Acronym idisdid Name invertidisnub dodecadodecahedron, compound of 2 isdid ` © ©` Vertex figure [32,5/3,3,5] Externallinks

Both, the pentagrams and the pentagons, coincide by their face planes pairwise each. So either all are considered separately (type A), or pentagram pairs are considered as (rotated) compounds while pentagons are considered separately (type B), or conversely pentagon pairs are considered as (rotated) compounds while pentagrams are considered separately (type C), or both are considered as compounds (type D).

Incidence matrix

```(Type A)

120 |   2  2   2 |  1   3  1 || 1
-----+------------+-----------++--
2 | 120  *   * |  1   1  0 || 1
2 |   * 60   * |  0   2  0 || 1
2 |   *  * 120 |  0   1  1 || 1
-----+------------+-----------++--
5 |   5  0   0 | 24   *  * || 1
3 |   1  1   1 |  * 120  * || 1
5 |   0  0   5 |  *   * 24 || 1
-----+------------+-----------++--
♦ 60 |  60 30  60 | 12  60 12 || 2
```

```(Type B)

120 |   2  2   2 |  1   3  1 || 1
-----+------------+-----------++--
2 | 120  *   * |  1   1  0 || 1
2 |   * 60   * |  0   2  0 || 1
2 |   *  * 120 |  0   1  1 || 1
-----+------------+-----------++--
10 |  10  0   0 | 12   *  * || 2
3 |   1  1   1 |  * 120  * || 1
5 |   0  0   5 |  *   * 24 || 1
-----+------------+-----------++--
♦ 60 |  60 30  60 | 12  60 12 || 2
```

```(Type C)

120 |   2  2   2 |  1   3  1 || 1
-----+------------+-----------++--
2 | 120  *   * |  1   1  0 || 1
2 |   * 60   * |  0   2  0 || 1
2 |   *  * 120 |  0   1  1 || 1
-----+------------+-----------++--
5 |   5  0   0 | 24   *  * || 1
3 |   1  1   1 |  * 120  * || 1
10 |   0  0  10 |  *   * 12 || 2
-----+------------+-----------++--
♦ 60 |  60 30  60 | 12  60 12 || 2
```

```(Type D)

120 |   2  2   2 |  1   3  1 || 1
-----+------------+-----------++--
2 | 120  *   * |  1   1  0 || 1
2 |   * 60   * |  0   2  0 || 1
2 |   *  * 120 |  0   1  1 || 1
-----+------------+-----------++--
10 |  10  0   0 | 12   *  * || 2
3 |   1  1   1 |  * 120  * || 1
10 |   0  0  10 |  *   * 12 || 2
-----+------------+-----------++--
♦ 60 |  60 30  60 | 12  60 12 || 2
```

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