4},{2,1,3},{0,1,4},{1,1,3},{0,1,3},{2,1,2},{1,1,2},{2,0,2},{0,1,2},{2,1,1},{1,0,2},{2,0,1},{1,1,1},{0,0,2},{0,1,1},{1,0,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,5,6,12,22,15,31,16,53,35,34,40,65,59,105,77,127,85,151,238},{0,1,1,3,5,12,5,15,5,31,15,16,16,35,34,65,40,77,40,85,151},{0,0,1,0,3,6,5,12,5,22,15,12,16,31,22,53,34,59,40,77,127},{0,0,0,1,1,5,1,5,1,15,5,5,5,15,16,35,16,40,16,40,85},{0,0,0,0,1,3,1,5,1,12,5,5,5,15,12,31,16,34,16,40,77},{0,0,0,0,0,1,0,1,0,5,1,1,1,5,5,15,5,16,5,16,40},{0,0,0,0,0,0,1,3,1,6,5,3,5,12,6,22,12,22,16,34,59},{0,0,0,0,0,0,0,1,0,3,1,1,1,5,3,12,5,12,5,16,34},{0,0,0,0,0,0,0,0,1,0,0,3,5,0,6,0,12,22,15,31,53},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,1,5,1,5,16},{0,T^2,0,3*T^2,0,0,0,0,0,0,1,T^2,1,3,3*T^2,6,3,6,5,12,22},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,3,0,5,12,5,15,31},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6,5,12,22},{0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,T^2,3,1,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5,1,5,15},{T^4,0,0,0,0,0,0,0,T^4,0,0,0,0,0,0,1,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,1,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,200)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 2 & 2 & 0 & 2 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 2 & 4 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (21): {{2,1,4},{1,1,4},{2,1,3},{1,1,3},{2,1,2},{0,1,4},{0,1,3},{1,1,2},{2,0,2},{2,1,1},{0,1,2},{2,0,1},{1,1,1},{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: {{1,3,3,9,6,6,18,18,7,10,36,13,30,21,42,60,21,39,78,63,126},{0,1,0,3,0,3,9,6,0,0,18,0,10,7,21,30,0,13,39,21,63},{0,0,1,3,3,0,6,9,3,6,18,7,18,9,18,36,13,21,42,39,78},{0,0,0,1,0,0,3,3,0,0,9,0,6,3,9,18,0,7,21,13,39},{0,0,0,0,1,0,0,3,1,3,6,3,9,3,6,18,7,9,18,21,42},{0,0,0,0,0,1,3,0,0,0,6,0,0,0,7,10,0,0,13,0,21},{0,0,0,0,0,0,1,0,0,0,3,0,0,0,3,6,0,0,7,0,13},{0,0,0,0,0,0,0,1,0,0,3,0,3,1,3,9,0,3,9,7,21},{0,0,0,0,0,0,0,0,1,0,0,3,0,3,6,0,6,9,18,18,36},{T^2,3*T^2,0,0,0,6*T^2,0,0,T^2,1,0,1,3,3*T^2,6*T^2,6,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,0,3,0,7},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,6,9,18},{0,T^2,0,0,0,3*T^2,0,0,0,0,0,0,1,T^2,3*T^2,3,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,3,9,6,18},{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,T^2,0,0,0,0,0,0,0,0,T^2,1,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,202)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}1 & 2 & 0 & 1 & -1 & 0 & 2 & 2 & -1 & 1 & 0 & 2 & 1 & -1 & 0 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 4 & 3 & 2 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, -1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3, 5}, {4, 6}, {0, 1, 7}}
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},{1,4,5},{1,3,5},{0,1,4},{2,4,5}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (23): {{1,1,4},{2,1,3},{0,1,4},{1,1,3},{-1,1,4},{0,1,3},{2,1,2},{2,0,2},{-1,1,3},{1,1,2},{0,1,2},{2,1,1},{1,0,2},{-1,1,2},{0,0,2},{1,1,1},{2,0,1},{0,1,1},{1,0,1},{2,0,0},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,1,3,5,6,12,5,6,22,15,31,15,18,53,37,35,20,65,47,50,87,101,173},{0,1,0,3,0,6,5,5,10,12,22,15,12,35,22,31,18,53,37,47,63,87,140},{0,0,1,1,3,5,1,1,12,5,15,5,6,31,18,15,6,35,20,20,47,50,101},{0,0,0,1,0,3,1,1,6,5,12,5,5,22,12,15,6,31,18,20,37,47,87},{0,2*T^2,0,0,1,1,3*T^2,3*T^2,5,1,5,1+4*T^2,1,15,6,5,1+4*T^2,15,6,6+5*T^2,20,20,50},{0,0,0,0,0,1,0,0,3,1,5,1,1,12,5,5,1,15,6,6,18,20,47},{0,0,0,0,0,0,1,1,0,3,6,5,3,10,6,12,5,22,12,18,22,37,63},{0,0,0,0,0,0,0,1,0,0,0,0,3,0,6,0,5,0,12,15,22,31,53},{0,T^2,0,0,0,0,2*T^2,2*T^2,1,0,1,3*T^2,0,5,1,1,3*T^2,5,1,1+4*T^2,6,6,20},{0,0,0,0,0,0,0,0,0,1,3,1,1,6,3,5,1,12,5,6,12,18,37},{0,0,0,0,0,0,0,0,0,0,1,0,0,3,1,1,0,5,1,1,5,6,18},{T^2,0,3*T^2,0,6*T^2,0,0,T^2,0,0,0,1,3*T^2,0,6*T^2,3,1,6,3,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,0,5,5,12,15,31},{0,0,0,0,0,0,T^2,T^2,0,0,0,2*T^2,0,1,0,0,2*T^2,1,0,3*T^2,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,5,5,15},{0,0,T^2,0,3*T^2,0,0,0,0,0,0,0,T^2,0,3*T^2,1,0,3,1,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,5,6,12,22},{0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,203)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 2 & 1 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 4 & 2 & 1 & 2 & 3 & 1 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3, 5}, {4, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,2},{-1,1,2}},{{0,2,3},{2,3,4},{1,3,4},{0,1,3}},{3,2,2})
Cox degrees: {{0,0,1},{0,0,1},{1,0,0},{1,0,0},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (21): {{2,1,4},{2,1,3},{1,1,4},{2,1,2},{1,1,3},{0,1,4},{2,0,2},{2,1,1},{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: {{1,3,3,6,9,6,9,10,18,18,19,30,24,36,33,48,46,60,81,90,150},{0,1,0,3,3,0,3,6,9,6,9,18,9,18,19,24,18,36,48,46,90},{0,0,1,0,3,3,1,0,6,9,3,10,9,18,6,19,24,30,33,48,81},{0,0,0,1,0,0,1,3,3,0,3,9,3,6,9,9,6,18,24,18,46},{0,0,0,0,1,0,0,0,3,3,1,6,3,9,3,9,9,18,19,24,48},{0,0,0,0,0,1,0,0,0,3,0,0,1,6,0,3,9,10,6,19,33},{0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,9,6,0,18,18,36},{T^2,0,3*T^2,0,0,6*T^2,3*T^2,1,0,0,1,3,6*T^2,0,3,3,10*T^2,6,9,6,18},{0,0,0,0,0,0,0,0,1,0,0,3,1,3,1,3,3,9,9,9,24},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,1,3,6,3,9,19},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,9,6,18},{0,0,T^2,0,0,3*T^2,T^2,0,0,0,0,1,3*T^2,0,0,1,6*T^2,3,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,0,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,3,9},{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,T^2,0,0,0,0,0,0,T^2,0,0,0,3*T^2,1,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,204)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & -1 & -1 & -1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}-1 & -2 & 0 & -1 & -2 & -2 & 1 & -1 & 0 & -2 & 0 & -1 & 1 & -1 & -2 & 1 & 0 & -2 & 0 & -1 & 1 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 4 & 2 & 2 & 2 & 3 & 3 & 1 & 1 & 2 & 2 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 2}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
Chambers: ({{0,1,0},{2,1,0},{0,0,1},{-1,0,1},{0,1,2}},{{2,3,4},{1,2,4},{0,3,4},{0,1,4}},{0,3,2})
Cox degrees: {{0,0,1},{0,0,1},{-1,0,1},{-1,0,1},{-1,0,1},{2,1,0},{0,1,0},{0,0,1}}
Theta-collection (24): {{-1,1,5},{-2,1,5},{0,1,4},{-1,1,4},{-2,1,4},{-2,1,3},{1,1,3},{-1,1,3},{0,1,3},{-2,0,4},{0,1,2},{-1,1,2},{1,1,2},{-1,0,3},{-2,0,3},{1,1,1},{0,1,1},{-2,0,2},{0,0,2},{-1,0,2},{1,1,0},{-1,0,1},{0,0,1},{0,0,0}}
Ext matrix: {{1,0,3,3,0,0,6,6,9,3,18,10,18,12,9,36,30,18,28,28,60,51,60,105},{0,1,0,3,3,6,0,9,6,3,18,18,10,9,12,30,36,28,18,28,60,60,51,105},{0,0,1,0,0,0,3,0,3,1,6,0,9,3,3,18,10,6,12,9,30,18,28,51},{0,0,0,1,0,0,0,3,3,0,9,6,6,3,3,18,18,9,9,12,36,28,28,60},{0,0,0,0,1,3,0,3,0,1,6,9,0,3,3,10,18,12,6,9,30,28,18,51},{3*T^2,0,6*T^2,0,0,1,10*T^2,0,0,6*T^2,0,3,0,10*T^2,1,0,6,3,15*T^2,3,10,9,6,18},{0,3*T^2,0,0,6*T^2,10*T^2,1,0,0,6*T^2,0,0,3,1,10*T^2,6,0,15*T^2,3,3,10,6,9,18},{0,0,0,0,0,0,0,1,0,0,3,3,0,1,0,6,9,3,3,3,18,12,9,28},{0,0,0,0,0,0,0,0,1,0,3,0,3,0,1,9,6,3,3,3,18,9,12,28},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,0,0,6,6,9,0,18,18,36},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,1,1,0,9,3,3,12},{T^2,0,3*T^2,0,0,0,6*T^2,0,0,3*T^2,0,1,0,6*T^2,0,0,3,0,10*T^2,1,6,3,3,9},{0,T^2,0,0,3*T^2,6*T^2,0,0,0,3*T^2,0,0,1,0,6*T^2,3,0,10*T^2,0,1,6,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,3,0,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,0,9,6,18},{0,0,0,0,T^2,3*T^2,0,0,0,T^2,0,0,0,0,3*T^2,1,0,6*T^2,0,0,3,1,0,3},{0,0,T^2,0,0,0,3*T^2,0,0,T^2,0,0,0,3*T^2,0,0,1,0,6*T^2,0,3,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,9},{0,0,0,0,0,T^2,T^2,0,0,0,0,0,0,T^2,T^2,0,0,3*T^2,3*T^2,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,205)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & 1 & -1 & 1 & -1 & 1 & 0 & 0 \\ 0 & -1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & -1 & 2 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
26: $\begin{pmatrix}1 & 2 & 0 & 1 & 0 & 2 & 0 & 1 & 0 & 2 & -1 & 1 & 0 & 1 & -1 & 1 & -1 & 0 & 1 & 0 & -1 & -1 & 0 & 0 & -1 & 0 \\ 1 & 0 & 2 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 2 & 1 & 1 & 0 & 1 & 0 \\ 4 & 2 & 5 & 3 & 4 & 1 & 4 & 2 & 3 & 0 & 5 & 2 & 3 & 1 & 4 & 1 & 4 & 2 & 0 & 2 & 3 & 3 & 1 & 1 & 2 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 1, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -2}}
Cones (20): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}}
Primitive collections: {{1, 3, 5}, {2, 4, 6}, {3, 5, 6}, {0, 1, 7}, {0, 2, 4, 7}}
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},{1,4,5},{0,1,2},{0,2,3},{0,1,4}},{4,1,2})
Cox degrees: {{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 (26): {{1,1,4},{2,0,2},{0,2,5},{1,1,3},{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: {{1,2,1,4,4,7,6,10,10,16,6,14,18,20,18,34,21,40,67,46,40,52,75,96,105,174},{0,1,0,1,1,4,1,4,4,10,1,6,6,10,6,18,6,18,40,21,18,21,40,52,52,105},{0,0,1,2,4,3,4,7,10,10,6,7,14,16,18,22,18,34,50,34,40,46,67,76,96,146},{0,0,0,1,1,2,1,4,4,7,1,4,6,10,6,14,6,18,34,18,18,21,40,46,52,96},{0,0,0,0,1,0,1,2,4,3,1,2,4,7,6,7,6,14,22,14,18,18,34,34,46,76},{0,0,0,0,0,1,0,1,1,4,0,1,1,4,1,6,1,6,18,6,6,6,18,21,21,52},{0,0,0,0,0,0,1,0,0,0,1,2,4,0,4,7,6,10,16,14,10,18,20,34,40,67},{0,0,0,0,0,0,0,1,1,2,0,1,1,4,1,4,1,6,14,6,6,6,18,18,21,46},{T^2,2*T^2,0,0,0,0,2*T^2,0,1,0,0,4*T^2,1,2,1,2,1+3*T^2,4,7,4+6*T^2,6,6,14,14,18,34},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,6,1,1,1,6,6,6,21},{0,3*T^2,0,0,0,4*T^2,0,0,0,5*T^2,1,0,2,0,4,3,4,7,10,7,10,14,16,22,34,50},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,4,1,4,10,6,4,6,10,18,18,40},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,1,4,7,4,4,6,10,14,18,34},{0,T^2,0,0,0,0,0,0,0,0,0,2*T^2,0,1,0,1,0,1,4,1+3*T^2,1,1,6,6,6,18},{0,2*T^2,0,0,0,3*T^2,0,0,0,4*T^2,0,0,0,0,1,0,1,2,3,2,4,4,7,7,14,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,1,1,1,4,6,6,18},{0,2*T^2,0,0,0,3*T^2,0,0,0,4*T^2,0,0,0,0,0,0,1,0,0,2,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,1,1,4,4,6,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,6},{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^2,0,0,0,2*T^2,T^2,0,0,3*T^2,0,2*T^2,0,0,0,0,2*T^2,0,0,4*T^2,1,1,2,2,4,7},{0,T^2,0,0,0,2*T^2,0,0,0,3*T^2,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,2*T^2,0,0,1,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,285)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 3 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {0, 0, 1, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4, 5}, {2, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,1,0},{0,0,1},{1,1,1}},{{1,3,4},{0,3,4},{0,2,4},{1,2,4}},{1,1,1})
