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Smooth Fano Toric 3-folds
There are 18 varieties in this class:
| $(\dim,\#)$ | $\operatorname{rk} \mathrm{Pic}$ | $\operatorname{rk} K_0$ | 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: $\begin{pmatrix}0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 2 & 0 & 0 & 1 & 2 & 1 & 2 & 1 & 2 & 4 & 7 \\ 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 4 \\ 0 & 0 & 1 & 2 & 1 & 2 & 2 & 3 & 1 & 2 & 5 & 8 \\ 0 & 0 & 0 & 1 & 0 & 1 & 1 & 2 & 0 & 1 & 2 & 5 \\ 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 0 & 0 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 0 & 2 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ |