Small snubspinosnub tetrishexacosichoron

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Small snubspinosnub tetrishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSosenstux
Elements
Cells600 great icosahedra, 600 icosahedra, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 small rhombidodecahedra, 600 rhombicosahedra
Faces21600 triangles, 32400 squares, 10800 hexagons, 1200 golden hexagrams, 3600 decagons, 600 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Prahi
RegimentSadros daskydox
ConjugateGosenstux
Abstract & topological properties
Euler characteristic13800
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small snubspinosnub tetrishexacosichoron, or sosenstux, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 600 icosahedra, 2400 cuboctahedra and 2400 cubohemioctahedra (some of which lie in the same hyperplanes, forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 small rhombidodecahedra, and 600 rhombicosahedra.

One great icosahedron, one icosahedron, four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five small rhombidodecahedra, and five rhombicosahedra join at each vertex.

It can be obtained as the blend of 5 small dipentary hecatonicosihexacosidishecatonicosachora and 5 small dipentary hexacosihecatonicosachora. In the process, some of the cuboctahedron and cubohemioctahedron cells blend into octahemioctahedra.

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]