Omnitruncated 120-cell
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| Omnitruncated 120-cell | |
|---|---|
 stereographic projection (centered on truncated icosidodecahedron) |
|
| Type | Uniform polychoron |
| Cells | 2640 total: 120 4.6.10, 600 4.6.6, 720 4.4.10, 1200 4.4.6 |
| Faces | 17040 total: 10800 {4}, 4800 {6} 1440 {10} |
| Edges | 28800 |
| Vertices | 14400 |
| Vertex figure | Chiral scalene tetrahedron |
| Schläfli symbol | t0,1,2,3{3,3,5} |
| Symmetry group | H4, [3,3,5] |
| Properties | convex |
In geometry, the omnitruncated 120-cell is a convex uniform polychoron composed of 2640 cells: 120 truncated icosidodecahedra, 600 truncated octahedra, 720 decagonal prisms, and 1200 pentagonal prisms.
It also has 14400 vertices, 28800 edges, and 17040 faces, and is the largest convex uniform polychoron.
The vertices and edges of the Omnitruncated 120-cell form the Cayley graph of the Coxeter group H4
Alternate names:
- Great diprismatohexacosihecatonicosachoron (George Olshevsky)
- Omnitruncated 120-cell (Norman Johnson)
- and Omnitruncated 600-cell
- Omnitruncated hecatonicosachoron
- and Omnitruncated hexacosichoron
- Omnitruncated polydodecahedron
- and Omnitruncated polytetrahedron
- Gidpixhi (Jonathan Bowers: for great diprismatohexacosihecatonicosachoron)
The first complete physical model of a 3D projection of the omnituncated 120-cell was built on Aug. 9th 2006 using the Zome system in the London Knowledge Lab for the 2006 Bridges Conference.