Cox degrees: {{0,0,1},{0,0,1},{0,1,0},{1,1,0},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{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: {{1,2,3,3,6,6,5,12,10,17,21,21,36,36,32,62,46,71,81,126},{0,1,0,1,0,3,3,6,3,10,6,10,10,21,21,36,21,46,36,81},{0,0,1,0,3,2,0,6,3,5,10,6,21,17,9,36,21,32,46,71},{0,0,0,1,0,0,2,0,3,6,6,10,10,12,17,20,21,36,36,62},{0,0,0,T^2,1,0,2*T^2,2,0,0,3,T^2,10,5,2*T^2,17,6,9,21,32},{0,0,0,0,0,1,0,3,1,3,3,3,6,10,6,21,10,21,21,46},{0,0,0,0,0,0,1,0,0,3,0,3,0,6,10,10,6,21,10,36},{0,0,0,0,0,0,T^2,1,0,0,1,0,3,3,T^2,10,3,6,10,21},{0,0,0,0,0,0,0,0,1,2,3,3,6,6,5,12,10,17,21,36},{0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,3,10,6,21},{0,0,0,0,0,0,0,0,0,0,1,0,3,2,0,6,3,5,10,17},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,6,6,12},{0,0,0,T^2,0,0,2*T^2,0,0,0,0,T^2,1,0,2*T^2,2,0,0,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,3,3,10},{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,T^2,0,0,0,0,0,0,0,T^2,1,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{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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$(5,320)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 1 & 3 & 2 & 2 & 1 & 3 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 0, 1}, {0, 0, 0, 0, -1}, {0, 0, 0, 1, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{2, 4, 5}, {3, 6}, {0, 1, 7}}
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},{0,2,5},{0,4,5},{0,2,3}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{1,1,1},{0,1,-1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (22): {{2,3,4},{2,3,3},{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: {{1,3,4,6,9,10,11,16,22,25,27,37,49,56,52,78,87,114,102,132,163,240},{0,1,1,3,4,6,4,9,11,16,12,22,27,37,27,49,52,78,57,87,102,163},{0,0,1,0,3,0,3,6,6,10,11,10,22,15,22,37,37,56,52,56,87,132},{0,0,0,1,1,3,1,4,4,9,4,11,12,22,12,27,27,49,28,52,57,102},{0,0,0,0,1,0,1,3,3,6,4,6,11,10,11,22,22,37,27,37,52,87},{T^2,0,T^2,0,0,1,2*T^2,1,1,4,1+2*T^2,4,4,11,4+3*T^2,12,12,27,12+3*T^2,27,28,57},{0,0,0,0,0,0,1,0,3,0,4,6,9,10,11,16,22,25,27,37,49,78},{0,0,0,0,0,0,0,1,1,3,1,3,4,6,4,11,11,22,12,22,27,52},{0,0,0,0,0,0,0,0,1,0,1,3,4,6,4,9,11,16,12,22,27,49},{0,0,T^2,0,0,0,0,0,0,1,2*T^2,1,1,3,1,4,4,11,4+3*T^2,11,12,27},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,3,6,6,10,11,10,22,37},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,4,4,9,4,11,12,27},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,3,6,4,6,11,22},{0,0,0,0,0,0,T^2,0,0,0,T^2,0,0,1,2*T^2,1,1,4,1+2*T^2,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,4,6,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,4,11},{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,T^2,0,0,0,0,0,0,1,2*T^2,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,344)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 4 & 3 & 3 & 2 & 4 & 3 & 2 & 3 & 1 & 2 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, -1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4}, {2, 5, 6}, {0, 1, 7}}
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},{1,5,6},{0,1,6},{1,2,5},{2,3,5},{4,5,6}},{1,2,1})
Cox degrees: {{0,0,1},{0,0,1},{-1,1,0},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (21): {{1,2,4},{0,2,4},{1,2,3},{0,2,3},{1,2,2},{1,1,4},{1,1,3},{0,2,2},{0,1,3},{0,2,1},{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: {{1,1,3,4,6,2,8,9,9,16,18,32,23,13,44,33,38,63,72,78,134},{0,1,0,3,0,1,3,6,8,10,6,10,18,8,32,18,33,32,50,63,103},{0,0,1,1,3,0,2,4,2,9,8,18,9,3,23,13,14,33,44,38,78},{0,0,0,1,0,0,1,3,2,6,3,6,8,2,18,8,13,18,32,33,63},{0,T^2,0,0,1,2*T^2,0,1,2*T^2,4,2,8,2,3*T^2,9,3,3+3*T^2,13,23,14,38},{0,0,0,0,0,1,3,0,4,0,6,10,9,8,16,18,23,32,25,44,72},{0,0,0,0,0,0,1,0,1,0,3,6,4,2,9,8,9,18,16,23,44},{0,0,0,0,0,0,0,1,0,3,1,3,2,0,8,2,3,8,18,13,33},{0,0,0,0,0,0,0,0,1,0,0,0,3,1,6,3,8,6,10,18,32},{0,T^2,0,0,0,T^2,0,0,2*T^2,1,0,1,0,2*T^2,2,0,3*T^2,2,8,3,13},{0,0,0,0,0,0,0,0,0,0,1,3,1,0,4,2,2,8,9,9,23},{0,0,0,0,0,T^2,0,0,T^2,0,0,1,0,2*T^2,1,0,2*T^2,2,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,3,6,8,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,4,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{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,T^2,0,0,0,0,T^2,0,0,2*T^2,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{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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$(5,381)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & -1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 2 & 1 & 2 & 1 & 2 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 3 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, -1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1}},{{0,2,4},{2,3,4},{0,1,4},{1,3,4}},{1,1,2})
Cox degrees: {{0,0,1},{-1,0,1},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,3},{1,1,3},{0,2,3},{0,1,3},{1,2,2},{0,2,2},{1,1,2},{1,2,1},{1,0,2},{0,1,2},{0,2,1},{1,1,1},{0,0,2},{0,1,1},{1,0,1},{0,0,1},{1,1,0},{0,1,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,4,7,9,10,14,16,16,24,25,39,39,64,50,76,84,129},{0,1,0,2,0,0,4,0,9,7,0,10,16,16,24,39,20,30,50,76},{0,0,1,2,1,4,2,4,3,9,10,9,14,24,14,39,24,50,39,84},{0,0,0,1,0,0,1,0,2,4,0,4,9,10,9,24,10,20,24,50},{0,0,0,0,1,2,2,4,3,4,7,9,6,16,14,25,24,39,39,64},{0,0,0,0,0,1,0,1,0,2,4,2,3,9,3,14,9,24,14,39},{0,0,0,0,0,0,1,0,2,2,0,4,4,7,9,16,10,16,24,39},{0,0,0,T^2,0,0,0,1,0,0,2,2,T^2,4,3,6,9,16,14,25},{0,0,0,0,0,0,0,0,1,0,0,0,2,0,4,7,0,0,10,16},{0,0,0,0,0,0,0,0,0,1,0,1,2,4,2,9,4,10,9,24},{0,T^3,0,0,0,0,0,0,T^3,0,1,0,0,2,0,3,2,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,4,4,7,9,16},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4},{0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,0,0,0,1,2,2,4},{0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,1,0,2},{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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$(5,437)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & -1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 3 & 2 & 2 & 1 & 3 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, -1, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{3, 4}, {1, 2, 5, 6}, {2, 4, 5, 6}, {0, 1, 7}, {0, 3, 7}}
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},{3,5,6},{0,4,5},{0,2,5},{0,1,4},{1,3,4}},{2,1,2})
Cox degrees: {{0,0,1},{-1,1,1},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,4},{0,3,4},{0,2,4},{1,2,3},{1,1,3},{0,3,3},{1,2,2},{0,2,3},{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: {{1,1,2,3,6,3,6,8,11,15,18,21,30,28,36,46,59,81,81,146},{0,1,1,1,1,3,3,6,6,6,15,6,21,15,21,21,46,56,46,111},{0,0,1,0,1,0,0,3,6,3,6,6,15,6,21,15,28,46,28,81},{0,0,0,1,1,1,3,2,2,6,8,6,11,15,11,21,30,36,46,81},{0,0,0,0,1,0,0,1,2,3,3,6,8,6,11,15,18,30,28,59},{0,0,0,0,0,1,1,1,1,1,6,1,6,6,6,6,21,21,21,56},{0,0,2*T^2,0,0,0,1,0,3*T^2,1,2,1,2,6,2+4*T^2,6,11,11,21,36},{0,0,0,0,0,0,0,1,1,1,3,1,6,3,6,6,15,21,15,46},{0,0,0,0,0,0,0,0,1,0,0,1,3,0,6,3,6,15,6,28},{0,0,0,0,0,0,0,0,0,1,1,1,2,3,2,6,8,11,15,30},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,3,3,8,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,3,6,3,15},{0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,1,3*T^2,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,443)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 2 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 1 & 1 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 3 & 3 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (20): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 6}, {0, 2, 3, 6, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3}, {2, 3, 4, 6}, {4, 5, 6}, {0, 1, 7}, {0, 5, 7}}
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},{3,5,6},{2,3,6},{0,1,5},{2,4,6},{0,3,5},{1,4,5}},{1,1,1})
Cox degrees: {{0,0,1},{1,0,1},{1,1,1},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (25): {{2,3,4},{2,2,4},{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: {{1,2,2,3,3,5,8,5,8,8,13,14,15,18,22,27,33,29,42,39,57,64,88,82,132},{0,1,0,0,0,2,3,0,3,5,8,8,5,6,7,15,18,9,22,27,29,42,57,40,82},{0,0,1,1,2,2,2,3,5,3,3,8,8,8,15,13,13,18,27,18,33,39,48,57,88},{0,0,0,1,0,0,2,2,0,0,3,0,5,8,8,8,13,15,14,11,27,20,39,42,64},{0,2*T^2,0,0,1,0,0,1,2,2*T^2,3*T^2,3,2,2,8,3,3,8,13,4+3*T^2,13,18,18,33,48},{0,0,0,0,0,1,1,0,2,2,2,5,3,3,5,8,8,6,15,13,18,27,33,29,57},{0,0,0,0,0,0,1,0,0,0,2,0,2,3,3,5,8,5,8,8,15,14,27,22,42},{0,T^2,0,0,0,0,0,1,0,T^2,2*T^2,0,2,2,5,3,3,8,8,4+2*T^2,13,11,18,27,39},{0,0,0,0,0,0,0,0,1,0,0,2,1,1,3,2,2,3,8,3,8,13,13,18,33},{0,0,0,T^2,0,0,0,2*T^2,0,1,1,2,0,T^2,0,3,3,2*T^2,5,8,6,15,18,9,29},{0,0,0,0,T^3,0,0,0,0,0,1,0,0,0,0,2,3,0,3,5,5,8,15,7,22},{0,0,0,0,0,0,0,T^2,0,0,0,1,0,0,0,1,1,T^2,3,2,3,8,8,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,2,3,5,3,8,8,13,15,27},{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,T^2,0,0,0,0,0,0,0,T^2,2*T^2,0,0,0,1,0,0,1,2,2*T^2,2,3,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,2,2,3,5,8,5,15},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,5,3,8},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,T^2,2,0,3,5,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,3,8},{0,0,0,T^2,T^3,0,0,2*T^2,0,0,0,0,0,T^2,0,0,0,2*T^2,0,1,0,2,3,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,5},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,T^2,0,0,0,1,1,0,3},{0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,455)$ |
3 |
18 |
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8: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & -1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}3 & 2 & 3 & 2 & 3 & 3 & 2 & 1 & 3 & 2 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 2 & 0 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 1 & 0 & -1 & 0 & 2 & -1 & 1 & 1 & 0 & 1 & -1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {1, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-1, -1, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 6}, {0, 2, 3, 6, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 6}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{0, 1, 2, 3}, {2, 3, 4, 6}, {4, 5, 6}, {0, 1, 7}, {5, 7}}
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},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (22): {{3,1,1},{2,2,1},{3,0,1},{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: {{1,2,2,6,3,3,10,10,5,8,20,16,14,30,30,24,30,50,50,80,70,120},{0,1,0,2,0,2*T^2,3,6,0,3,10,5,4+3*T^2,14,20,7,16,30,24,50,32,70},{0,0,1,2,1,2,6,3,3,2,10,8,10,20,14,16,13,30,30,44,50,80},{0,0,0,1,0,0,2,2,0,1,6,3,3,10,10,5,8,20,16,30,24,50},{0,0,0,0,1,0,0,0,2,2,0,6,0,0,0,10,10,0,20,30,30,50},{0,2*T^2,0,0,0,1,2,3*T^2,1,0,3,2,6,10,4+4*T^2,8,3,14,13,18,30,44},{0,0,0,0,0,0,1,0,0,0,2,1,2,6,3,3,2,10,8,13,16,30},{0,0,0,0,0,T^2,0,1,0,0,2,0,2*T^2,3,6,0,3,10,5,16,7,24},{0,2*T^2,0,0,0,0,0,3*T^2,1,0,0,2,0,0,4*T^2,6,3,0,10,14,20,30},{0,0,0,0,0,2*T^2,0,0,0,1,0,2,3*T^2,0,0,3,6,0,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,1,6,3,8,5,16},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,2,0,6,10,10,20},{0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,1,2,3*T^2,1,0,3,2,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,2,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,1,0,0,2,0,3,0,5},{0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,0,3*T^2,1,0,0,2,3,6,10},{0,0,0,0,0,T^2,0,0,0,0,0,0,2*T^2,0,0,0,1,0,2,6,3,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{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,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,457)$ |
