Great snubretrosnub snub prismatodisnub dishexacosipentishecatonicosachoron

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Great snubretrosnub snub prismatodisnub dishexacosipentishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGosirsospid sidoxphi
Elements
Cells600 great icosahedra, 600 icosahedra, 2400 compound of octahemioctahedron and cuboctahedron, 120 great antirhombicosahedra, 120 truncated chiricosahedra, 2400 truncated tetrahedra, 6000 triangular prisms
Faces38400 triangles, 18000 squares, 10800 hexagons, 2400 golden hexagrams, 600 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall snubretrosnub snub prismatodisnub dishexacosipentishecatonicosachoron
Abstract & topological properties
Euler characteristic7200
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great snubretrosnub snub prismatodisnub dishexacosipentishecatonicosachoron, or gosirsospid sidoxphi, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 600 icosahedra, 2400 octahemioctahedra and 2400 cuboctahedra (falling into pairs in the same hyperplanes, forming 2400 compounds of one of each), 600 cubohemioctahedra (forming 120 great antirhombicosahedra), 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra), and 6000 triangular prisms.

One great icosahedron, one icosahedron, four octahemioctahedra and four cuboctahedra (eight compounds), one cubohemioctahedron (one compound), five truncated tetrahedra (one compound, four single), and five triangular prisms join at each vertex.

It has the same facet counts as its conjugate, the small snubretrosnub snub prismatodisnub dishexacosipentishecatonicosachoron, although the icosahedra and great icosahedra are in opposite positions.

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