Great snubretrosnub heptishexacosichoron
| Great snubretrosnub heptishexacosichoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Gesorshex |
| Elements | |
| Cells | 600 compound of small stellated dodecahedron and great icosahedron, 600 snub disoctahedra, 2400 compound of octahemioctahedron and cuboctahedron, 120 great antirhombicosahedra, 600 great rhombidodecahedra, 600 icosidodecadodecahedra, 600 great ditrigonal dodecicosidodecahedra |
| Faces | 33600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 10800 hexagons, 4800 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 snubretrosnub heptishexacosichoron |
| Abstract & topological properties | |
| Euler characteristic | 34800 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The great snubretrosnub heptishexacosichoron, or gesorshex, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra and 600 great icosahedra (falling into pairs in the same hyperplanes, forming 600 compounds of one of each), 1200 icosahedra (forming 600 snub disoctahedra), 2400 octahemioctahedra and 2400 cuboctahedra (forming 2400 compounds of one of each), 600 cubohemioctahedra (forming 120 great antirhombicosahedra), 600 great rhombidodecahedra, 600 icosidodecadodecahedra, and 600 great ditrigonal dodecicosidodecahedra.
One small stellated dodecahedron and one great icosahedron (two compounds), two icosahedra (two compounds), four octahemioctahedra and four cuboctahedra (eight compounds), one cubohemioctahedron (one compound), five great rhombidodecahedra, five icosidodecadodecahedra, and five great ditrigonal dodecicosidodecahedra join at each vertex.
It can be obtained as the blend of 5 great dipentary hecatonicosihexacosidishecatonicosachora and 5 great 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 great diretrosnub disnub decahecatonicosadishexacosichoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 29: Dircospids" (#1793).