3 |
18 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 3 & 4 & 2 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-2, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 6}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{0, 1}, {0, 4, 6}, {3, 4, 5, 6}, {1, 2, 7}, {2, 3, 5, 7}}
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},{0,2,5},{1,3,4},{0,1,4},{2,3,5}},{1,1,1})
Cox degrees: {{1,2,1},{1,0,0},{0,0,1},{0,1,1},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{1,5,4},{1,4,4},{1,5,3},{1,3,4},{1,4,3},{1,3,3},{1,4,2},{1,2,3},{0,3,3},{1,3,2},{0,3,2},{1,3,1},{1,2,2},{0,2,3},{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: {{1,2,2,3,6,10,10,14,11,20,22,30,30,16,36,50,40,50,70,60,90,120,135,190},{0,1,0,2,2,6,3,10,6,10,10,14,20,11,22,30,30,36,50,33,60,90,84,135},{0,0,1,T^2,2,3,6,4+2*T^2,3,10,11,20,14,4,16,30,18+3*T^2,21,40,36,50,64,90,120},{0,0,3*T^2,1,0,2,4*T^2,6,2,3,3,4+5*T^2,10,6,10,14,20,22,30,14,33,60,44,84},{0,0,0,0,1,2,2,3,2,6,6,10,10,3,11,20,14,16,30,22,36,50,60,90},{0,0,0,0,0,1,0,2,1,2,2,3,6,2,6,10,10,11,20,10,22,36,33,60},{0,0,0,0,0,0,1,T^2,0,2,2,6,3,0,3,10,4+2*T^2,4,14,11,16,21,36,50},{0,0,2*T^2,0,0,0,3*T^2,1,0,0,0,4*T^2,2,1,2,3,6,6,10,3,10,22,14,33},{0,0,0,0,0,0,0,0,1,0,2,0,0,2,6,0,0,10,0,10,20,30,30,50},{0,0,0,0,0,0,0,0,0,1,1,2,2,0,2,6,3,3,10,6,11,16,22,36},{0,0,0,T^2,0,0,0,2*T^2,0,0,1,0,0,0,2,0,3*T^2,3,0,6,10,14,20,30},{0,0,0,T^3,0,0,0,0,0,0,0,1,0,0,0,2,T^2,0,3,2,3,4,11,16},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,2,6,2,6,11,10,22},{0,0,2*T^2,0,0,0,3*T^2,0,0,0,0,4*T^2,0,1,2,0,0,6,0,3,10,20,14,30},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,2,6,10,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,2,3,6,11},{T^3,0,T^2+2*T^3,0,0,0,2*T^2,0,T^3,0,2*T^3,3*T^2,0,0,0,0,1,1,2,0,2,6,3,10},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,3*T^2,0,0,0,0,0,1,0,0,2,6,3,10},{0,0,T^3,0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,0,1,2,2,6},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,6},{0,0,0,0,0,0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,458)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & -1 & 1 & 0 & 0 & 1\end{pmatrix}$
21: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 3 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 3 & 2 & 3 & 1 & 2 & 0 & 3 & 2 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {0, 0, 1, 1, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {2, 3, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{0,2,5},{1,2,5},{0,2,3},{0,4,5},{1,2,3}},{1,2,1})
Cox degrees: {{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 (21): {{1,3,3},{1,3,2},{1,2,3},{1,3,1},{1,2,2},{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: {{1,3,5,6,12,10,15,13,22,25,31,35,36,41,53,65,81,80,103,136,208},{0,1,1,3,5,6,5,5,12,13,15,22,16,25,31,36,53,40,65,80,136},{0,0,1,0,3,0,5,3,6,6,12,10,13,10,22,25,35,36,41,65,103},{0,0,0,1,1,3,1,1,5,5,5,12,5,13,15,16,31,16,36,40,80},{0,0,0,0,1,0,1,1,3,3,5,6,5,6,12,13,22,16,25,36,65},{T^2,0,2*T^2,0,0,1,3*T^2,T^2,1,1,1,5,1+2*T^2,5,5,5,15,5+3*T^2,16,16,40},{0,0,0,0,0,0,1,0,0,0,3,0,3,0,6,6,10,13,10,25,41},{0,0,0,0,0,0,0,1,0,3,0,0,5,6,0,12,0,15,22,31,53},{0,0,0,0,0,0,0,0,1,1,1,3,1,3,5,5,12,5,13,16,36},{0,0,0,0,0,0,0,0,0,1,0,0,1,3,0,5,0,5,12,15,31},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,3,6,5,6,13,25},{0,0,T^2,0,0,0,2*T^2,0,0,0,0,1,T^2,1,1,1,5,1+2*T^2,5,5,16},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,5,13},{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,T^2,0,0,0,0,0,0,0,0,0,1,T^2,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,462)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,2,4},{0,1,4},{1,3,4}},{1,1,1})
Cox degrees: {{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 (20): {{1,3,4},{1,2,4},{1,3,3},{1,2,3},{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: {{1,2,3,7,6,11,8,15,13,18,26,25,32,45,32,46,60,90,97,150},{0,1,0,3,0,7,3,6,8,6,10,15,18,26,10,32,32,60,50,97},{0,0,1,2,3,3,2,7,3,8,15,11,13,25,18,18,32,46,60,90},{0,0,0,1,0,2,1,3,2,3,6,7,8,15,6,13,18,32,32,60},{0,T^2,0,0,1,T^2,0,2,2*T^2,2,7,3,3,11,8,4+2*T^2,13,18,32,46},{0,0,0,0,0,1,0,0,1,0,0,3,3,6,0,8,6,18,10,32},{0,0,0,0,0,0,1,0,2,3,0,0,7,0,6,11,15,25,26,45},{0,0,0,0,0,0,0,1,0,1,3,2,2,7,3,3,8,13,18,32},{0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,7,6,15,10,26},{0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,3,7,11,15,25},{0,T^2,0,0,0,T^2,0,0,2*T^2,0,1,0,0,2,1,2*T^2,2,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,2,3,8,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,7,6,15},{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,T^2,0,0,0,0,0,1,T^2,2,3,7,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,465)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,3},{1,1,3},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,1,2},{1,2,1},{1,0,2},{0,2,1},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,4,6,7,6,11,12,14,15,22,30,26,25,50,45,52,90},{0,1,0,0,2,0,3,0,7,0,6,6,14,12,10,15,30,26,20,52},{0,0,1,0,2,3,0,0,0,6,7,0,11,15,0,0,25,0,26,45},{0,0,0,1,0,2,2,3,3,6,4,7,6,14,15,11,22,25,30,50},{0,0,0,0,1,0,0,0,0,0,3,0,7,6,0,0,15,0,10,26},{0,0,0,0,0,1,0,0,0,3,2,0,3,7,0,0,11,0,15,25},{0,0,0,0,0,0,1,0,2,0,2,3,4,6,6,7,14,15,12,30},{0,T^2,0,0,2*T^2,0,0,1,T^2,2,0,2,2*T^2,4,7,3,6,11,14,22},{0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,3,6,6,0,12},{0,0,0,0,T^2,0,0,0,0,1,0,0,T^2,2,0,0,3,0,7,11},{0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,0,7,0,6,15},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,2,4,7,6,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,0,3,7},{0,T^2,0,0,2*T^2,0,0,0,T^2,0,0,0,2*T^2,0,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,T^2,0,0,0,0,0,0,0,T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,467)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4}, {2, 5, 6}, {0, 1, 7}}
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},{0,1,1},{1,0,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,5},{1,2,4},{1,1,4},{0,2,4},{1,2,3},{0,2,3},{1,1,3},{1,2,2},{0,2,2},{1,1,2},{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: {{1,3,5,4,6,9,12,10,16,22,15,17,34,35,31,46,53,57,84,134},{0,1,1,1,3,4,5,6,9,12,5,6,17,22,15,20,31,34,46,84},{0,0,1,0,0,0,3,0,0,6,5,4,9,10,12,17,22,16,34,57},{0,0,0,1,0,3,0,0,6,0,0,5,12,0,0,15,0,22,31,53},{0,0,0,0,1,1,1,3,4,5,1,1,6,12,5,6,15,17,20,46},{0,0,0,0,0,1,0,0,3,0,0,1,5,0,0,5,0,12,15,31},{0,0,0,0,0,0,1,0,0,3,1,1,4,6,5,6,12,9,17,34},{T^2,0,2*T^2,T^2,0,0,0,1,1,1,3*T^2,2*T^2,1,5,1,1+3*T^2,5,6,6,20},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,1,0,0,1,3,1,1,5,4,6,17},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,4,6,0,9,16},{0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,5,0,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3,5,12},{0,0,T^2,0,0,0,0,0,0,0,2*T^2,T^2,0,1,0,2*T^2,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3,0,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,468)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 2 & 2 & 1 & 2 & 1 & 0 & 2 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 4 & 4 & 3 & 4 & 2 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 2 & 0 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{3, 4}, {2, 5, 6}, {0, 1, 7}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{1,0,1},{0,1,1}},{{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},{0,1,1},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,4},{1,1,4},{1,2,3},{0,2,4},{1,2,2},{1,1,3},{0,2,3},{1,1,2},{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: {{1,1,3,2,6,5,8,12,5,18,15,22,10,27,31,30,53,53,66,118},{0,1,0,1,0,3,3,6,5,6,12,10,8,18,22,27,35,32,53,88},{0,0,1,0,3,1,2,5,1,8,5,12,2,10,15,10,31,27,30,66},{0,0,0,1,0,0,3,0,0,6,0,0,5,12,0,15,0,22,31,53},{0,2*T^2,0,2*T^2,1,0,0,1,3*T^2,2,1,5,3*T^2,2,5,2+4*T^2,15,10,10,30},{0,0,0,0,0,1,1,3,1,3,5,6,2,8,12,10,22,18,27,53},{0,0,0,0,0,0,1,0,0,3,0,0,1,5,0,5,0,12,15,31},{0,0,0,0,0,0,0,1,0,1,1,3,0,2,5,2,12,8,10,27},{0,0,0,0,0,0,0,0,1,0,3,0,1,3,6,8,10,6,18,32},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,3,2,6,3,8,18},{0,T^2,0,T^2,0,0,0,0,2*T^2,0,0,1,2*T^2,0,1,3*T^2,5,2,2,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,5,0,6,12,22},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,2,8},{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,T^2,0,0,0,T^2,0,0,2*T^2,1,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,469)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & -1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & -1 & -1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
24: $\begin{pmatrix}2 & 1 & 0 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 1 & 0 \\ 0 & 1 & 2 & 0 & 0 & 1 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 1 & -1 & 0 & 0 & 1 & -1 & -1 & 0 & 0 & -1 & 0 \\ 3 & 3 & 3 & 3 & 2 & 2 & 2 & 3 & 2 & 2 & 1 & 1 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, -1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (20): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{2, 3, 4}, {1, 5, 6}, {4, 5, 6}, {0, 1, 7}, {0, 2, 3, 7}}
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},{1,3,4},{0,4,5},{3,5,6},{0,2,5},{2,5,6},{0,1,4}},{2,1,2})
Cox degrees: {{0,0,1},{-1,1,1},{1,-1,0},{1,-1,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (24): {{2,0,3},{1,1,3},{0,2,3},{1,0,3},{2,0,2},{1,1,2},{2,-1,2},{0,1,3},{0,2,2},{1,0,2},{2,0,1},{2,-1,1},{1,1,1},{0,1,2},{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: {{1,2,3,3,4,7,6,5,10,13,10,18,16,20,15,33,26,48,40,43,68,66,93,138},{0,1,2,1,1,4,1,3,7,6,4,6,10,13,6,18,15,33,18,21,43,40,52,93},{0,0,1,0,0,1,0,1,4,1,1,1,4,6,1,6,6,18,6,6,21,18,21,52},{0,0,0,1,0,0,1,2,0,4,0,4,0,7,6,10,13,16,10,18,33,20,40,66},{0,0,0,0,1,2,1,0,3,3,4,6,7,5,3,13,6,20,18,15,26,33,43,68},{0,0,0,0,0,1,0,0,2,1,1,1,4,3,1,6,3,13,6,6,15,18,21,43},{0,0,2*T^2,0,0,0,1,0,3*T^2,2,0,4,0,3,3,7,5,10,10,13,20,16,33,48},{0,0,0,0,0,0,0,1,0,1,0,1,0,4,1,4,6,10,4,6,18,10,18,40},{0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,1,6,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,1,0,1,0,2,1,4,3,7,4,6,13,10,18,33},{0,0,0,T^2,0,0,0,2*T^2,0,0,1,1,2,0,T^2,3,2*T^2,5,6,3,6,13,15,26},{0,0,T^2,0,0,0,0,0,2*T^2,0,0,1,0,0,0,2,0,3,4,3,5,7,13,20},{0,0,0,0,0,0,0,T^2,0,0,0,0,1,0,0,1,T^2,3,1,1,3,6,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,1,1,6,4,6,18},{0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,0,0,1,0,2,0,0,4,7,0,10,16},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,3,4,6,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,6},{0,0,0,T^2,0,0,0,2*T^2,T^2,0,0,0,0,0,T^2,0,2*T^2,0,1,0,0,2,3,5},{0,0,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,0,0,0,1,2,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,T^2,0,0,0,0,1,1,3},{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},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,470)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
23: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 2 & 1 & 1 & 2 & 1 & 0 & 0 & 2 & 0 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 2 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (20): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 6}, {0, 2, 3, 6, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3}, {2, 3, 4, 6}, {4, 5, 6}, {0, 1, 7}, {0, 5, 7}}
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},{3,4,5},{0,1,4},{1,3,4}},{2,1,1})
Cox degrees: {{0,0,1},{1,-1,0},{1,0,0},{1,0,0},{0,1,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (23): {{2,2,2},{2,1,2},{2,2,1},{2,0,2},{1,2,2},{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: {{1,2,2,3,4,5,7,9,8,8,10,10,14,18,16,24,30,27,42,48,60,72,108},{0,1,0,2,1,2,4,2,3,5,7,4,8,9,10,9,14,18,24,30,42,39,72},{0,0,1,2*T^2,0,2,0,4,5,3,3*T^2,0,8,7,0,10,18,10,16,27,22,42,60},{0,0,0,1,0,0,1,0,0,2,4,1,3,2,4,2,3,9,9,14,24,14,39},{0,0,0,0,1,0,2,2,0,0,3,4,0,5,7,9,8,8,18,14,27,30,48},{0,0,0,0,0,1,0,1,2,2,0,0,5,4,0,4,9,7,10,18,16,24,42},{0,0,0,0,0,0,1,0,0,0,2,1,0,2,4,2,3,5,9,8,18,14,30},{0,0,0,T^2,0,0,0,1,0,0,2*T^2,0,0,2,0,4,5,3,7,8,10,18,27},{0,0,0,2*T^2,0,0,0,0,1,0,3*T^2,0,2,0,0,0,4,0,0,7,0,10,16},{0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,1,2,4,4,9,10,9,24},{0,0,T^3,0,0,0,0,0,T^3,0,1,0,0,0,1,0,0,2,2,3,9,3,14},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,0,0,5,0,8,8,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,4,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,2,4,5,7,9,18},{0,0,T^3,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,0,2,0,5,3,8},{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,T^2,0,0,0,0,0,0,2*T^2,0,0,0,0,0,1,0,0,2,0,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,4,2,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{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},{0,0,0,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,472)$ |
3 |
20 |
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8: $\begin{pmatrix}0 & 1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
22: $\begin{pmatrix}2 & 2 & 1 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 1 & 2 & 0 & 0 & 2 & 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 0 & 1 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 0, 1, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (20): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 6}, {0, 2, 5, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{1, 2, 5}, {3, 4, 6}, {2, 3, 5, 6}, {0, 1, 7}, {0, 4, 7}}
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},{0,1,3},{0,2,4},{3,4,5}},{2,1,2})
Cox degrees: {{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 (22): {{2,1,2},{2,0,2},{1,2,2},{1,1,2},{2,1,1},{0,2,2},{1,0,2},{2,0,1},{1,2,1},{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: {{1,2,1,4,3,4,7,8,3,6,12,10,16,12,18,24,30,24,52,51,60,108},{0,1,0,1,0,1,4,3,0,0,3,4,10,3,6,12,12,6,30,24,24,60},{0,0,1,2,1,4,3,2,3,3,8,7,10,12,8,13,24,18,36,33,51,82},{0,0,0,1,0,1,2,1,0,0,3,4,7,3,3,8,12,6,24,18,24,51},{0,0,0,0,1,0,0,2,1,3,4,0,0,4,8,7,10,12,16,24,30,52},{0,0,0,0,0,1,0,0,0,0,1,2,3,3,1,2,8,3,13,8,18,33},{0,0,0,0,0,0,1,0,0,0,0,1,4,0,0,3,3,0,12,6,6,24},{0,0,0,0,0,0,0,1,0,0,1,0,0,1,3,4,4,3,10,12,12,30},{0,2*T^2,0,0,0,0,3*T^2,0,1,1,2,0,4*T^2,4,2,3,7,8,10,13,24,36},{0,2*T^2,0,0,0,0,3*T^2,0,0,1,0,0,4*T^2,0,2,0,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,2,4,3,7,8,12,24},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,1,3,0,8,3,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,3,0,0,6},{0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,3*T^2,1,0,0,2,1,3,2,8,13},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,4,3,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,3,8},{0,T^2,0,0,0,0,2*T^2,0,0,0,0,0,3*T^2,0,0,0,0,1,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{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,T^2,0,0,0,0,0,2*T^2,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,473)$ |
3 |
20 |
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8: $\begin{pmatrix}-1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
25: $\begin{pmatrix}-1 & -2 & 0 & -1 & -1 & 0 & -2 & 1 & -1 & 0 & 1 & -2 & 0 & -2 & -1 & 1 & 0 & -1 & 1 & -1 & 0 & 0 & -1 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 0 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 3 & 1 & 2 & 1 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {-1, -1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (20): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 6}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 6}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{0, 1, 4}, {3, 4, 6}, {2, 3, 5, 6}, {0, 1, 7}, {2, 5, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-1,0,1},{0,1,1},{-1,1,1}},{{2,4,5},{1,4,5},{0,2,4},{0,1,4},{2,3,5}},{1,1,2})
Cox degrees: {{-1,0,1},{-1,0,1},{1,0,0},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (25): {{-1,2,3},{-2,2,3},{0,2,2},{-1,1,3},{-1,2,2},{0,1,2},{-2,1,3},{1,2,1},{-1,1,2},{0,2,1},{1,1,1},{-2,2,2},{0,0,2},{-2,1,2},{-1,0,2},{1,0,1},{0,1,1},{-1,2,1},{1,1,0},{-1,1,1},{0,0,1},{0,1,0},{-1,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,2,5,5,4,3,12,8,8,8,8,19,19,14,21,14,30,36,36,54,61,54,96},{0,1,0,0,2,0,2,0,5,3,0,5,0,12,8,0,8,8,11,21,14,30,36,20,54},{0,0,1,0,2,2,0,2,4,5,5,3,3,6,6,8,12,8,21,19,19,36,30,36,61},{0,0,0,1,0,2,2,0,5,0,3,0,5,8,12,8,8,0,11,14,21,20,36,30,54},{0,0,0,0,1,0,0,0,2,2,0,2,0,4,3,0,5,5,8,12,8,21,19,14,36},{0,0,0,0,0,1,0,0,2,0,2,0,2,3,4,5,5,0,8,8,12,14,19,21,36},{0,0,0,0,0,0,1,T^3,2,0,0,0,0,5,5,0,3,0,4,8,8,11,21,11,30},{0,2*T^2,0,2*T^2,0,0,6*T^2,1,0,2,2,2*T^2,2*T^2,3*T^2,3*T^2,3,4,3,12,6,6,19,9,19,30},{0,0,0,0,0,0,0,0,1,0,0,0,0,2,2,0,2,0,3,5,5,8,12,8,21},{0,0,0,T^2,0,0,2*T^2,0,0,1,0,0,T^2,0,2*T^2,0,2,2,5,4,3,12,6,8,19},{0,T^2,0,0,0,0,2*T^2,0,0,0,1,T^2,0,2*T^2,0,2,2,0,5,3,4,8,6,12,19},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,0,0,0,2,0,5,0,8,8,0,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,0,0,0,0,5,0,8,8,14},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,1,0,0,0,0,0,2,0,3,5,0,8},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,1,0,0,0,0,0,2,0,5,3,8},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,1,0,0,0,0,2,0,3,5,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,2,5,4,5,12},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,T^2,0,0,1,0,2,0,5,3,0,8},{0,T^2,0,T^2,0,0,4*T^2,0,0,0,0,T^2,T^2,2*T^2,2*T^2,0,0,0,1,0,0,2,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,2,0,5},{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,T^2,0,0,0,0,0,0,0,T^2,0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,T^2,0,0,0,0,0,0,T^2,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,474)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, -1, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {0, 4, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}}
Primitive collections: {{2, 5}, {3, 4, 6}, {0, 1, 7}}
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},{0,1,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (20): {{1,2,3},{1,1,3},{0,2,3},{1,2,2},{0,1,3},{0,2,2},{1,1,2},{1,2,1},{1,0,2},{0,2,1},{0,1,2},{1,1,1},{0,0,2},{0,1,1},{1,1,0},{1,0,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,3,4,6,8,6,13,12,15,18,24,33,32,33,58,63,58,108},{0,1,0,0,2,0,3,0,8,0,6,6,15,12,10,18,33,32,20,58},{0,0,1,0,2,3,1,0,2,6,8,3,13,18,6,8,33,18,32,63},{0,0,0,1,0,2,2,3,3,6,4,8,6,15,18,13,24,33,33,58},{0,0,0,0,1,0,0,0,1,0,3,0,8,6,0,3,18,6,10,32},{0,0,0,0,0,1,0,0,0,3,2,1,3,8,3,2,13,8,18,33},{0,0,0,0,0,0,1,0,2,0,2,3,4,6,6,8,15,18,12,33},{0,2*T^2,0,0,3*T^2,0,0,1,3*T^2,2,0,2,4*T^2,4,8,3,6,13,15,24},{0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,3,6,6,0,12},{0,T^2,0,0,2*T^2,0,0,0,2*T^2,1,0,0,3*T^2,2,1,0,3,2,8,13},{0,0,0,0,0,0,0,0,0,0,1,0,2,3,0,1,8,3,6,18},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,2,4,8,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,3,8},{0,T^2,0,0,2*T^2,0,0,0,2*T^2,0,0,0,3*T^2,0,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,T^2,0,0,0,T^2,0,0,0,2*T^2,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,658)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 4 & 3 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}, {0, 1, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 5}, {0, 1, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {0, 3, 4, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{2, 3, 4, 5}, {0, 6}, {1, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (16): {{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: {{1,2,2,4,7,12,12,21,27,42,42,67,77,112,112,167},{0,1,0,2,2,7,3,12,12,27,17,42,42,77,57,112},{0,0,1,2,2,3,7,12,12,17,27,42,42,57,77,112},{0,0,0,1,1,2,2,7,7,12,12,27,27,42,42,77},{0,0,0,0,1,2,2,4,7,12,12,21,27,42,42,67},{0,0,0,0,0,1,0,2,2,7,3,12,12,27,17,42},{0,0,0,0,0,0,1,2,2,3,7,12,12,17,27,42},{0,0,0,0,0,0,0,1,1,2,2,7,7,12,12,27},{0,0,0,0,0,0,0,0,1,2,2,4,7,12,12,21},{0,0,0,0,0,0,0,0,0,1,0,2,2,7,3,12},{0,0,0,0,0,0,0,0,0,0,1,2,2,3,7,12},{0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,7},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,725)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 1 & 0 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 1, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{1, 4}, {2, 3, 5, 6}, {0, 7}}
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},{1,0,0},{0,1,1},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (16): {{1,3,4},{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},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,6,11,11,20,21,36,36,61,56,91,91,146},{0,1,0,2,1,2,6,11,6,21,11,36,21,56,36,91},{0,0,1,2,1,6,2,11,6,11,21,36,21,36,56,91},{0,0,0,1,0,1,1,6,1,6,6,21,6,21,21,56},{0,0,0,0,1,2,2,4,6,11,11,20,21,36,36,61},{0,0,0,0,0,1,0,2,1,2,6,11,6,11,21,36},{0,0,0,0,0,0,1,2,1,6,2,11,6,21,11,36},{0,0,0,0,0,0,0,1,0,1,1,6,1,6,6,21},{0,0,0,0,0,0,0,0,1,2,2,4,6,11,11,20},{0,0,0,0,0,0,0,0,0,1,0,2,1,6,2,11},{0,0,0,0,0,0,0,0,0,0,1,2,1,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,763)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, -1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}}
Primitive collections: {{1, 2, 3, 4}, {5, 6}, {0, 7}}
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},{1,1,1},{1,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (16): {{3,4,5},{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: {{1,2,3,6,5,11,15,21,24,36,46,56,71,91,111,166},{0,1,1,1,3,6,6,6,15,21,21,21,46,56,56,111},{0,0,1,1,2,2,6,6,11,11,21,21,36,36,56,91},{0,0,0,1,0,2,3,6,5,11,15,21,24,36,46,71},{0,0,0,0,1,1,1,1,6,6,6,6,21,21,21,56},{0,0,0,0,0,1,1,1,3,6,6,6,15,21,21,46},{0,0,0,0,0,0,1,1,2,2,6,6,11,11,21,36},{0,0,0,0,0,0,0,1,0,2,3,6,5,11,15,24},{0,0,0,0,0,0,0,0,1,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,1,1,1,3,6,6,15},{0,0,0,0,0,0,0,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,802)$ |
