FanoCats

(Toric) Fano Categories Database

Also see: https://www.fanography.info/toric

Smooth Fano Toric 3-folds

ID $\operatorname{rk} \mathrm{Pic}$ $\operatorname{rk} K_0$ Fan Chambers Cox degrees and $\Theta$-collection Ext table
$(3,0)$ 1 4 4: $\begin{pmatrix}1 & 1 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}3 & 2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 4 & 10 & 20 \\ 0 & 1 & 4 & 10 \\ 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$(3,1)$ 2 6 5: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & -2\end{pmatrix}$
7: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & -1 & 2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 3 & 6 & 10 & 7 & 13 & 21 \\ 0 & 1 & 3 & 6 & 3 & 7 & 13 \\ 0 & 0 & 1 & 3 & 1 & 3 & 7 \\ T^2 & 0 & 0 & 1 & T^2 & 1 & 3 \\ 0 & 0 & 0 & 0 & 1 & 3 & 6 \\ 0 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,2)$ 2 6 5: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & -1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 3 & 4 & 6 & 9 & 16 \\ 0 & 1 & 1 & 3 & 4 & 9 \\ 0 & 0 & 1 & 0 & 3 & 6 \\ 0 & 0 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,3)$ 2 6 5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 1 & 1\end{pmatrix}$
6: $\begin{pmatrix}2 & 2 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 4 & 7 & 10 & 16 \\ 0 & 1 & 1 & 4 & 4 & 10 \\ 0 & 0 & 1 & 2 & 4 & 7 \\ 0 & 0 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,4)$ 2 6 5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1\end{pmatrix}$
6: $\begin{pmatrix}2 & 2 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 6 & 6 & 12 \\ 0 & 1 & 0 & 3 & 0 & 6 \\ 0 & 0 & 1 & 2 & 3 & 6 \\ 0 & 0 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,5)$ 3 8 6: $\begin{pmatrix}1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 & 5 & 8 & 8 & 13 \\ 0 & 1 & 0 & 2 & 2 & 5 & 3 & 8 \\ 0 & 0 & 1 & 2 & 2 & 3 & 5 & 8 \\ 0 & 0 & 0 & 1 & 1 & 2 & 2 & 5 \\ 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,6)$ 3 8 6: $\begin{pmatrix}1 & 1 & 0 & -1 & 0 & 0 \\ 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 7 & 9 & 14 \\ 0 & 1 & 1 & 1 & 3 & 4 & 4 & 9 \\ 0 & 0 & 1 & 1 & 2 & 2 & 4 & 7 \\ 0 & 0 & 0 & 1 & 0 & 2 & 3 & 5 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,7)$ 3 8 6: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 & 2 & 4 & 4 & 8 \\ 0 & 1 & 0 & 2 & 0 & 2 & 0 & 4 \\ 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,8)$ 3 8 6: $\begin{pmatrix}1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 & 3 & 6 & 5 & 10 \\ 0 & 1 & 0 & 2 & 0 & 3 & 0 & 5 \\ 0 & 0 & 1 & 2 & 1 & 2 & 3 & 6 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,9)$ 3 8 6: $\begin{pmatrix}1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 0 & -1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 & 4 & 7 & 7 & 12 \\ 0 & 1 & 0 & 2 & 1 & 4 & 2 & 7 \\ 0 & 0 & 1 & 2 & 1 & 2 & 4 & 7 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,10)$ 3 8 6: $\begin{pmatrix}1 & 1 & -2 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1\end{pmatrix}$
9: $\begin{pmatrix}2 & 1 & 1 & 0 & 0 & 2 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 3 & 3 & 6 & 4 & 6 & 9 & 16 \\ 0 & 1 & 1 & 3 & 3 & 3 & 6 & 7 & 13 \\ 0 & 0 & 1 & 1 & 3 & 1 & 3 & 4 & 9 \\ 0 & 0 & 0 & 1 & 1 & 1 & 3 & 3 & 7 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 6 \\ T^2 & 0 & 0 & 0 & 0 & T^2 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,11)$ 3 8 6: $\begin{pmatrix}-1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & 1 & 1 & 1 & -1\end{pmatrix}$
8: $\begin{pmatrix}1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 2 & 3 & 3 & 6 & 6 & 12 \\ 0 & 1 & 1 & 1 & 3 & 4 & 3 & 9 \\ 0 & 0 & 1 & 0 & 0 & 3 & 0 & 6 \\ 0 & 0 & 0 & 1 & 1 & 2 & 3 & 6 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,12)$ 4 10 7: $\begin{pmatrix}1 & -1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 1 & 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & -1\end{pmatrix}$
10: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 1 & 2 & 2 & 4 & 3 & 5 & 6 & 10 \\ 0 & 1 & 0 & 1 & 0 & 2 & 1 & 3 & 2 & 6 \\ 0 & 0 & 1 & 2 & 1 & 2 & 2 & 3 & 5 & 8 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 2 & 2 & 5 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,13)$ 4 10 7: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & -1 \\ 1 & -1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 1 & -1\end{pmatrix}$
10: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 3 & 3 & 3 & 5 & 5 & 8 & 12 \\ 0 & 1 & 1 & 2 & 1 & 1 & 3 & 3 & 4 & 8 \\ 0 & 0 & 1 & 2 & 1 & 1 & 2 & 2 & 4 & 7 \\ 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 1 & 0 & 2 & 0 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,14)$ 4 10 7: $\begin{pmatrix}1 & -1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & -1\end{pmatrix}$
10: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 2 & 2 & 2 & 4 & 2 & 4 & 4 & 8 \\ 0 & 1 & 0 & 2 & 1 & 2 & 1 & 2 & 3 & 6 \\ 0 & 0 & 1 & 1 & 0 & 2 & 0 & 2 & 0 & 4 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,15)$ 4 10 7: $\begin{pmatrix}1 & -1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 1 & 1 & -1 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 1 & -1\end{pmatrix}$
10: $\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 1 & 2 & 3 & 5 & 2 & 4 & 6 & 10 \\ 0 & 1 & 0 & 1 & 1 & 3 & 0 & 2 & 2 & 6 \\ 0 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 4 & 7 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,16)$ 5 12 8: $\begin{pmatrix}1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
12: $\begin{pmatrix}0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 0 & 2 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 3 & 6 \\ 0 & 1 & 0 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 3 & 6 \\ 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$(3,17)$ 5 12 8: $\begin{pmatrix}1 & -1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1 & 1 & 0 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & -1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
12: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 0 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 4 & 7 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 4 \\ 0 & 0 & 1 & 2 & 1 & 2 & 2 & 3 & 1 & 2 & 5 & 8 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 2 & 0 & 1 & 2 & 5 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 0 & 0 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$