Great diretrosnub snub prismatodisnub pentishecatonicositetrishexacosichoron

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Great diretrosnub snub prismatodisnub pentishecatonicositetrishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGadersospid sphitux
Elements
Cells600 compound of great icosahedron and small stellated dodecahedron, 2400 compound of two octahemioctahedra, 600 quasirhombicosidodecahedra, 600 great dodecicosahedra, 6000 triangular prisms, 120 truncated chiricosahedra, 2400 truncated tetrahedra
Faces38400 triangles, 18000 squares, 7200 pentagrams, 19200 hexagons, 2400 golden hexagrams, 3600 decagrams, 1200 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall diretrosnub snub prismatodisnub pentishecatonicositetrishexacosichoron
Abstract & topological properties
Euler characteristic27000
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great diretrosnub snub prismatodisnub pentishecatonicositetrishexacosichoron, or gadersospid sphitux, is a nonconvex uniform polychoron that consists of 600 great icosahedra and 600 small stellated dodecahedra (falling into pairs in the same hyperplanes, forming 600 compounds of one of each), 4800 octahemioctahedra (forming 2400 compounds of two), 600 quasirhombicosidodecahedra, 600 great dodecicosahedra, 6000 triangular prisms, and 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra).

One great icosahedron and one small stellated dodecahedron (two compounds), eight octahemioctahedra (eight compounds), five quasirhombicosidodecahedra, five great dodecicosahedra, five triangular prisms, and five truncated tetrahedra (one compound and four single) join at each vertex.

It can be obtained as the blend of 5 great dipentary hecatonicosidishexacosichora and 5 great dipentary trishecatonicosiprismatohexacosichora. In the process, some of the octahemioctahedron cells blend out.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great diretrosnub disnub decahecatonicosadishexacosichoron.

External links[edit | edit source]