FanoCats

(Toric) Fano Categories Database

See smallAmpleToricDivisor(2,i) for more information.

Toric Varieties Corresponding to Small 2D Polytopes

ID $\operatorname{rk} \mathrm{Pic}$ $\operatorname{rk} K_0$ Fan Chambers Cox degrees and $\Theta$-collection Ext table
$0$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$1$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$2$ 2 4 4: $\begin{pmatrix}1 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$3$ 2 4 4: $\begin{pmatrix}1 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$4$ 2 4 4: $\begin{pmatrix}-1 & -1 & 2 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}-1 & 0 & 1 & -1 & 0 \\ 1 & 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 6 \\ 0 & 1 & 2 & 2 & 4 \\ T & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$5$ 1 3 3: $\begin{pmatrix}1 & 1 & 1\end{pmatrix}$
3: $\begin{pmatrix}2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 3 & 6 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{pmatrix}$
$6$ 1 3 3: $\begin{pmatrix}1 & 1 & 1\end{pmatrix}$
3: $\begin{pmatrix}2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 3 & 6 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{pmatrix}$
$7$ 1 3 3: $\begin{pmatrix}1 & 1 & 1\end{pmatrix}$
3: $\begin{pmatrix}2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 3 & 6 \\ 0 & 1 & 3 \\ 0 & 0 & 1\end{pmatrix}$
$8$ 3 5 5: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 2 & 2 & 4 \\ 0 & 1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$9$ 3 5 5: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 2 & 2 & 4 \\ 0 & 1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$10$ 3 5 5: $\begin{pmatrix}-1 & -1 & 2 & 0 & 0 \\ 0 & -1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1\end{pmatrix}$
6: $\begin{pmatrix}-1 & 0 & 0 & 1 & -1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 1 & 2 & 2 & 3 & 5 \\ 0 & 1 & 1 & 2 & 2 & 4 \\ 0 & 0 & 1 & 1 & 1 & 3 \\ T & 0 & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$11$ 4 6 6: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 \\ -1 & 0 & 0 & 0 & -1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 1 & 1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 3 \\ 0 & 1 & 1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$12$ 4 6 6: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 \\ -1 & 0 & 0 & 0 & -1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 1 & 1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 3 \\ 0 & 1 & 1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$13$ 4 6 6: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 0 & 1 & 1 & 0 \\ -1 & 0 & 0 & 0 & -1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 1 & 1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 0 & 1 & 1 & 1 & 3 \\ 0 & 1 & 1 & 1 & 1 & 3 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$14$ 2 4 4: $\begin{pmatrix}-1 & -1 & 1 & 0 \\ 1 & 1 & 0 & 1\end{pmatrix}$
4: $\begin{pmatrix}-1 & 0 & -1 & 0 \\ 2 & 1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$15$ 6 8 8: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & -1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
12: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 1 & 0 & 1 & 2 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 2 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 0 & 0 & T & 0 & 1 & 0 & 1 & 1+T & 0 & 1 & 2 \\ 0 & 1 & T & 0 & 0 & 1 & 1 & 0 & 0 & 1+T & 1 & 2 \\ 0 & T & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1+T & 1 & 2 \\ T & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1+T & 0 & 1 & 2 \\ T & T & 0 & 0 & 1 & 0 & 0 & 0 & T & T & 1 & 1 \\ 0 & 0 & T & T & 0 & 1 & 0 & 0 & T & T & 1 & 1 \\ T & 0 & T & 0 & 0 & 0 & 1 & 0 & T & T & 1 & 1 \\ 0 & T & 0 & T & 0 & 0 & 0 & 1 & T & T & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 \\ T & T & T & T & 0 & 0 & 0 & 0 & 2T & 2T & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$16$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$17$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -1 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$18$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -2 & 0 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 6 \\ 0 & 1 & 2 & 2 & 4 \\ T & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$19$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -3 & 0 & 1 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 7 \\ 0 & 1 & 2 & 3 & 3 & 5 \\ T & 0 & 1 & 2 & 2+T & 3 \\ 2T & T & 0 & 1 & 1+2T & 2+T \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$20$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -4 & 0 & 1 & 1\end{pmatrix}$
7: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 8 \\ 0 & 1 & 2 & 3 & 4 & 4 & 6 \\ T & 0 & 1 & 2 & 3 & 3+T & 4 \\ 2T & T & 0 & 1 & 2 & 2+2T & 3+T \\ T & 2T & T & 0 & 1 & 1+T & 2+2T \\ 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$21$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -5 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 9 \\ 0 & 1 & 2 & 3 & 4 & 5 & 5 & 7 \\ T & 0 & 1 & 2 & 3 & 4 & 4+T & 5 \\ 2T & T & 0 & 1 & 2 & 3 & 3+2T & 4+T \\ T & 2T & T & 0 & 1 & 2 & 2+T & 3+2T \\ 0 & T & 2T & T & 0 & 1 & 1 & 2+T \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$22$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -6 & 0 & 1 & 1\end{pmatrix}$
