Acronym	gidisdrid
Name	great disnub dirhombicosidodecahedron, Skilling's figure
	©
Circumradius	1/sqrt(2) = 0.707107
Face vector	60, 360, 204
Vertex figure	[5/4,4,3,3,3,4,5/3,4,3/2,3/2,3/2,4] (type A) or [5/2,3,4,3,4,3,5/3,3/2,4,3/2,4,3/2] (type B)
External links

This figure can be obtained as the blend of the great dirhombicosidodecahedron (Miller's monster, gidrid) and the compound dasi of 20 octahedra (oct).

Half the edges of that figure are tetradic instead of dyadic (type C), but can be re-interpreted as being a pair of coincident dyadic edges (types A and B). As such gidisdrid is a exotic polyhedron.

Incidence matrix

(Type A)

60 |   4   4   4 |   6  4  2
---+-------------+----------
 2 | 120   *   * |   2  0  0 :3-3 (coinciding with 4-5/2)
 2 |   * 120   * |   1  1  0 :3-4
 2 |   *   * 120 |   0  1  1 :4-5/2 (coinciding with 3-3)
---+-------------+----------
 3 |   2   1   0 | 120  *  *
 4 |   0   2   2 |   * 60  *
 5 |   0   0   5 |   *  * 24 :pairwise coplanar pentagrams

(Type B)

60 |   8   4 |   6  4  2
---+---------+----------
 2 | 240   * |   1  1  0 :3-4 (half of those coincide with 3-5/2)
 2 |   * 120 |   1  0  1 :3-5/2
---+---------+----------
 3 |   2   1 | 120  *  *
 4 |   4   0 |   * 60  *
 5 |   0   5 |   *  * 24 :pairwise coplanar pentagrams

(Type C)

60 |   4   4 |   6  4  2
---+---------+----------
 2 | 120   * |   1  1  0 :2 incident faces
 2 |   * 120 |   2  1  1 :4 incident faces
---+---------+----------
 3 |   1   2 | 120  *  *
 4 |   2   2 |   * 60  *
 5 |   0   5 |   *  * 24 :pairwise coplanar pentagrams