Small spinoretrosnub prismatosnub hexishexacosichoron

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Small spinoretrosnub prismatosnub hexishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSnarspishax
Elements
Cells600 compound of great icosahedron and small stellated dodecahedron, 600 compound of icosahedron and great dodecahedron, 2400 compound of octahemioctahedron and cubohemioctahedron, 120 antirhombicosicosahedra, 600 small dodecicosahedra, 600 truncated icosahedra, 3600 pentagrammic prisms
Faces21600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 1200 golden hexagrams, 3600 decagons, 1200 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Prahi
RegimentSadros daskydox
ConjugateGnarspishax
Abstract & topological properties
Euler characteristic18600
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small spinoretrosnub prismatosnub hexishexacosichoron, or snarspishax, is a nonconvex uniform polychoron that consists of 600 great icosahedra and 600 small stellated dodecahedra (some of which lie in the same hyperplanes, forming 600 compounds of one of each), 600 icosahedra and 600 great dodecahedra (forming 600 compounds of one of each), 2400 octahemioctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 cuboctahedra (forming 120 antirhombicosicosahedra), 600 small dodecicosahedra, 600 truncated icosahedra, and 3600 pentagrammic prisms.

One great icosahedron and one small stellated dodecahedron (two compounds), one icosahedron and one great dodecahedron (two compounds), four octahemioctahedra and four cubohemioctahedra (eight compounds), one cuboctahedron (one compound), five small dodecicosahedra, five truncated icosahedra, and five pentagrammic prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary dishecatonicosihexacosihecatonicosachora and 5 small capped dipentary prismatohexacositrishecatonicosachora. In the process, some of the octahemioctahedron and cubohemioctahedron cells blend out.

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]