Small snubretrosnub heptishexacosichoron
| Small snubretrosnub heptishexacosichoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Sesorshex |
| Elements | |
| Cells | 600 small retrosnub disoctahedra, 600 compound of great dodecahedron and icosahedron, 2400 compound of octahemioctahedron and cuboctahedron, 120 great antirhombicosahedra, 600 small rhombidodecahedra, 600 icosidodecadodecahedra, 600 small ditrigonal dodecicosidodecahedra |
| Faces | 33600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 10800 hexagons, 4800 golden hexagrams, 7200 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 | Gesorshex |
| Abstract & topological properties | |
| Euler characteristic | 34800 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The small snubretrosnub heptishexacosichoron, or sesorshex, is a nonconvex uniform polychoron that consists of 1200 great icosahedra (some of which lie in the same hyperplanes, forming 600 small retrosnub disoctahedra), 600 great dodecahedra and 600 icosahedra (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 small rhombidodecahedra, 600 icosidodecadodecahedra, and 600 small ditrigonal dodecicosidodecahedra.
Two great icosahedra (two compounds), one great dodecahedron and one icosahedron (two compounds), four octahemioctahedra and four cuboctahedra (eight compounds), one cubohemioctahedron (one compound), five small rhombidodecahedra, five icosidodecadodecahedra, and five small ditrigonal dodecicosidodecahedra join at each vertex.
It can be obtained as the blend of 5 small dipentary hecatonicosihexacosidishecatonicosachora and 5 small dipentary trishecatonicosihecatonicosihexacosichora. 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" (#1616).
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