Smooth Fano Toric 4-folds with $\rho=3$
| ID | $\operatorname{rk} \mathrm{Pic}$ | $\operatorname{rk} K_0$ | Fan | Chamers | Cox degrees and $\Theta$-collection | Ext table |
|---|---|---|---|---|---|---|
| $(4,10)$ | 3 | 11 |
7: $\begin{pmatrix}-3 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 14: $\begin{pmatrix}3 & 2 & 2 & 1 & 1 & 0 & 3 & 0 & -1 & 2 & -1 & -2 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,11)$ | 3 | 11 |
7: $\begin{pmatrix}-2 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}3 & 2 & 2 & 1 & 1 & 3 & 0 & 0 & 2 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,12)$ | 3 | 11 |
7: $\begin{pmatrix}-1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 11: $\begin{pmatrix}3 & 2 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,13)$ | 3 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 1 & 1 & 1 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 2 & 1 & 1 & 0 & -1 & 0 & -1 & 2 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,14)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 15: $\begin{pmatrix}2 & 1 & 0 & -1 & 2 & 2 & 1 & 0 & 1 & -1 & 0 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,15)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 14: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & -1 & 2 & 0 & -1 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,16)$ | 3 | 12 |
7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 1 & 1 & 0 & 2 & 0 & -1 & 2 & -1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,17)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 14: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 0 & 2 & -1 & -1 & 1 & 2 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$ |
|||
| $(4,18)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 0 & 2 & 1 & 2 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,19)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,20)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,21)$ | 3 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & -1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 13: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 2 & 2 & 1 & 1 & -1 & 0 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,22)$ | 3 | 12 |
7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 1 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,23)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$ |
|||
| $(4,24)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,25)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,26)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,27)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,28)$ | 3 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & -1 & 0 & 0 & -1\end{pmatrix}$ 13: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 1 & 2 & 0 & 1 & -1 & 2 & 0 & 1 & 2 & 0 & -1 & 1 & 0\end{pmatrix}$ |
|||
| $(4,29)$ | 3 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,30)$ | 3 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 & 0 & -2\end{pmatrix}$ 14: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 1 & -1 & 2 & 0 & 1 & 2 & -1 & 0 & 1 & 0\end{pmatrix}$ |
|||
| $(4,31)$ | 3 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 & 0 & -1\end{pmatrix}$ 12: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
|||
| $(4,32)$ | 3 | 13 |
7: $\begin{pmatrix}-2 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & -1 & 0 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1\end{pmatrix}$ 17: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & -1 & 0 & -1 & 1 & 2 & 1 & 1 & 0 & 0 \\ 0 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 2 & 0 & 1 & 1 & -1 & 0 & -1 & 1 & 0 \\ 1 & 0 & 2 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 0 & -1 & 1 & 0 & 1 & -1 & 0\end{pmatrix}$ |
|||
| $(4,33)$ | 3 | 13 |
7: $\begin{pmatrix}-2 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$ 15: $\begin{pmatrix}2 & 1 & 1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,34)$ | 3 | 13 |
7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & -1 & 0 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1\end{pmatrix}$ 15: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & -1 & 2 & 0 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & -1 & 1 & 0 \\ 1 & 0 & 2 & -1 & 1 & 0 & 0 & -1 & 1 & 2 & 1 & 0 & 1 & -1 & 0\end{pmatrix}$ |
|||
| $(4,35)$ | 3 | 13 |
7: $\begin{pmatrix}-1 & -1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$ 14: $\begin{pmatrix}1 & 1 & 0 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$ |
|||
| $(4,36)$ | 3 | 13 |
7: $\begin{pmatrix}1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$ 14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & -1 & 1 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$ |
|||
| $(4,37)$ | 3 | 13 |
7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$ 13: $\begin{pmatrix}2 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$ |