9: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & -5 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 10 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 6 & 8 \\ T & 0 & 1 & 2 & 3 & 4 & 5 & 5+T & 6 \\ 2T & T & 0 & 1 & 2 & 3 & 4 & 4+2T & 5+T \\ T & 2T & T & 0 & 1 & 2 & 3 & 3+T & 4+2T \\ 0 & T & 2T & T & 0 & 1 & 2 & 2 & 3+T \\ 0 & 0 & T & 2T & T & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$23$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -7 & 0 & 1 & 1\end{pmatrix}$
10: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & -5 & -6 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 11 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 7 & 9 \\ T & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 6+T & 7 \\ 2T & T & 0 & 1 & 2 & 3 & 4 & 5 & 5+2T & 6+T \\ T & 2T & T & 0 & 1 & 2 & 3 & 4 & 4+T & 5+2T \\ 0 & T & 2T & T & 0 & 1 & 2 & 3 & 3 & 4+T \\ 0 & 0 & T & 2T & T & 0 & 1 & 2 & 2 & 3 \\ 0 & 0 & 0 & T & 2T & T & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$24$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -8 & 0 & 1 & 1\end{pmatrix}$
11: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & -5 & -6 & -7 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 12 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 8 & 10 \\ T & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 7+T & 8 \\ 2T & T & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 6+2T & 7+T \\ T & 2T & T & 0 & 1 & 2 & 3 & 4 & 5 & 5+T & 6+2T \\ 0 & T & 2T & T & 0 & 1 & 2 & 3 & 4 & 4 & 5+T \\ 0 & 0 & T & 2T & T & 0 & 1 & 2 & 3 & 3 & 4 \\ 0 & 0 & 0 & T & 2T & T & 0 & 1 & 2 & 2 & 3 \\ 0 & 0 & 0 & 0 & T & 2T & T & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$25$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$26$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -1 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$27$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -2 & 0 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 6 \\ 0 & 1 & 2 & 2 & 4 \\ T & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$28$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -3 & 0 & 1 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 7 \\ 0 & 1 & 2 & 3 & 3 & 5 \\ T & 0 & 1 & 2 & 2+T & 3 \\ 2T & T & 0 & 1 & 1+2T & 2+T \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$29$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -4 & 0 & 1 & 1\end{pmatrix}$
7: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 8 \\ 0 & 1 & 2 & 3 & 4 & 4 & 6 \\ T & 0 & 1 & 2 & 3 & 3+T & 4 \\ 2T & T & 0 & 1 & 2 & 2+2T & 3+T \\ T & 2T & T & 0 & 1 & 1+T & 2+2T \\ 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$30$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -5 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 9 \\ 0 & 1 & 2 & 3 & 4 & 5 & 5 & 7 \\ T & 0 & 1 & 2 & 3 & 4 & 4+T & 5 \\ 2T & T & 0 & 1 & 2 & 3 & 3+2T & 4+T \\ T & 2T & T & 0 & 1 & 2 & 2+T & 3+2T \\ 0 & T & 2T & T & 0 & 1 & 1 & 2+T \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$31$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -6 & 0 & 1 & 1\end{pmatrix}$
9: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & -4 & -5 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 10 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 6 & 8 \\ T & 0 & 1 & 2 & 3 & 4 & 5 & 5+T & 6 \\ 2T & T & 0 & 1 & 2 & 3 & 4 & 4+2T & 5+T \\ T & 2T & T & 0 & 1 & 2 & 3 & 3+T & 4+2T \\ 0 & T & 2T & T & 0 & 1 & 2 & 2 & 3+T \\ 0 & 0 & T & 2T & T & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$32$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$33$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -1 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$34$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -2 & 0 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 6 \\ 0 & 1 & 2 & 2 & 4 \\ T & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$35$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -3 & 0 & 1 & 1\end{pmatrix}$
6: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 7 \\ 0 & 1 & 2 & 3 & 3 & 5 \\ T & 0 & 1 & 2 & 2+T & 3 \\ 2T & T & 0 & 1 & 1+2T & 2+T \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$36$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -4 & 0 & 1 & 1\end{pmatrix}$
7: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & -2 & -3 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 5 & 6 & 8 \\ 0 & 1 & 2 & 3 & 4 & 4 & 6 \\ T & 0 & 1 & 2 & 3 & 3+T & 4 \\ 2T & T & 0 & 1 & 2 & 2+2T & 3+T \\ T & 2T & T & 0 & 1 & 1+T & 2+2T \\ 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$37$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$38$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -1 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 5 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$
$39$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ -2 & 0 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 \\ 1 & 0 & -1 & 1 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 3 & 4 & 6 \\ 0 & 1 & 2 & 2 & 4 \\ T & 0 & 1 & 1+T & 2 \\ 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 1\end{pmatrix}$
$40$ 2 4 4: $\begin{pmatrix}1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$
4: $\begin{pmatrix}1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0\end{pmatrix}$		 $\begin{pmatrix}1 & 2 & 2 & 4 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1\end{pmatrix}$