3 |
14 |
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8: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
14: $\begin{pmatrix}4 & 4 & 3 & 4 & 3 & 2 & 3 & 2 & 1 & 2 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {1, 1, 1, 1, 0}, {0, 0, 0, -1, 0}, {-1, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (14): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 6, 7}}
Primitive collections: {{0, 1, 2, 3, 4}, {1, 2, 3, 4, 6}, {5, 6}, {0, 7}, {5, 7}}
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},{0,1,4},{1,3,4},{3,4,5}},{2,1,1})
Cox degrees: {{1,-1,0},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (14): {{4,1,1},{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: {{1,1,5,2,5,15,10,15,35,30,35,70,70,140},{0,1,1,1,5,5,6,15,15,20,35,35,50,105},{0,0,1,0,1,5,2,5,15,10,15,35,30,70},{0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,1,1,1,5,5,6,15,15,20,50},{0,0,0,0,0,1,0,1,5,2,5,15,10,30},{0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,1,1,1,5,5,6,20},{0,0,0,0,0,0,0,0,1,0,1,5,2,10},{0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,806)$ |
3 |
14 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 2 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
17: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 7 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 6 & 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-3, 1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (14): {{0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {0, 3, 4, 5, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{0, 1}, {0, 6}, {2, 3, 4, 5, 6}, {1, 7}, {2, 3, 4, 5, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,3,2},{1,3,3}},{{3,4,5},{0,1,4},{2,3,5},{1,3,4},{0,2,5},{0,4,5}},{1,1,1})
Cox degrees: {{1,3,2},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (17): {{1,7,6},{1,6,6},{1,6,5},{1,5,5},{1,5,4},{1,4,4},{0,4,4},{1,4,3},{1,3,3},{0,3,3},{1,3,2},{1,2,2},{0,2,2},{1,2,1},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,5,5,15,15,16,35,35,40,70,70,85,126,126,161,280},{0,1,1,5,5,15,15,15,35,36,35,70,75,70,126,141,245},{0,0,1,1,5,5,5,15,15,16,35,35,40,70,70,85,161},{0,0,0,1,1,5,5,5,15,15,15,35,36,35,70,75,141},{0,0,0,0,1,1,1,5,5,5,15,15,16,35,35,40,85},{0,0,0,0,0,1,1,1,5,5,5,15,15,15,35,36,75},{0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,16,40},{0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,36},{0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,16},{T^4,0,0,0,0,0,T^4,0,0,0,0,1,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{T^4,T^4,0,0,0,0,T^4,0,0,0,0,0,0,1,1,1,5},{5*T^4,T^4,T^4,0,0,0,5*T^4,0,0,T^4,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,807)$ |
3 |
14 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
15: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-2, 1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (14): {{0, 2, 3, 4, 5}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {0, 3, 4, 5, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{0, 1}, {0, 6}, {2, 3, 4, 5, 6}, {1, 7}, {2, 3, 4, 5, 7}}
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},{0,4,5},{1,3,4},{2,3,5},{0,2,5}},{1,1,1})
Cox degrees: {{1,2,1},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (15): {{1,6,5},{1,5,5},{1,5,4},{1,4,4},{0,4,4},{1,4,3},{1,3,3},{0,3,3},{1,3,2},{1,2,2},{0,2,2},{1,2,1},{1,1,1},{0,1,1},{0,0,0}}
Ext matrix: {{1,1,5,5,6,15,15,20,35,35,50,70,70,105,196},{0,1,1,5,5,5,15,16,15,35,40,35,70,85,161},{0,0,1,1,1,5,5,6,15,15,20,35,35,50,105},{0,0,0,1,1,1,5,5,5,15,16,15,35,40,85},{0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,1,1,1,5,5,6,15,15,20,50},{0,0,0,0,0,0,1,1,1,5,5,5,15,16,40},{0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{0,0,0,0,0,0,0,0,1,1,1,5,5,6,20},{0,0,0,0,0,0,0,0,0,1,1,1,5,5,16},{0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{T^4,0,0,0,T^4,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,808)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 2 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 5 & 5 & 4 & 3 & 4 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}, {0, 1, 1, 1, -2}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {0, 6}, {1, 2, 3, 7}}
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: {{0,1,0},{0,0,1},{0,0,1},{0,0,1},{1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{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: {{1,2,4,10,8,20,20,21,35,40,32,70,44,68,80,125,132,208},{0,1,0,0,4,10,0,10,0,20,21,35,20,44,35,80,56,132},{0,0,1,4,2,8,10,8,20,20,12,40,21,32,44,68,80,125},{0,0,0,1,0,2,4,2,10,8,3,20,8,12,21,32,44,68},{0,0,0,0,1,4,0,4,0,10,8,20,10,21,20,44,35,80},{0,0,0,0,0,1,0,1,0,4,2,10,4,8,10,21,20,44},{0,0,0,0,0,0,1,0,4,2,0,8,2,3,8,12,21,32},{0,0,0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{T^3,2*T^3,0,0,0,0,0,T^3,1,0,2*T^3,2,0,0,2,3,8,12},{0,0,0,0,0,0,0,0,0,1,0,4,1,2,4,8,10,21},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,T^3,0,0,0,0,0,0,0,0,T^3,1,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,811)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 2 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}, {0, 1, 1, 0, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 5}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 1, 4, 5, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {0, 2, 4, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{3, 4, 5}, {0, 6}, {1, 2, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,3,4},{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: {{1,2,3,6,6,8,12,13,18,30,32,33,54,48,63,94,103,156},{0,1,0,3,0,3,6,8,6,18,10,18,32,33,32,63,50,103},{0,0,1,2,3,2,6,3,8,13,18,13,30,18,33,48,63,94},{0,0,0,1,0,1,3,2,3,8,6,8,18,13,18,33,32,63},{0,0,0,0,1,0,2,0,2,3,8,3,13,4,13,18,33,48},{0,0,0,0,0,1,0,2,3,6,6,8,12,13,18,30,32,54},{0,0,0,0,0,0,1,0,1,2,3,2,8,3,8,13,18,33},{0,0,0,0,0,0,0,1,0,3,0,3,6,8,6,18,10,32},{0,0,0,0,0,0,0,0,1,2,3,2,6,3,8,13,18,30},{0,0,0,0,0,0,0,0,0,1,0,1,3,2,3,8,6,18},{0,0,0,0,0,0,0,0,0,0,1,0,2,0,2,3,8,13},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,814)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 1 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 1, 1, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 4, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{1, 2, 4}, {3, 5, 6}, {0, 7}}
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},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,2,3},{1,2,3},{2,2,2},{0,2,3},{1,2,2},{2,1,2},{1,1,2},{0,2,2},{2,1,1},{2,0,1},{1,1,1},{0,1,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,2,6,6,6,15,12,11,21,27,28,50,36,46,81,77,134},{0,1,0,3,2,1,6,6,2,6,11,15,27,11,21,46,36,77},{0,0,1,0,3,1,3,6,6,6,15,6,28,21,15,28,46,81},{0,0,0,1,0,0,1,2,0,1,2,6,11,2,6,21,11,36},{0,0,0,0,1,0,1,3,1,1,6,3,15,6,6,15,21,46},{0,0,0,0,0,1,3,0,2,6,6,6,12,11,15,28,27,50},{0,0,0,0,0,0,1,0,0,1,2,3,6,2,6,15,11,27},{0,0,0,0,0,0,0,1,0,0,1,1,6,1,1,6,6,21},{0,0,0,0,0,0,0,0,1,1,3,0,6,6,3,6,15,28},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,6,2,11},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,815)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 0 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 1, 1, -2, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{3, 4}, {1, 2, 5, 6}, {0, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,2,2}},{{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},{1,2,2},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,5,6},{1,5,5},{1,4,5},{1,4,4},{1,3,4},{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: {{1,2,5,9,15,16,25,27,35,55,40,64,70,85,105,130,161,237},{0,1,1,5,5,5,15,16,15,35,16,40,35,40,70,85,85,161},{0,0,1,2,5,5,9,9,15,25,16,27,35,40,55,64,85,130},{0,0,0,1,1,1,5,5,5,15,5,16,15,16,35,40,40,85},{0,0,0,0,1,1,2,2,5,9,5,9,15,16,25,27,40,64},{0,0,0,0,0,1,0,2,0,0,5,9,0,15,0,25,35,55},{0,0,0,0,0,0,1,1,1,5,1,5,5,5,15,16,16,40},{0,0,0,0,0,0,0,1,0,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,0,0,1,2,1,2,5,5,9,9,16,27},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,5,5,5,16},{0,0,0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,T^3,0,0,0,0,0,T^3,0,0,0,0,1,1,2,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{T^4,0,0,0,0,T^4,0,0,0,0,0,0,0,0,1,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,824)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{1, 2}, {3, 4, 5, 6}, {0, 7}}
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},{1,0,0},{0,1,1},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (16): {{1,4,5},{1,4,4},{1,3,4},{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: {{1,2,5,6,9,11,15,25,20,34,35,50,55,80,105,160},{0,1,1,1,5,6,5,15,6,20,15,20,35,50,50,105},{0,0,1,1,2,2,5,9,6,11,15,20,25,34,50,80},{0,0,0,1,0,2,0,0,5,9,0,15,0,25,35,55},{0,0,0,0,1,1,1,5,1,6,5,6,15,20,20,50},{0,0,0,0,0,1,0,0,1,5,0,5,0,15,15,35},{0,0,0,0,0,0,1,2,1,2,5,6,9,11,20,34},{0,0,0,0,0,0,0,1,0,1,1,1,5,6,6,20},{0,0,0,0,0,0,0,0,1,2,0,5,0,9,15,25},{0,0,0,0,0,0,0,0,0,1,0,1,0,5,5,15},{0,0,0,0,0,0,0,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,5,9},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,825)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{1, 2}, {3, 4, 5, 6}, {0, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (16): {{1,3,4},{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},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,2,2,4,5,9,10,18,15,30,25,50,35,70,55,110},{0,1,0,2,0,0,5,9,0,15,0,25,0,35,0,55},{0,0,1,2,1,5,2,10,5,10,15,30,15,30,35,70},{0,0,0,1,0,0,1,5,0,5,0,15,0,15,0,35},{0,0,0,0,1,2,2,4,5,10,9,18,15,30,25,50},{0,0,0,0,0,1,0,2,1,2,5,10,5,10,15,30},{0,0,0,0,0,0,1,2,0,5,0,9,0,15,0,25},{0,0,0,0,0,0,0,1,0,1,0,5,0,5,0,15},{0,0,0,0,0,0,0,0,1,2,2,4,5,10,9,18},{0,0,0,0,0,0,0,0,0,1,0,2,0,5,0,9},{0,0,0,0,0,0,0,0,0,0,1,2,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,826)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 1, 0, -1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{2, 3, 4}, {1, 5, 6}, {0, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{0,1,1},{1,1,1}},{{2,3,4},{0,2,4},{0,1,4},{1,3,4}},{1,1,1})
