Great spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron

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Great spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGnarsis pastuxphi
Elements
Cells600 compound of great icosahedron and small stellated dodecahedron, 600 great dodecahedra, 2400 compound of octahemioctahedron and cubohemioctahedron, 120 antirhombicosicosahedra, 600 truncated great icosahedra, 120 truncated chiricosahedra, 2400 truncated tetrahedra, 3600 pentagonal prisms
Faces21600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 1200 golden hexagrams, 1200 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron
Abstract & topological properties
Euler characteristic13200
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron, or gnarsis pastuxphi, 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), 600 great dodecahedra, 2400 octahemioctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 cuboctahedra (forming 120 antirhombicosicosahedra), 600 truncated great icosahedra, 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra), and 3600 pentagonal prisms.

One great icosahedron and one small stellated dodecahedron (two compounds), one great dodecahedron, four octahemioctahedra and four cubohemioctahedra (eight compounds), one cuboctahedron (one compound), five truncated great icosahedra, five truncated tetrahedra (one compound, four single), and five pentagonal prisms join at each vertex.

It can be obtained as the blend of 5 great dipentary hecatonicosidishexacosichora and 5 great capped dipentary prismatohexacositrishecatonicosachora. In the process, some of the octahemioctahedron and cubohemioctahedron 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]