Small snubspinosnub heptishexacosichoron

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Small snubspinosnub heptishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSosenshex
Elements
Cells600 great icosahedra, 600 pentagonal retrosnub pseudodisoctahedra, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 small ditrigonal dodecicosidodecahedra, 600 rhombidodecadodecahedra, 600 truncated icosahedra, 600 small rhombidodecahedra
Faces21600 triangles, 32400 squares, 14400 pentagons, 7200 pentagrams, 10800 hexagons, 1200 golden hexagrams, 7200 decagons, 600 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Prahi
RegimentSadros daskydox
ConjugateGosenshex
Abstract & topological properties
Euler characteristic37200
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small snubspinosnub heptishexacosichoron, or sosenshex, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 1200 great dodecahedra (some of which lie in the same hyperplanes, forming 600 pentagonal retrosnub pseudodisoctahedra), 2400 cuboctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 small ditrigonal dodecicosidodecahedra, 600 rhombidodecadodecahedra, 600 truncated icosahedra, and 600 small rhombidodecahedra.

One great icosahedron, two great dodecahedra (two compounds), four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five small ditrigonal dodecicosidodecahedra, five rhombidodecadodecahedra, five truncated icosahedra, and five small rhombidodecahedra join at each vertex.

It can be obtained as the blend of 5 small dipentary dishecatonicosihexacosidishecatonicosachora and 5 small spinobased dipentary hexacositrishecatonicosachora. 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 small diretrosnub disnub decahecatonicosadishexacosichoron.

External links[edit | edit source]