Great spinoretrosnub prismatosnub heptishexacosichoron
| Great spinoretrosnub prismatosnub heptishexacosichoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Gnarsipshex |
| Elements | |
| Cells | 600 compound of great icosahedron and small stellated dodecahedron, 600 pentagonal retrosnub pseudodisoctahedra, 2400 compound of octahemioctahedron and cubohemioctahedron, 120 antirhombicosicosahedra, 600 icosidodecadodecahedra, 600 great dodecicosidodecahedra, 600 truncated great icosahedra, 3600 pentagonal prisms |
| Faces | 21600 triangles, 18000 squares, 14400 pentagons, 14400 pentagrams, 19200 hexagons, 1200 golden hexagrams, 3600 decagrams, 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 prismatosnub heptishexacosichoron |
| Abstract & topological properties | |
| Euler characteristic | 32400 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The great spinoretrosnub prismatosnub heptishexacosichoron, or gnarsipshex, 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), 1200 great dodecahedra (forming 600 pentagonal retrosnub pseudodisoctahedra), 2400 octahemioctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 cuboctahedra (forming 120 antirhombicosicosahedra), 600 icosidodecadodecahedra, 600 great dodecicosidodecahedra, 600 truncated great icosahedra, and 3600 pentagonal prisms.
One great icosahedron and one small stellated dodecahedron (two compounds), two great dodecahedra (two compounds), four octahemioctahedra and four cubohemioctahedra (eight compounds), one cuboctahedron (one compound), five icosidodecadodecahedra, five great dodecicosidodecahedra, five truncated great icosahedra, and five pentagonal prisms join at each vertex.
It can be obtained as the blend of 5 great dipentary tetrishecatonicosihexacosichora 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" (#1825).