Small snubretrosnub snub pentishexacosipentishecatonicosachoron
| Small snubretrosnub snub pentishexacosipentishecatonicosachoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Sosirsaspoxphi |
| Elements | |
| Cells | 600 great icosahedra, 600 compound of icosahedron and great dodecahedron, 2400 compound of octahemioctahedron and cuboctahedron, 120 great antirhombicosahedra, 600 rhombidodecadodecahedra, 600 small ditrigonal dodecicosidodecahedra, 120 truncated chiricosahedra, 2400 truncated tetrahedra |
| Faces | 38400 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 10800 hexagons, 2400 golden hexagrams, 3600 decagons, 600 compound of two hexagons |
| Edges | 14400+2×21600 |
| Vertices | 7200 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Semi-uniform Prahi |
| Regiment | Sadros daskydox |
| Conjugate | Gosirsaspoxphi |
| Abstract & topological properties | |
| Euler characteristic | 29400 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The small snubretrosnub snub pentishexacosipentishecatonicosachoron, or sosirsaspoxphi, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 600 icosahedra and 600 great dodecahedra (some of which lie in the same hyperplanes, forming 600 compounds of one of each), 2400 octahemioctahedra and 2400 cuboctahedra (forming 2400 compounds of one of each), 600 cubohemioctahedra (forming 120 great antirhombicosahedra), 600 rhombidodecadodecahedra, 600 small ditrigonal dodecicosidodecahedra, and 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra).
One great icosahedron, one icosahedron and one great dodecahedron (two compounds), four octahemioctahedra and four cuboctahedra (eight compounds), one cubohemioctahedron (one compound), five rhombidodecadodecahedra, five small ditrigonal dodecicosidodecahedra, and five truncated tetrahedra (one compound, four single) join at each vertex.
It can be obtained as the blend of 5 small dipentary dishecatonicosihexacosidishecatonicosachora and 5 small 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 small diretrosnub disnub decahecatonicosadishexacosichoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 28: Idcossids" (#1611).
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