FanoCats

Smooth Fano Toric 4-folds with $\rho=7$

ID	$\operatorname{rk} \mathrm{Pic}$	$\operatorname{rk} K_0$	Fan	Chambers	Cox degrees and $\Theta$-collection	Ext table
$(4,119)$	7	30			11: $\begin{pmatrix}1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 1\end{pmatrix}$ 30: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
Details: Rays (11): {{1, 0, 0, 0}, {0, 1, 0, 0}, {-1, 1, 0, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, -1, 1}, {0, 0, -1, 0}, {0, 0, 0, -1}, {0, 0, 1, -1}} Cones (30): {{0, 1, 5, 6}, {0, 1, 5, 10}, {0, 1, 6, 7}, {0, 1, 7, 8}, {0, 1, 8, 9}, {0, 1, 9, 10}, {0, 4, 5, 6}, {0, 4, 5, 10}, {0, 4, 6, 7}, {0, 4, 7, 8}, {0, 4, 8, 9}, {0, 4, 9, 10}, {1, 2, 5, 6}, {1, 2, 5, 10}, {1, 2, 6, 7}, {1, 2, 7, 8}, {1, 2, 8, 9}, {1, 2, 9, 10}, {2, 3, 5, 6}, {2, 3, 5, 10}, {2, 3, 6, 7}, {2, 3, 7, 8}, {2, 3, 8, 9}, {2, 3, 9, 10}, {3, 4, 5, 6}, {3, 4, 5, 10}, {3, 4, 6, 7}, {3, 4, 7, 8}, {3, 4, 8, 9}, {3, 4, 9, 10}} Primitive collections: {{0, 2}, {0, 3}, {1, 3}, {1, 4}, {2, 4}, {5, 7}, {5, 8}, {6, 8}, {5, 9}, {6, 9}, {7, 9}, {6, 10}, {7, 10}, {8, 10}} Chambers: 90 Cox degrees: {{1,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{1,-1,1,0,0,0,0},{0,1,-1,0,0,0,0},{0,0,1,0,0,0,0},{0,0,0,1,0,0,-1},{0,0,0,-1,1,0,1},{0,0,0,1,-1,1,0},{0,0,0,0,1,-1,0},{0,0,0,0,0,1,0},{0,0,0,0,0,0,1}} Theta-collection (30): {{1,0,1,0,1,0,1},{1,0,1,1,0,1,0},{0,1,0,1,0,1,0},{0,1,0,0,1,0,1},{1,0,0,0,1,0,1},{0,0,1,1,0,1,0},{0,0,1,0,1,0,1},{1,0,1,0,0,1,1},{1,0,1,1,0,0,0},{1,0,1,0,1,0,0},{1,0,0,1,0,1,0},{0,1,0,1,0,0,0},{0,1,0,0,0,1,1},{0,1,0,0,1,0,0},{0,0,1,0,0,1,1},{0,0,0,1,0,1,0},{0,0,1,0,1,0,0},{0,0,1,1,0,0,0},{1,0,0,0,1,0,0},{1,0,0,1,0,0,0},{0,0,0,0,1,0,1},{1,0,0,0,0,1,1},{0,0,0,0,0,1,1},{0,0,0,0,1,0,0},{0,0,0,1,0,0,0},{1,0,1,0,0,0,0},{0,1,0,0,0,0,0},{0,0,1,0,0,0,0},{1,0,0,0,0,0,0},{0,0,0,0,0,0,0}} Ext matrix: {{1,0,0,1,2,0,2,1,1,1,0,1,1,1,2,0,2,2,2,2,4,2,4,4,4,3,3,6,6,12},{0,1,1,0,0,2,0,1,1,1,2,1,1,1,2,4,2,2,2,2,0,2,4,4,4,3,3,6,6,12},{0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,3,1,1,1,1,0,1,3,3,3,0,3,3,3,9},{0,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,1,1,1,1,3,1,3,3,3,0,3,3,3,9},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,2,2,2,0,0,0,3,6},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,2,1,1,0,0,0,0,2,2,2,0,0,3,0,6},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,2,0,2,2,2,0,0,3,0,6},{0,0,0,0,0,0,0,1,0,0,0,0,1,0,2,0,0,0,0,0,0,2,4,0,0,2,2,4,4,8},{0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,2,0,2,0,0,0,0,4,2,2,4,4,8},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,2,0,2,0,0,0,0,4,0,2,2,4,4,8},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,1,1,0,1,2,2,2,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,3,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,3,0,0,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,3,0,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}