Cox degrees: {{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 (18): {{2,4,5},{2,4,4},{2,3,4},{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: {{1,2,4,6,7,11,10,18,16,21,30,36,40,52,62,83,105,158},{0,1,1,1,4,6,4,6,10,6,18,21,18,21,40,52,52,105},{0,0,1,1,2,2,4,6,7,6,11,11,18,21,30,36,52,83},{0,0,0,1,0,2,0,4,0,6,7,11,10,18,16,30,40,62},{0,0,0,0,1,1,1,1,4,1,6,6,6,6,18,21,21,52},{0,0,0,0,0,1,0,1,0,1,4,6,4,6,10,18,18,40},{0,0,0,0,0,0,1,1,2,1,2,2,6,6,11,11,21,36},{0,0,0,0,0,0,0,1,0,1,2,2,4,6,7,11,18,30},{0,0,0,0,0,0,0,0,1,0,1,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,1,0,2,0,4,0,7,10,16},{0,0,0,0,0,0,0,0,0,0,1,1,1,1,4,6,6,18},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,4,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,7},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,827)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 4 & 3 & 4 & 2 & 3 & 1 & 3 & 0 & 2 & 2 & 1 & 3 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}, {-1, 1, 1, 1, -1}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {0, 6}, {1, 2, 3, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,2,0},{0,1,-1},{0,0,1},{1,1,1}},{{1,4,5},{0,2,3},{0,2,5},{1,2,5},{0,4,5},{1,2,3}},{1,2,1})
Cox degrees: {{0,1,-1},{0,0,1},{0,0,1},{0,0,1},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,2,4},{1,2,3},{1,1,4},{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: {{1,4,5,10,14,20,15,35,30,34,55,39,91,65,79,111,141,230},{0,1,1,4,5,10,5,20,14,15,30,16,55,34,39,65,79,141},{0,0,1,0,4,0,4,0,10,10,20,15,35,20,34,35,65,111},{0,0,0,1,1,4,1,10,5,5,14,5,30,15,16,34,39,79},{0,0,0,0,1,0,1,0,4,4,10,5,20,10,15,20,34,65},{0,0,0,0,0,1,0,4,1,1,5,1,14,5,5,15,16,39},{0,0,0,0,0,0,1,0,0,4,0,5,0,10,14,20,30,55},{T^3,0,T^3,0,0,0,T^3,1,0,0,1,T^3,5,1,1,5,5,16},{0,0,0,0,0,0,0,0,1,1,4,1,10,4,5,10,15,34},{0,0,0,0,0,0,0,0,0,1,0,1,0,4,5,10,14,30},{0,0,0,0,0,0,0,0,0,0,1,0,4,1,1,4,5,15},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,T^3,0,0,0,0,0,0,0,0,T^3,1,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,828)$ |
3 |
16 |
|
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8: $\begin{pmatrix}-2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}3 & 2 & 1 & 3 & 0 & -1 & 2 & 3 & 2 & 1 & 0 & 1 & 0 & -1 & 3 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {-2, 1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}}
Primitive collections: {{1, 2, 3, 4}, {5, 6}, {0, 7}}
Chambers: ({{1,0,0},{0,1,0},{0,0,1},{-2,0,1},{0,1,1}},{{0,2,4},{1,3,4},{2,3,4},{0,1,4}},{1,1,3})
Cox degrees: {{-2,0,1},{1,0,0},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (19): {{3,1,2},{2,1,2},{1,1,2},{3,1,1},{0,1,2},{-1,1,2},{2,1,1},{3,0,1},{2,0,1},{1,1,1},{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: {{1,4,10,11,20,35,24,12,28,45,76,55,96,119,57,154,104,174,272},{0,1,4,4,10,20,11,4,12,24,45,28,55,76,28,96,57,104,174},{0,0,1,1,4,10,4,1,4,11,24,12,28,45,12,55,28,57,104},{0,0,0,1,0,0,4,1,4,10,20,10,20,35,12,35,28,55,96},{0,0,0,0,1,4,1,0,1,4,11,4,12,24,4,28,12,28,57},{T^3,0,0,T^3,0,1,0,2*T^3,0,1,4,1,4,11,1+2*T^3,12,4,12,28},{0,0,0,0,0,0,1,0,1,4,10,4,10,20,4,20,12,28,55},{0,0,0,0,0,0,0,1,4,0,0,10,20,0,11,35,24,45,76},{0,0,0,0,0,0,0,0,1,0,0,4,10,0,4,20,11,24,45},{0,0,0,0,0,0,0,0,0,1,4,1,4,10,1,10,4,12,28},{0,0,0,0,0,0,0,0,0,0,1,0,1,4,0,4,1,4,12},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,1,10,4,11,24},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,1,4,11},{0,0,0,T^3,0,0,0,T^3,0,0,0,0,0,1,2*T^3,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10,20},{0,0,0,0,0,0,0,T^3,0,0,0,0,0,0,T^3,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,829)$ |
3 |
16 |
|
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}, {0, 1, 1, 1, -1}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {0, 6}, {1, 2, 3, 7}}
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},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (16): {{1,2,4},{1,1,4},{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: {{1,2,4,8,10,9,20,20,14,40,24,38,50,80,90,145},{0,1,0,4,0,4,0,10,9,20,10,24,20,50,35,90},{0,0,1,2,4,2,10,8,3,20,9,14,24,38,50,80},{0,0,0,1,0,1,0,4,2,10,4,9,10,24,20,50},{0,0,0,0,1,0,4,2,0,8,2,3,9,14,24,38},{0,0,0,0,0,1,0,0,2,0,4,8,10,20,20,40},{0,0,0,0,0,0,1,0,0,2,0,0,2,3,9,14},{0,0,0,0,0,0,0,1,0,4,1,2,4,9,10,24},{0,0,0,0,0,0,0,0,1,0,0,4,0,10,0,20},{0,0,0,0,0,0,0,0,0,1,0,0,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,1,2,4,8,10,20},{0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,831)$ |
3 |
16 |
|
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8: $\begin{pmatrix}-1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}3 & 2 & 3 & 1 & 0 & 3 & 2 & 1 & 2 & 0 & 3 & 1 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {-1, 1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}}
Primitive collections: {{1, 2, 3, 4}, {5, 6}, {0, 7}}
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},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (16): {{3,1,2},{2,1,2},{3,1,1},{1,1,2},{0,1,2},{3,0,1},{2,1,1},{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: {{1,4,5,10,20,6,14,30,18,55,20,40,75,48,95,166},{0,1,1,4,10,1,5,14,6,30,6,18,40,20,48,95},{0,0,1,0,0,1,4,10,4,20,6,10,20,18,40,75},{0,0,0,1,4,0,1,5,1,14,1,6,18,6,20,48},{0,0,0,0,1,0,0,1,0,5,0,1,6,1,6,20},{0,0,0,0,0,1,0,0,4,0,5,10,20,14,30,55},{0,0,0,0,0,0,1,4,1,10,1,4,10,6,18,40},{0,0,0,0,0,0,0,1,0,4,0,1,4,1,6,18},{0,0,0,0,0,0,0,0,1,0,1,4,10,5,14,30},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,10,20},{0,0,0,0,0,0,0,0,0,0,0,1,4,1,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,832)$ |
3 |
16 |
|
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 0 & 1 & 3 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 1, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}}
Primitive collections: {{1, 2, 3, 4}, {5, 6}, {0, 7}}
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},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (16): {{3,1,2},{2,1,2},{3,1,1},{1,1,2},{2,1,1},{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: {{1,4,2,10,8,3,20,20,5,12,40,20,30,60,50,100},{0,1,0,4,2,0,10,8,0,3,20,5,12,30,20,50},{0,0,1,0,4,1,0,10,3,4,20,12,10,20,30,60},{0,0,0,1,0,0,4,2,0,0,8,0,3,12,5,20},{0,0,0,0,1,0,0,4,0,1,10,3,4,10,12,30},{0,0,0,0,0,1,0,0,2,4,0,8,10,20,20,40},{0,0,0,0,0,0,1,0,0,0,2,0,0,3,0,5},{0,0,0,0,0,0,0,1,0,0,4,0,1,4,3,12},{0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,1,0,2,4,10,8,20},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,833)$ |
3 |
16 |
|
|
8: $\begin{pmatrix}-1 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
17: $\begin{pmatrix}2 & 1 & 3 & 0 & 3 & 2 & -1 & 1 & 2 & 0 & 3 & 1 & -1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {-1, 1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 6}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3, 5}, {4, 6}, {0, 7}}
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},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (17): {{2,1,2},{1,1,2},{3,1,1},{0,1,2},{3,0,1},{2,1,1},{-1,1,2},{1,1,1},{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: {{1,4,1,10,2,5,20,14,9,30,10,24,55,29,50,64,120},{0,1,0,4,0,1,10,5,2,14,2,9,30,10,24,29,64},{0,0,1,0,1,4,0,10,4,20,9,10,35,24,20,50,90},{0,0,0,1,0,0,4,1,0,5,0,2,14,2,9,10,29},{0,0,0,0,1,0,0,0,4,0,5,10,0,14,20,30,55},{0,0,0,0,0,1,0,4,1,10,2,4,20,9,10,24,50},{0,0,T^3,0,T^3,0,1,0,0,1,T^3,0,5,0,2,2,10},{0,0,0,0,0,0,0,1,0,4,0,1,10,2,4,9,24},{0,0,0,0,0,0,0,0,1,0,1,4,0,5,10,14,30},{0,0,0,0,0,0,0,0,0,1,0,0,4,0,1,2,9},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,1,0,1,4,5,14},{0,0,T^3,0,T^3,0,0,0,0,0,T^3,0,1,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,834)$ |
3 |
16 |
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|
8: $\begin{pmatrix}0 & 1 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
16: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 3 & 0 & 1 & 3 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 1, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 5, 6}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3, 5}, {4, 6}, {0, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (16): {{3,1,2},{2,1,2},{3,1,1},{1,1,2},{2,1,1},{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: {{1,4,2,10,8,6,20,20,11,18,40,32,40,75,70,130},{0,1,0,4,2,1,10,8,2,6,20,11,18,40,32,70},{0,0,1,0,4,1,0,10,6,4,20,18,10,20,40,75},{0,0,0,1,0,0,4,2,0,1,8,2,6,18,11,32},{0,0,0,0,1,0,0,4,1,1,10,6,4,10,18,40},{0,0,0,0,0,1,0,0,2,4,0,8,10,20,20,40},{0,0,0,0,0,0,1,0,0,0,2,0,1,6,2,11},{0,0,0,0,0,0,0,1,0,0,4,1,1,4,6,18},{0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,1,0,2,4,10,8,20},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,835)$ |
3 |
18 |
|
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8: $\begin{pmatrix}-1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 1 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 2 & 1 & 0 \\ 2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {-1, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3}, {4, 5, 6}, {0, 7}}
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},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,2,3},{1,2,3},{0,2,3},{2,2,2},{2,1,2},{1,2,2},{1,1,2},{0,2,2},{0,1,2},{2,1,1},{2,0,1},{1,1,1},{1,0,1},{0,1,1},{0,0,1},{2,0,0},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,6,4,6,9,15,16,28,18,21,37,46,63,81,52,99,162},{0,1,3,1,1,4,6,9,15,6,6,18,21,37,46,21,52,99},{0,0,1,0,0,1,1,4,6,1,1,6,6,18,21,6,21,52},{0,0,0,1,1,3,3,6,6,6,6,15,15,28,28,21,46,81},{0,0,0,0,1,0,3,0,6,4,6,9,15,16,28,18,37,63},{0,0,0,0,0,1,1,3,3,1,1,6,6,15,15,6,21,46},{0,0,0,0,0,0,1,0,3,1,1,4,6,9,15,6,18,37},{0,0,0,0,0,0,0,1,1,0,0,1,1,6,6,1,6,21},{0,0,0,0,0,0,0,0,1,0,0,1,1,4,6,1,6,18},{0,0,0,0,0,0,0,0,0,1,1,3,3,6,6,6,15,28},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,6,4,9,16},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,3,1,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,1,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,836)$ |
3 |
18 |
|
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8: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\ 4 & 4 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 3 & 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {1, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {-1, 1, 1, -1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{0, 3, 4}, {3, 4, 6}, {1, 2, 5, 6}, {0, 7}, {1, 2, 5, 7}}
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},{1,4,5},{2,4,6},{2,3,6},{0,1,5}},{1,1,1})
Cox degrees: {{1,0,1},{0,1,1},{0,1,1},{1,1,1},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (19): {{2,4,5},{2,4,4},{1,4,4},{2,3,4},{2,3,3},{1,3,4},{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: {{1,1,2,4,4,6,9,10,18,11,10,20,24,33,40,50,74,75,140},{0,1,1,1,4,1,6,4,6,6,10,10,18,21,18,40,52,40,105},{0,0,1,0,0,1,4,0,4,6,0,0,10,18,10,20,40,20,75},{0,0,0,1,1,1,2,4,6,2,4,10,9,11,18,24,33,40,74},{0,0,0,0,1,0,1,1,1,1,4,4,6,6,6,18,21,18,52},{0,0,0,0,0,1,1,0,4,2,0,0,4,9,10,10,24,20,50},{0,0,0,0,0,0,1,0,1,1,0,0,4,6,4,10,18,10,40},{0,0,0,0,0,0,0,1,1,0,1,4,2,2,6,9,11,18,33},{0,0,0,0,0,0,0,0,1,0,0,0,1,2,4,4,9,10,24},{0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,6,6,6,21},{0,0,T^3,0,0,0,0,0,0,T^3,0,1,0,0,1,2,2,6,11},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,6,4,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,T^3,0,0,0,0,0,0,T^3,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,837)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}3 & 3 & 2 & 3 & 2 & 3 & 1 & 3 & 2 & 1 & 2 & 0 & 2 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 1 & 0 & 2 & 0 & 1 & 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {1, 0, 1, 1, 0}, {0, 0, 0, -1, 0}, {-1, 1, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{0, 2, 3, 4}, {2, 3, 4, 6}, {1, 5, 6}, {0, 7}, {1, 5, 7}}
