Great dispinosnub trishexacositetrishexacosichoron

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Great dispinosnub trishexacositetrishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGidnastixtux
Elements
Cells600 small stellated dodecahedra, 600 compound of great dodecahedron and icosahedron, 2400 compound of two cubohemioctahedra, 600 rhombidodecadodecahedra, 600 great dodecicosahedra, 600 quasirhombicosidodecahedra, 600 truncated great icosahedra
Faces12000 triangles, 32400 squares, 7200 pentagons, 14400 pentagrams, 19200 hexagons, 1200 compound of two hexagons, 3600 decagrams
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall dispinosnub trishexacositetrishexacosichoron
Abstract & topological properties
Euler characteristic31800
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great dispinosnub trishexacositetrishexacosichoron, or gidnastixtux, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra, 600 great dodecahedra and 600 icosahedra (falling into pairs in the same hyperplanes, forming 600 compounds of one of each), 4800 cubohemioctahedra (forming 2400 compounds of two), 600 rhombidodecadodecahedra, 600 great dodecicosahedra, 600 quasirhombicosidodecahedra, and 600 truncated great icosahedra.

One small stellated dodecahedron, one great dodecahedron and one icosahedron (two compounds), eight cubohemioctahedra (eight compounds), five rhombidodecadodecahedra, five great dodecicosahedra, five quasirhombicosidodecahedra, and five truncated great icosahedra join at each vertex.

It can be obtained as the blend of 5 great capped dipentary tetrishecatonicosihexacosichora and 5 great based dipentary hexacositrishecatonicosachora. In the process, some of the cubohemioctahedron cells blend out.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great diretrosnub disnub decahecatonicosadishexacosichoron.

External links[edit | edit source]