Acronym dird Name dirhimbidodecahedron,compound of 12 pip ` © ©` Circumradius sqrt[(15+2 sqrt(5))/20] = 0.986715 Vertex figure 2[42,5] General of army f3x5o Colonel of regiment (itself, although not being locally convex) Externallinks

As abstract polytope dird is isomorphic to giddird, thereby replacing pentagons by pentagrams, respectively pip by stip.

Vertices coincide by pairs. So either both can be considered separately (type A) or are identified (type B). Finally, instead of considering individual pip, it can likewise be seen as a compound of 2 (different handed) kred (type C).

Incidence matrix

```(Type A)

120 |   2  1 |  2  1 ||  1
-----+--------+-------++---
2 | 120  * |  1  1 ||  1
2 |   * 60 |  2  0 ||  1
-----+--------+-------++---
4 |   2  2 | 60  * ||  1
5 |   5  0 |  * 24 ||  1
-----+--------+-------++---
♦ 10 |  10  5 |  5  2 || 12
```

```(Type B)

60 |   4  2 |  4  2 ||  2
-----+--------+-------++---
2 | 120  * |  1  1 ||  1
2 |   * 60 |  2  0 ||  1
-----+--------+-------++---
4 |   2  2 | 60  * ||  1
5 |   5  0 |  * 24 ||  1
-----+--------+-------++---
♦ 10 |  10  5 |  5  2 || 12
```

```(Type C)

120 |   2  1 |  2  1 || 1
-----+--------+-------++--
2 | 120  * |  1  1 || 1
2 |   * 60 |  2  0 || 1
-----+--------+-------++--
4 |   2  2 | 60  * || 1
5 |   5  0 |  * 24 || 1
-----+--------+-------++--
♦ 60 |  60 30 | 30 12 || 2
```