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},{0,1,1},{1,0,0},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{3,2,2},{3,1,2},{2,2,2},{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: {{1,1,4,3,4,3,10,6,12,10,12,20,24,30,30,60,60,120},{0,1,1,1,4,3,4,3,6,10,12,10,15,18,30,40,42,90},{0,0,1,0,1,0,4,0,3,4,3,10,6,12,12,30,24,60},{0,0,0,1,0,1,0,3,4,0,4,0,12,10,10,20,30,60},{0,0,0,0,1,0,1,0,1,4,3,4,3,6,12,18,15,42},{0,0,0,0,0,1,0,1,1,0,4,0,6,4,10,10,18,40},{0,0,0,0,0,0,1,0,0,1,0,4,0,3,3,12,6,24},{0,0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,10,20},{0,0,0,0,0,0,0,0,1,0,1,0,3,4,4,10,12,30},{0,0,0,0,0,0,0,0,0,1,0,1,0,1,3,6,3,15},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,4,3,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,838)$ |
3 |
18 |
|
|
8: $\begin{pmatrix}1 & -1 & 1 & 1 & -1 & 1 & 0 & 0 \\ -1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}2 & 1 & 3 & 1 & 2 & 0 & 3 & 2 & 0 & 1 & -1 & 2 & 1 & -1 & 0 & 1 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {-1, 1, 0, 0, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 6}, {0, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 4, 5, 6, 7}, {3, 4, 5, 6, 7}}
Primitive collections: {{0, 2, 3, 5}, {1, 4, 6}, {2, 3, 5, 6}, {0, 7}, {1, 4, 7}}
Chambers: ({{1,0,0},{1,-1,0},{0,1,0},{0,0,1},{0,1,1},{-1,1,1}},{{0,3,4},{3,4,5},{0,1,3},{2,4,5},{0,2,4}},{2,1,2})
Cox degrees: {{1,-1,0},{-1,1,1},{1,0,0},{1,0,0},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (19): {{2,1,2},{1,2,2},{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: {{1,1,2,4,3,4,5,9,10,12,10,21,24,20,30,54,50,60,110},{0,1,0,1,2,4,3,2,4,9,10,14,9,10,24,39,24,50,84},{0,0,1,0,1,0,3,4,0,4,0,12,10,0,10,30,20,20,60},{0,0,0,1,0,1,0,2,4,3,4,5,9,10,12,21,24,30,54},{0,0,0,0,1,0,2,1,0,4,0,9,4,0,10,24,10,20,50},{0,0,0,0,0,1,0,0,1,2,4,3,2,4,9,14,9,24,39},{0,0,0,0,0,0,1,0,0,0,0,4,0,0,0,10,0,0,20},{0,0,0,0,0,0,0,1,0,1,0,3,4,0,4,12,10,10,30},{0,0,0,0,0,0,0,0,1,0,1,0,2,4,3,5,9,12,21},{0,0,0,0,0,0,0,0,0,1,0,2,1,0,4,9,4,10,24},{0,0,T^3,0,0,0,T^3,0,0,0,1,0,0,1,2,3,2,9,14},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,4,4,12},{0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,1,0,0,2,3,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,1,4,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,3},{0,0,T^3,0,0,0,T^3,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,839)$ |
3 |
18 |
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8: $\begin{pmatrix}1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ -2 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ -1 & 1 & 1 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
20: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ 3 & 2 & 2 & 1 & 3 & 1 & 0 & 2 & 2 & 0 & 1 & -1 & 3 & 1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 3 & 3 & 2 & 2 & 3 & 1 & 1 & 3 & 2 & 0 & 2 & 0 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {1, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {-2, 1, 1, 0, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 4, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {2, 4, 5, 6, 7}}
Primitive collections: {{0, 3, 4}, {3, 4, 6}, {1, 2, 5, 6}, {0, 7}, {1, 2, 5, 7}}
Chambers: ({{1,0,0},{0,1,0},{1,-2,-1},{0,0,1},{1,0,1},{0,1,1}},{{0,4,5},{0,2,4},{0,1,5},{0,1,2},{2,3,4},{3,4,5}},{4,1,1})
Cox degrees: {{1,-2,-1},{0,1,1},{0,1,1},{1,0,0},{1,0,0},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (20): {{2,3,3},{2,2,3},{2,2,2},{2,1,2},{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: {{1,1,4,4,6,10,10,6,18,20,18,20,21,40,40,52,75,75,105,186},{0,1,1,4,4,4,10,6,12,10,18,20,18,28,40,43,55,75,87,156},{0,0,1,1,1,4,4,1,6,10,6,10,6,18,18,21,40,40,52,105},{0,0,0,1,1,1,4,1,4,4,6,10,6,12,18,18,28,40,43,87},{0,0,0,0,1,0,0,1,4,0,4,0,6,10,10,18,20,20,40,75},{0,0,0,0,0,1,1,0,1,4,1,4,1,6,6,6,18,18,21,52},{0,0,0,0,0,0,1,0,1,1,1,4,1,4,6,6,12,18,18,43},{0,0,0,0,0,0,0,1,1,0,4,0,4,4,10,12,10,20,28,55},{0,0,0,0,0,0,0,0,1,0,1,0,1,4,4,6,10,10,18,40},{0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,1,6,6,6,21},{0,0,0,0,0,0,0,0,0,0,1,0,1,1,4,4,4,10,12,28},{T^3,0,0,0,2*T^3,0,0,0,0,0,0,1,3*T^3,1,1,1,4,6,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,6,18},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,4,4,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,6},{0,0,0,0,T^3,0,0,0,0,0,0,0,2*T^3,0,0,0,0,1,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,840)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 2 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 0, 0, 0, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 5}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}, {2, 3, 4, 5, 7}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}}
Primitive collections: {{1, 2, 3}, {4, 5, 6}, {0, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,2,3},{1,2,3},{2,2,2},{0,2,3},{1,2,2},{2,1,2},{1,1,2},{0,2,2},{2,1,1},{2,0,1},{1,1,1},{0,1,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,2,6,6,4,12,12,7,10,21,24,42,16,30,60,48,96},{0,1,0,3,2,0,4,6,0,0,7,12,21,0,10,30,16,48},{0,0,1,0,3,1,3,6,4,4,12,6,24,10,12,24,30,60},{0,0,0,1,0,0,0,2,0,0,0,4,7,0,0,10,0,16},{0,0,0,0,1,0,1,3,0,0,4,3,12,0,4,12,10,30},{0,0,0,0,0,1,3,0,2,4,6,6,12,7,12,24,21,42},{0,0,0,0,0,0,1,0,0,0,2,3,6,0,4,12,7,21},{0,0,0,0,0,0,0,1,0,0,0,1,4,0,0,4,0,10},{0,0,0,0,0,0,0,0,1,1,3,0,6,4,3,6,12,24},{0,0,0,0,0,0,0,0,0,1,0,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,4,0,7},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,843)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 2 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 5 & 4 & 4 & 3 & 2 & 3 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -2}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,1,5},{0,1,5},{1,1,4},{0,1,4},{1,1,3},{1,1,2},{1,0,3},{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: {{1,2,4,8,10,20,11,20,40,24,35,22,48,45,70,90,76,152},{0,1,0,4,0,0,0,10,20,0,0,11,24,0,35,45,0,76},{0,0,1,2,4,10,4,8,20,11,20,8,22,24,40,48,45,90},{0,0,0,1,0,0,0,4,10,0,0,4,11,0,20,24,0,45},{0,0,0,0,1,4,1,2,8,4,10,2,8,11,20,22,24,48},{0,0,0,0,0,1,0,0,2,1,4,0,2,4,8,8,11,22},{0,0,0,0,0,0,1,0,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,0,1,4,0,0,1,4,0,10,11,0,24},{0,0,0,0,0,0,0,0,1,0,0,0,1,0,4,4,0,11},{0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{T^3,2*T^3,0,0,0,0,T^3,0,0,0,1,2*T^3,0,1,2,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,T^3,0,0,0,0,0,0,0,0,0,T^3,0,0,1,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,844)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 2 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 5 & 4 & 5 & 3 & 4 & 2 & 3 & 3 & 2 & 1 & 2 & 3 & 1 & 2 & 1 & 0 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, 0, -2}}
Cones (16): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 5, 6, 7}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}}
Primitive collections: {{3, 5}, {4, 6}, {0, 1, 2, 7}}
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},{-1,1,2},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,1,5},{1,1,4},{0,1,5},{1,1,3},{0,1,4},{1,1,2},{1,0,3},{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: {{1,4,2,10,8,20,12,20,28,35,40,23,55,52,70,96,100,172},{0,1,0,4,2,10,4,8,12,20,20,8,28,23,40,55,52,100},{0,0,1,0,4,0,1,10,4,0,20,12,10,28,35,20,55,96},{0,0,0,1,0,4,1,2,4,10,8,2,12,8,20,28,23,52},{0,0,0,0,1,0,0,4,1,0,10,4,4,12,20,10,28,55},{0,0,0,0,0,1,0,0,1,4,2,0,4,2,8,12,8,23},{0,0,0,0,0,0,1,0,4,0,0,2,10,8,0,20,20,40},{0,0,0,0,0,0,0,1,0,0,4,1,1,4,10,4,12,28},{0,0,0,0,0,0,0,0,1,0,0,0,4,2,0,10,8,20},{T^3,0,2*T^3,0,0,0,2*T^3,0,0,1,0,3*T^3,1,0,2,4,2,8},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,4,1,4,12},{0,0,0,0,0,0,0,0,0,0,0,1,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,2,8},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,T^3,0,0,0,T^3,0,0,0,0,2*T^3,0,0,1,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,846)$ |
3 |
16 |
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8: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$
17: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 4 & 3 & 3 & 2 & 3 & 3 & 2 & 1 & 2 & 2 & 1 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 1, -1, -1}}
Cones (16): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 5, 7}, {0, 1, 3, 6, 7}, {0, 1, 4, 5, 7}, {0, 1, 4, 6, 7}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}}
Primitive collections: {{3, 4}, {5, 6}, {0, 1, 2, 7}}
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},{3,4,5},{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},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (17): {{1,1,5},{1,1,4},{1,0,4},{0,1,4},{1,1,3},{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: {{1,4,5,5,10,14,20,14,19,30,35,30,44,55,55,85,146},{0,1,1,1,4,5,10,5,6,14,20,14,19,30,30,44,85},{0,0,1,0,0,0,0,4,5,0,0,10,14,20,0,30,55},{0,0,0,1,0,4,0,0,5,10,0,0,14,0,20,30,55},{0,0,0,0,1,1,4,1,1,5,10,5,6,14,14,19,44},{0,0,0,0,0,1,0,0,1,4,0,0,5,0,10,14,30},{0,0,0,0,0,0,1,0,0,1,4,1,1,5,5,6,19},{0,0,0,0,0,0,0,1,1,0,0,4,5,10,0,14,30},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10,20},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,5,14},{T^3,0,T^3,T^3,0,0,0,0,T^3,0,1,0,0,1,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,1,1,4,0,5,14},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4,10},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,848)$ |
3 |
18 |
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8: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2 & 3 & 1 & 3 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -1}, {0, 0, 1, 1, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 6}, {0, 2, 3, 5, 6}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{4, 5}, {0, 1, 6}, {2, 3, 7}}
