# Great disnub dirhombidodecahedron

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Great disnub dirhombidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidisdrid
Elements
Faces120 triangles, 60 squares, 24 pentagrams
Edges120+120+120
Vertices60
Vertex figureMirror-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$\frac{\sqrt2}{2} ≈ 0.70711$ Dihedral angles3–3: $\arccos\left(-\frac13\right) ≈ 109.47122°$ 5/2–4: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{5}}\right) ≈ 71.03929°$ 3–4: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$ Related polytopes
ArmySemi-uniform Srid
RegimentGidrid
DualGreat disnub dirhombidodecacron
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great disnub dirhombidodecahedron, or gidisdrid, also known as Skilling's figure, is a 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.

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.