Small dispinosnub snub hexishexacosipentishexacosichoron

From Polytope Wiki
Jump to navigation Jump to search
Small dispinosnub snub hexishexacosipentishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSedansoshexphi
Elements
Cells600 compound of small stellated dodecahedron and great icosahedron, 600 great dodecahedra, 2400 compound of two cubohemioctahedra, 600 rhombidodecadodecahedra, 600 small dodecicosahedra, 600 small rhombidodecahedra, 120 truncated chiricosahedra, 2400 truncated tetrahedra
Faces12000 triangles, 32400 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 1200 compound of two hexagons, 7200 decagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Prahi
RegimentSadros daskydox
ConjugateGreat dispinosnub snub hexishexacosipentishexacosichoron
Abstract & topological properties
Euler characteristic25800
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The small dispinosnub snub hexishexacosipentishexacosichoron, or sedansoshexphi, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra and 600 great icosahedra (falling into pairs in the same hyperplanes, forming 600 compounds of one of each), 600 great dodecahedra, 4800 cubohemioctahedra (forming 2400 compounds of two), 600 rhombidodecadodecahedra, 600 small dodecicosahedra, 600 small rhombidodecahedra, and 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra).

One small stellated dodecahedron and one great icosahedron (two compounds), one great dodecahedron, eight cubohemioctahedra (eight compounds), five rhombidodecadodecahedra, five small dodecicosahedra, five small rhombidodecahedra, and five truncated tetrahedra (one compound, four single) join at each vertex.

It can be obtained as the blend of 5 small capped dipentary tetrishecatonicosihexacosichora and 5 small dipentary dishecatonicosidishexacosichora. 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]