Small dispinosnub prismatosnub hexacosidishexacosichoron

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Small dispinosnub prismatosnub hexacosidishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSedansposixdox
Elements
Cells600 icosahedra, 2400 compound of two cubohemioctahedra, 600 small icosicosidodecahedra, 600 rhombicosahedra, 3600 pentagrammic prisms
Faces12000 triangles, 32400 squares, 7200 pentagrams, 19200 hexagons, 1200 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Prahi
RegimentSadros daskydox
ConjugateGedansposixdox
Abstract & topological properties
Euler characteristic12600
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small dispinosnub prismatosnub hexacosidishexacosichoron, or sedansposixdox, is a nonconvex uniform polychoron that consists of 600 icosahedra, 4800 cubohemioctahedra (some of which lie in the same hyperplanes, forming 2400 compounds of two), 600 small icosicosidodecahedra, 600 rhombicosahedra, and 3600 pentagrammic prisms.

One icosahedron, eight cubohemioctahedra (eight compounds), five small icosicosidodecahedra, five rhombicosahedra, and five pentagrammic prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary hexacosihecatonicosachora and 5 small dipentary prismatohecatonicosihexacosihecatonicosachora. In the process, some of the 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]