Great spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron
Great spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron | |
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Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Gnarsis pastuxphi |
Elements | |
Cells | 600 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 |
Faces | 21600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 1200 golden hexagrams, 1200 compound of two hexagons |
Edges | 14400+2×21600 |
Vertices | 7200 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Semi-uniform Grix |
Regiment | Gadros daskydox |
Conjugate | Small spinoretrosnub snub prismatosnub tetrishexacosipentishecatonicosachoron |
Abstract & topological properties | |
Euler characteristic | 13200 |
Orientable | No |
Properties | |
Symmetry | H4+, order 7200 |
Convex | No |
Nature | Wild |
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]
- Bowers, Jonathan. "Category 29: Dircospids" (#1809).