$\operatorname{rk} \mathrm{Pic}$

$\operatorname{rk} K_0$

Fan

Chambers

Cox degrees and $\Theta$-collection

Ext table

11: $\begin{pmatrix}1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 1 & 0 & 0 & 0 & 1\end{pmatrix}$
30: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$

Details:
Rays (11): {{1, 0, 0, 0}, {0, 1, 0, 0}, {-1, 1, 0, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, -1, 1}, {0, 0, -1, 0}, {0, 0, 0, -1}, {0, 0, 1, -1}}
Cones (30): {{0, 1, 5, 6}, {0, 1, 5, 10}, {0, 1, 6, 7}, {0, 1, 7, 8}, {0, 1, 8, 9}, {0, 1, 9, 10}, {0, 4, 5, 6}, {0, 4, 5, 10}, {0, 4, 6, 7}, {0, 4, 7, 8}, {0, 4, 8, 9}, {0, 4, 9, 10}, {1, 2, 5, 6}, {1, 2, 5, 10}, {1, 2, 6, 7}, {1, 2, 7, 8}, {1, 2, 8, 9}, {1, 2, 9, 10}, {2, 3, 5, 6}, {2, 3, 5, 10}, {2, 3, 6, 7}, {2, 3, 7, 8}, {2, 3, 8, 9}, {2, 3, 9, 10}, {3, 4, 5, 6}, {3, 4, 5, 10}, {3, 4, 6, 7}, {3, 4, 7, 8}, {3, 4, 8, 9}, {3, 4, 9, 10}}
Primitive collections: {{0, 2}, {0, 3}, {1, 3}, {1, 4}, {2, 4}, {5, 7}, {5, 8}, {6, 8}, {5, 9}, {6, 9}, {7, 9}, {6, 10}, {7, 10}, {8, 10}}
Chambers: 90
Cox degrees: {{1,0,0,0,0,0,0},{-1,1,0,0,0,0,0},{1,-1,1,0,0,0,0},{0,1,-1,0,0,0,0},{0,0,1,0,0,0,0},{0,0,0,1,0,0,-1},{0,0,0,-1,1,0,1},{0,0,0,1,-1,1,0},{0,0,0,0,1,-1,0},{0,0,0,0,0,1,0},{0,0,0,0,0,0,1}}
Theta-collection (30): {{1,0,1,0,1,0,1},{1,0,1,1,0,1,0},{0,1,0,1,0,1,0},{0,1,0,0,1,0,1},{1,0,0,0,1,0,1},{0,0,1,1,0,1,0},{0,0,1,0,1,0,1},{1,0,1,0,0,1,1},{1,0,1,1,0,0,0},{1,0,1,0,1,0,0},{1,0,0,1,0,1,0},{0,1,0,1,0,0,0},{0,1,0,0,0,1,1},{0,1,0,0,1,0,0},{0,0,1,0,0,1,1},{0,0,0,1,0,1,0},{0,0,1,0,1,0,0},{0,0,1,1,0,0,0},{1,0,0,0,1,0,0},{1,0,0,1,0,0,0},{0,0,0,0,1,0,1},{1,0,0,0,0,1,1},{0,0,0,0,0,1,1},{0,0,0,0,1,0,0},{0,0,0,1,0,0,0},{1,0,1,0,0,0,0},{0,1,0,0,0,0,0},{0,0,1,0,0,0,0},{1,0,0,0,0,0,0},{0,0,0,0,0,0,0}}
Ext matrix: {{1,0,0,1,2,0,2,1,1,1,0,1,1,1,2,0,2,2,2,2,4,2,4,4,4,3,3,6,6,12},{0,1,1,0,0,2,0,1,1,1,2,1,1,1,2,4,2,2,2,2,0,2,4,4,4,3,3,6,6,12},{0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,3,1,1,1,1,0,1,3,3,3,0,3,3,3,9},{0,0,0,1,1,0,1,0,0,0,0,1,1,1,1,0,1,1,1,1,3,1,3,3,3,0,3,3,3,9},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,1,2,2,2,0,0,0,3,6},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,2,1,1,0,0,0,0,2,2,2,0,0,3,0,6},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,2,0,2,2,2,0,0,3,0,6},{0,0,0,0,0,0,0,1,0,0,0,0,1,0,2,0,0,0,0,0,0,2,4,0,0,2,2,4,4,8},{0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,2,0,2,0,0,0,0,4,2,2,4,4,8},{0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,2,0,2,0,0,0,0,4,0,2,2,4,4,8},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,1,1,0,1,2,2,2,0,0,0,3,6},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,3,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,3,0,0,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,3,0,0,2,2,2,6},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2,0,0,2,0,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,2,4},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,3},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}}