Great diretrosnub snub prismatosnub pentishecatonicosidishexacosidishexacosichoron

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Great diretrosnub snub prismatosnub pentishecatonicosidishexacosidishexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGadersospis phidexdix
Elements
Cells600 small retrosnub disoctahedra, 2400 compound of two octahemioctahedra, 600 icosidodecadodecahedra, 600 quasirhombicosidodecahedra, 3600 pentagonal prisms, 120 truncated chiricosahedra, 2400 truncated tetrahedra
Faces33600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 4800 golden hexagrams, 1200 compound of two hexagons
Edges14400+2×21600
Vertices7200
Measures (edge length 1)
Circumradius
Related polytopes
ArmySemi-uniform Grix
RegimentGadros daskydox
ConjugateSmall diretrosnub snub prismatosnub pentishecatonicosidishexacosidishexacosichoron
Abstract & topological properties
Euler characteristic33000
OrientableNo
Properties
SymmetryH4+, order 7200
ConvexNo
NatureWild

The great diretrosnub snub prismatosnub pentishecatonicosidishexacosidishexacosichoron, or gadersospis phidexdix, is a nonconvex uniform polychoron that consists of 1200 great icosahedra (falling into pairs in the same hyperplanes, forming 600 small retrosnub disoctahedra), 4800 octahemioctahedra (forming 2400 compounds of two), 600 icosidodecadodecahedra, 600 quasirhombicosidodecahedra, 3600 pentagonal prisms, and 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra).

Two great icosahedra (two compounds), eight octahemioctahedra (eight compounds), five icosidodecadodecahedra, five quasirhombicosidodecahedra, five pentagonal 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 capped 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]