Great snubspinosnub heptishexacosichoron
| Great snubspinosnub heptishexacosichoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Gosenshex |
| Elements | |
| Cells | 600 pentagrammatic snub pseudodisoctahedra, 600 icosahedra, 2400 compound of cuboctahedron and cubohemioctahedron, 120 icosidisicosahedra, 600 great ditrigonal dodecicosidodecahedra, 600 rhombidodecadodecahedra, 600 truncated great icosahedra, 600 great rhombidodecahedra |
| Faces | 21600 triangles, 32400 squares, 7200 pentagons, 14400 pentagrams, 10800 hexagons, 1200 golden hexagrams, 7200 decagrams, 600 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 snubspinosnub heptishexacosichoron |
| Abstract & topological properties | |
| Euler characteristic | 37200 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The great snubspinosnub heptishexacosichoron, or gosenshex, is a nonconvex uniform polychoron that consists of 1200 small stellated dodecahedra (falling into pairs in the same hyperplanes, forming 600 pentagrammatic snub pseudodisoctahedra), 600 icosahedra, 2400 cuboctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 octahemioctahedra (forming 120 icosidisicosahedra), 600 great ditrigonal dodecicosidodecahedra, 600 rhombidodecadodecahedra, 600 truncated great icosahedra, and 600 great rhombidodecahedra.
Two small stellated dodecahedra (two compounds), one icosahedron, four cuboctahedra and four cubohemioctahedra (eight compounds), one octahemioctahedron (one compound), five great ditrigonal dodecicosidodecahedra, five rhombidodecadodecahedra, five truncated great icosahedra, and five great rhombidodecahedra join at each vertex.
It can be obtained as the blend of 5 great dipentary dishecatonicosihexacosidishecatonicosachora and 5 great spinocapped dipentary hexacositrishecatonicosachora. In the process, some of the cuboctahedron 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" (#1827).