Great spinoretrosnub tetrishexacositrishexacosichoron
| Great spinoretrosnub tetrishexacositrishexacosichoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Gnarstuxtix |
| Elements | |
| Cells | 600 compound of great icosahedron and small stellated dodecahedron, 600 compound of icosahedron and great dodecahedron, 2400 compound of octahemioctahedron and cubohemioctahedron, 120 antirhombicosicosahedra, 600 great dodecicosahedra, 600 icosidodecadodecahedra, 600 great rhombidodecahedra |
| Faces | 21600 triangles, 18000 squares, 7200 pentagons, 7200 pentagrams, 19200 hexagons, 1200 golden hexagrams, 7200 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 tetrishexacositrishexacosichoron |
| Abstract & topological properties | |
| Euler characteristic | 25200 |
| Orientable | No |
| Properties | |
| Symmetry | H4+, order 7200 |
| Convex | No |
| Nature | Wild |
The great spinoretrosnub tetrishexacositrishexacosichoron, or gnarstuxtix, 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), 600 icosahedra and 600 great dodecahedra (forming 600 compounds of one of each), 2400 octahemioctahedra and 2400 cubohemioctahedra (forming 2400 compounds of one of each), 600 cuboctahedra (forming 120 antirhombicosicosahedra), 600 great dodecicosahedra, 600 icosidodecadodecahedra, and 600 great rhombidodecahedra.
One great icosahedron and one small stellated dodecahedron (two compounds), one icosahedron and one great dodecahedron (two compounds), four octahemioctahedra and four cubohemioctahedra (eight compounds), one cuboctahedron (one compound), five great dodecicosahedra, five icosidodecadodecahedra, and five great rhombidodecahedra join at each vertex.
It can be obtained as the blend of 5 great dipentary dishecatonicosihexacosihecatonicosachora and 5 great capped dipentary hexacositetrishecatonicosachora. 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" (#1817).