Great disnub dirhombidodecahedron

The great disnub dirhombidodecahedron, or gidisdrid, also known as Skilling's figure, is an exotic uniform polyhedroid. It consists of 120 snub triangles, 60 snub squares, and 24 pentagrams, the latter two of which fall into coinciding planes in pairs. Six triangles, four squares, and two pentagrams meet at each vertex.

Great disnub dirhombidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Gidisdrid
Elements
Faces	120 triangles, 60 squares, 24 pentagrams
Edges	120+120+120
Vertices	60
Vertex figure	Mirror-symmetric dodecagon, edge lengths (√5–1)/2, √2, 1, 1, 1, √2, (√5–1)/2, √2, 1, 1, 1, √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Dihedral angles	3–3: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	5/2–4: $\arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{5}}}\right)\approx 71.03929^{\circ }$
	3–4: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Semi-uniform Srid
Regiment	Gidrid
Dual	Great disnub dirhombidodecacron
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

As a polyhedron, it is usually considered degenerate because some of the edges coincide in pairs, leading to some edges where four faces can appear to connect. It is the only exotic uniform polyhedroid not analyzable as a compound, and the most well-known example of an exotic polytopoid. J. Skilling announced the discovery of the great disnub dirhombidodecahedron in a 1975 paper, in which computer search was used to prove the list of uniform polyhedra complete.

It can be constructed as a blend of the uniform great dirhombicosidodecahedron and the disnub icosahedron, the uniform compound of 20 octahedra with which it shares its edge skeleton.

External links

• Klitzing, Richard. "gidisdrid".
• Wikipedia contributors. "Great disnub dirhombidodecahedron".