Great snubspinosnub prismatodisnub pentishexacosichoron

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Great snubspinosnub prismatodisnub pentishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGosenspidspox
Elements
Cells600 small stellated dodecahedra, 600 compound of icosahedron and great dodecahedron, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 rhombidodecadodecahedra, 600 great dodecicosahedra, 6000 triangular prisms
Faces21600 triangles, 32400 squares, 7200 pentagons, 7200 pentagrams, 10800 hexagons, 1200 golden hexagrams, 3600 decagrams, 600 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall snubspinosnub prismatodisnub pentishexacosichoron
Abstract & topological properties
Euler characteristic21600
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great snubspinosnub prismatodisnub pentishexacosichoron, or gosenspidspox, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra, 600 icosahedra and 600 great dodecahedra (some of which lie in the same hyperplanes, forming 600 compounds of one of each), 2400 cuboctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 rhombidodecadodecahedra, 600 great dodecicosahedra, and 6000 triangular prisms.

One small stellated dodecahedron, one icosahedron and one great dodecahedron (two compounds), four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five rhombidodecadodecahedra, five great dodecicosahedra, and five triangular prisms join at each vertex.

It can be obtained as the blend of 5 great dipentary prismatohexacosihecatonicosachora and 5 great capped dipentary tetrishecatonicosihexacosichora. In the process, some of the cuboctahedron and 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]