Small retrospinosnub tetrishexacosichoron

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Small retrospinosnub tetrishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSarnistux
Elements
Cells600 icosahedra, 2400 compound of octahemioctahedron and cubohemioctahedron, 120 antirhombicosicosahedra, 600 truncated icosahedra, 600 small dodecicosidodecahedra, 600 rhombicosahedra
Faces21600 triangles, 18000 squares, 7200 pentagons, 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
ConjugateGarnistux
Abstract & topological properties
Euler characteristic16200
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small retrospinosnub tetrishexacosichoron, or sarnistux, is a nonconvex uniform polychoron that consists of 600 icosahedra, 2400 octahemioctahedra and 2400 cubohemioctahedra (some of which lie in the same hyperplanes, forming 2400 compounds of one of each), 600 cuboctahedra (forming 120 antirhombicosicosahedra), 600 truncated icosahedra, 600 small dodecicosidodecahedra, and 600 rhombicosahedra.

One icosahedron, four octahemioctahedra and four cubohemioctahedra (eight compounds), one cuboctahedron (one compound), five truncated icosahedra, five small dodecicosidodecahedra, and five rhombicosahedra join at each vertex.

It can be obtained as the blend of 5 small invertidipentary hecatonicosihexacosidishecatonicosachora and 5 small dipentary hexacosihecatonicosachora. 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]