Small snubspinosnub prismatosnubdisnub trishexacosichoron

From Polytope Wiki
Jump to navigation Jump to search
Small snubspinosnub prismatosnubdisnub trishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSosenspasidstix
Elements
Cells600 compound of great icosahedron and small stellated dodecahedron, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 small dodecicosahedra, 3600 pentagrammic prisms, 6000 triangular prisms
Faces21600 triangles, 32400 squares, 7200 pentagrams, 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
ConjugateGosenspasidstix
Abstract & topological properties
Euler characteristic12000
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small snubspinosnub prismatosnubdisnub trishexacosichoron, or sosenspasidstix, 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), 2400 cuboctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 small dodecicosahedra, 3600 pentagrammic prisms, and 6000 triangular prisms.

One great icosahedron and one small stellated dodecahedron (two compounds), four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five small dodecicosahedra, five pentagrammic prisms, and five triangular prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary prismatohexacosihecatonicosachora and 5 small dipentary hecatonicosiprismatohecatonicosihexacosichora. 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]