As abstract polytope gadtap is isomorph to sadtap, thereby replacing decagrams by decagons, resp. stiddip by dip and stadidip by dedip.

Gadtap occurs in 3 different forms depending on whether the vertices (coincident by 6) will be counted separately (type A), or will be identified (type B). Also edges coincide pairwise, which might be identified additionally (type C).

Incidence matrix

```(Type A)

3600 |    4 |    4   2 |   4 ||  1
------+------+----------+-----++---
2 | 7200 |    2   1 |   3 ||  1
------+------+----------+-----++---
4 |    4 | 3600   * |   2 ||  1
10 |   10 |    * 720 |   2 ||  1
------+------+----------+-----++---
♦  20 |   30 |   10   2 | 720 ||  1
------+------+----------+-----++---
♦ 100 |  200 |  100  20 |  20 || 36
```

```(Type B)

600 |   24 |   24  12 |  24 ||  6
------+------+----------+-----++---
2 | 7200 |    2   1 |   3 ||  1
------+------+----------+-----++---
4 |    4 | 3600   * |   2 ||  1
10 |   10 |    * 720 |   2 ||  1
------+------+----------+-----++---
♦  20 |   30 |   10   2 | 720 ||  1
------+------+----------+-----++---
♦ 100 |  200 |  100  20 |  20 || 36
```

```(Type C)

600 |   12 |   24  12 |  24 ||  6
------+------+----------+-----++---
2 | 3600 |    4   2 |   6 ||  2
------+------+----------+-----++---
4 |    4 | 3600   * |   2 ||  1
10 |   10 |    * 720 |   2 ||  1
------+------+----------+-----++---
♦  20 |   30 |   10   2 | 720 ||  1
------+------+----------+-----++---
♦ 100 |  200 |  100  20 |  20 || 36
```