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},{1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{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: {{1,3,3,6,6,9,10,18,18,21,36,21,36,36,45,78,78,136},{0,1,0,3,0,3,3,6,9,10,18,6,21,10,21,45,36,78},{0,0,1,0,3,3,3,9,6,6,18,10,10,21,21,36,45,78},{0,0,0,1,0,0,0,0,3,3,6,0,10,0,6,21,10,36},{0,0,0,0,1,0,0,3,0,0,6,3,0,10,6,10,21,36},{0,0,0,0,0,1,1,3,3,3,9,3,6,6,10,21,21,45},{0,0,0,0,0,0,1,0,0,3,0,3,6,6,9,18,18,36},{0,0,0,0,0,0,0,1,0,0,3,1,0,3,3,6,10,21},{0,0,0,0,0,0,0,0,1,1,3,0,3,0,3,10,6,21},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,3,9,6,18},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,3,3,10},{0,0,0,0,0,0,0,0,0,0,0,1,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,850)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 4 & 3 & 3 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 2 & 1 & 1 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, -1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{0,0,1},{1,1,1},{1,0,0},{0,1,1},{0,1,1},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,3,5},{1,3,4},{1,2,4},{1,3,3},{0,2,4},{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: {{1,3,5,6,6,12,15,15,22,20,28,31,43,53,50,75,96,158},{0,1,1,3,1,5,6,5,12,6,15,15,20,31,20,43,50,96},{0,0,1,0,1,3,3,5,6,6,6,12,15,22,20,28,43,75},{0,0,0,1,0,1,1,1,5,1,6,5,6,15,6,20,20,50},{0,0,0,0,1,0,3,0,0,5,6,0,12,0,15,22,31,53},{0,0,0,0,0,1,1,1,3,1,3,5,6,12,6,15,20,43},{0,0,0,0,0,0,1,0,0,1,3,0,5,0,5,12,15,31},{0,0,0,0,0,0,0,1,0,1,0,3,3,6,6,6,15,28},{0,0,0,0,0,0,0,0,1,0,1,1,1,5,1,6,6,20},{0,0,0,0,0,0,0,0,0,1,0,0,3,0,5,6,12,22},{0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,1,1,3,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,3,5,12},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,851)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 2 & 1 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 2 & 3 & 2 & 2 & 2 & 1 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -1}}
Cones (18): {{0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3}, {4, 5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (18): {{1,2,4},{0,2,4},{1,2,3},{0,2,3},{1,2,2},{1,1,3},{1,1,2},{0,1,3},{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: {{1,2,3,6,6,5,12,10,12,24,15,22,44,30,31,62,53,106},{0,1,0,3,0,0,0,5,6,12,0,0,22,15,0,31,0,53},{0,0,1,2,3,1,5,2,6,10,5,12,24,10,15,30,31,62},{0,0,0,1,0,0,0,1,3,5,0,0,12,5,0,15,0,31},{0,0,0,0,1,0,1,0,2,2,1,5,10,2,5,10,15,30},{0,0,0,0,0,1,3,2,0,6,5,6,12,10,12,24,22,44},{0,0,0,0,0,0,1,0,0,2,1,3,6,2,5,10,12,24},{0,0,0,0,0,0,0,1,0,3,0,0,6,5,0,12,0,22},{0,0,0,0,0,0,0,0,1,1,0,0,5,1,0,5,0,15},{0,0,0,0,0,0,0,0,0,1,0,0,3,1,0,5,0,12},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,6,6,12},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,1,2,5,10},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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|
$(5,852)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 1, 1, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{2, 3, 4}, {5, 6}, {0, 1, 7}}
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},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,1,3},{1,1,3},{2,1,2},{0,1,3},{1,1,2},{2,0,2},{2,1,1},{1,0,2},{0,1,2},{2,0,1},{1,1,1},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,6,9,4,6,12,18,9,18,24,36,16,27,54,48,96},{0,1,0,3,3,0,0,4,9,0,6,12,18,0,9,27,16,48},{0,0,1,0,3,1,3,3,6,4,9,6,18,9,12,24,27,54},{0,0,0,1,0,0,0,0,3,0,0,4,6,0,0,9,0,16},{0,0,0,0,1,0,0,1,3,0,3,3,9,0,4,12,9,27},{0,0,0,0,0,1,0,3,0,3,0,6,0,6,9,18,18,36},{0,0,0,0,0,0,1,0,0,1,3,0,6,4,3,6,12,24},{0,0,0,0,0,0,0,1,0,0,0,3,0,0,3,9,6,18},{0,0,0,0,0,0,0,0,1,0,0,1,3,0,0,4,0,9},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,1,0,3,0,1,3,4,12},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,853)$ |
3 |
18 |
|
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8: $\begin{pmatrix}0 & 0 & 1 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
18: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 2 & 1 & 0 & 2 & 1 & 0 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|
Details:
Rays (8): {{-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 0, 1}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}, {1, 1, 0, 0, -1}}
Cones (18): {{0, 1, 2, 3, 4}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 5}, {0, 1, 2, 5, 6}, {0, 1, 3, 4, 5}, {0, 1, 3, 5, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 7}, {0, 3, 5, 6, 7}, {1, 2, 3, 4, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{2, 3, 5}, {4, 6}, {0, 1, 7}}
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},{-1,1,1},{1,0,0},{0,1,0},{0,0,1}}
Theta-collection (18): {{2,1,3},{1,1,3},{2,1,2},{0,1,3},{1,1,2},{2,0,2},{2,1,1},{1,0,2},{0,1,2},{2,0,1},{1,1,1},{0,0,2},{0,1,1},{2,0,0},{1,0,1},{0,0,1},{1,0,0},{0,0,0}}
Ext matrix: {{1,3,3,6,9,6,6,15,18,15,18,28,36,28,36,66,66,120},{0,1,0,3,3,1,0,6,9,3,6,15,18,6,15,36,28,66},{0,0,1,0,3,1,3,3,6,6,9,6,18,15,15,28,36,66},{0,0,0,1,0,0,0,1,3,0,0,6,6,0,3,15,6,28},{0,0,0,0,1,0,0,1,3,1,3,3,9,3,6,15,15,36},{0,0,0,0,0,1,0,3,0,3,0,6,0,6,9,18,18,36},{0,0,0,0,0,0,1,0,0,1,3,0,6,6,3,6,15,28},{0,0,0,0,0,0,0,1,0,0,0,3,0,0,3,9,6,18},{0,0,0,0,0,0,0,0,1,0,0,1,3,0,1,6,3,15},{0,0,0,0,0,0,0,0,0,1,0,0,0,3,3,6,9,18},{0,0,0,0,0,0,0,0,0,0,1,0,3,1,1,3,6,15},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,3,9},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,857)$ |
3 |
16 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 3 & 2 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, -1, 1, 1, 1}, {0, 0, 0, 0, -1}}
Cones (16): {{0, 2, 4, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 6}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7}}
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}}
Theta-collection (16): {{1,1,4},{0,1,4},{1,1,3},{0,1,3},{1,1,2},{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: {{1,2,4,8,10,5,20,14,20,10,28,30,40,60,55,110},{0,1,0,4,0,0,10,0,0,5,14,0,20,30,0,55},{0,0,1,2,4,1,8,5,10,2,10,14,20,28,30,60},{0,0,0,1,0,0,4,0,0,1,5,0,10,14,0,30},{0,0,0,0,1,0,2,1,4,0,2,5,8,10,14,28},{0,0,0,0,0,1,0,4,0,2,8,10,0,20,20,40},{0,0,0,0,0,0,1,0,0,0,1,0,4,5,0,14},{0,0,0,0,0,0,0,1,0,0,2,4,0,8,10,20},{0,0,0,0,0,0,0,0,1,0,0,1,2,2,5,10},{0,0,0,0,0,0,0,0,0,1,4,0,0,10,0,20},{0,0,0,0,0,0,0,0,0,0,1,0,0,4,0,10},{0,0,0,0,0,0,0,0,0,0,0,1,0,2,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,858)$ |
3 |
16 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\end{pmatrix}$
16: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 3 & 3 & 3 & 2 & 2 & 3 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 1, 1, 1}, {0, 0, 0, 0, -1}}
Cones (16): {{0, 2, 4, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 2, 5, 6, 7}, {0, 3, 4, 5, 6}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {0, 3, 5, 6, 7}, {1, 2, 4, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {1, 3, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}, {1, 3, 5, 6, 7}}
Primitive collections: {{0, 1}, {2, 3}, {4, 5, 6, 7}}
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}}
Theta-collection (16): {{1,1,3},{1,0,3},{0,1,3},{1,1,2},{0,1,2},{0,0,3},{1,0,2},{1,1,1},{0,0,2},{1,0,1},{1,1,0},{0,1,1},{0,0,1},{1,0,0},{0,1,0},{0,0,0}}
Ext matrix: {{1,2,2,4,8,4,8,10,16,20,20,20,40,40,40,80},{0,1,0,0,0,2,4,0,8,10,0,0,20,20,0,40},{0,0,1,0,4,2,0,0,8,0,0,10,20,0,20,40},{0,0,0,1,2,0,2,4,4,8,10,8,16,20,20,40},{0,0,0,0,1,0,0,0,2,0,0,4,8,0,10,20},{0,0,0,0,0,1,0,0,4,0,0,0,10,0,0,20},{0,0,0,0,0,0,1,0,2,4,0,0,8,10,0,20},{0,0,0,0,0,0,0,1,0,2,4,2,4,8,8,16},{0,0,0,0,0,0,0,0,1,0,0,0,4,0,0,10},{0,0,0,0,0,0,0,0,0,1,0,0,2,4,0,8},{0,0,0,0,0,0,0,0,0,0,1,0,0,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,1,2,0,4,8},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,859)$ |
3 |
18 |
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8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
18: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 2 & 1 & 2 & 1 & 2 & 0 & 0 & 1 & 0 & 1 & 2 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 2 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{1, 0, 0, 0, 0}, {-1, 0, 0, 0, 0}, {0, -1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, -1, 0, 0}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, 0, -1}}
Cones (18): {{0, 2, 3, 5, 6}, {0, 2, 3, 5, 7}, {0, 2, 3, 6, 7}, {0, 2, 4, 5, 6}, {0, 2, 4, 5, 7}, {0, 2, 4, 6, 7}, {0, 3, 4, 5, 6}, {0, 3, 4, 5, 7}, {0, 3, 4, 6, 7}, {1, 2, 3, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 6, 7}, {1, 2, 4, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 6, 7}, {1, 3, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 6, 7}}
Primitive collections: {{0, 1}, {2, 3, 4}, {5, 6, 7}}
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}}
Theta-collection (18): {{1,2,2},{1,1,2},{0,2,2},{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: {{1,3,2,3,6,6,9,6,6,12,18,18,18,12,36,36,36,72},{0,1,0,0,2,0,3,0,3,6,6,9,6,0,18,18,12,36},{0,0,1,0,3,3,0,0,0,6,9,0,0,6,18,0,18,36},{0,0,0,1,0,2,3,3,0,0,6,6,9,6,12,18,18,36},{0,0,0,0,1,0,0,0,0,3,3,0,0,0,9,0,6,18},{0,0,0,0,0,1,0,0,0,0,3,0,0,3,6,0,9,18},{0,0,0,0,0,0,1,0,0,0,2,3,3,0,6,9,6,18},{0,0,0,0,0,0,0,1,0,0,0,0,3,2,0,6,6,12},{0,0,0,0,0,0,0,0,1,2,0,3,0,0,6,6,0,12},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,3,0,0,6},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,3,0,3,9},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,3,0,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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$(5,865)$ |
3 |
14 |
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8: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 4 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & -1 & -1 & 0 & 1\end{pmatrix}$
19: $\begin{pmatrix}8 & 7 & 7 & 6 & 6 & 5 & 5 & 4 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & -1 & 0 & -1 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 0\end{pmatrix}$ |
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Details:
Rays (8): {{-1, -1, -1, 3, -1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 1}, {0, 0, 0, -1, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}
Cones (14): {{0, 1, 2, 3, 5}, {0, 1, 2, 3, 6}, {0, 1, 2, 4, 6}, {0, 1, 2, 4, 7}, {0, 1, 2, 5, 7}, {0, 1, 3, 4, 6}, {0, 1, 3, 4, 7}, {0, 1, 3, 5, 7}, {0, 2, 3, 4, 6}, {0, 2, 3, 4, 7}, {0, 2, 3, 5, 7}, {1, 2, 3, 4, 6}, {1, 2, 3, 4, 7}, {1, 2, 3, 5, 7}}
Primitive collections: {{0, 1, 2, 3, 4}, {4, 5}, {5, 6}, {0, 1, 2, 3, 7}, {6, 7}}
Chambers: ({{1,0,0},{0,1,0},{4,1,0},{1,0,-1},{4,1,-1},{0,0,1}},{{0,2,4},{1,3,4},{1,2,5},{0,3,4},{1,2,4},{0,2,5}},{2,1,1})
Cox degrees: {{1,0,0},{1,0,0},{1,0,0},{1,0,0},{1,0,-1},{4,1,-1},{0,1,0},{0,0,1}}
Theta-collection (19): {{8,1,-1},{7,1,0},{7,1,-1},{6,1,0},{6,1,-1},{5,1,0},{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: {{1,1,5,5,15,15,35,35,36,70,70,75,126,126,141,210,210,245,400},{0,1,1,5,5,15,15,35,35,35,70,71,70,126,131,126,210,225,365},{0,0,1,1,5,5,15,15,15,35,35,36,70,70,75,126,126,141,245},{0,0,0,1,1,5,5,15,15,15,35,35,35,70,71,70,126,131,225},{0,0,0,0,1,1,5,5,5,15,15,15,35,35,36,70,70,75,141},{0,0,0,0,0,1,1,5,5,5,15,15,15,35,35,35,70,71,131},{0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,35,35,36,75},{0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,35,35,71},{0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,0,0,35,70},{0,0,0,0,0,0,0,0,0,1,1,1,5,5,5,15,15,15,36},{T^4,0,0,0,0,0,0,0,T^4,0,1,1,1,5,5,5,15,15,35},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,0,0,15,35},{T^4,T^4,0,0,0,0,0,0,T^4,0,0,0,1,1,1,5,5,5,15},{5*T^4,T^4,T^4,0,0,0,0,0,5*T^4,0,0,T^4,0,1,1,1,5,5,15},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,5,15},{5*T^4,5*T^4,T^4,T^4,0,0,0,0,5*T^4,0,0,T^4,0,0,0,1,1,1,5},{15*T^4,5*T^4,5*T^4,T^4,T^4,0,0,0,15*T^4,0,0,5*T^4,0,0,T^4,0,1,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,5},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}
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