| Omnitruncated 5-cell | ||
Schlegel diagram with half of the truncated octahedral cells shown. |
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| Type | Uniform polychoron | |
| Schläfli symbol | t0,1,2,3{3,3,3} | |
| Coxeter-Dynkin diagram | or |
|
| Cells | 30 | 10 (4.6.6) 20 (4.4.6) |
| Faces | 150 | 90{4} 60{6} |
| Edges | 240 | |
| Vertices | 120 | |
| Vertex figure | (Chiral irregular tetrahedron) |
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| Coxeter group | A4, ], order 240 | |
| Properties | convex, isogonal, zonotope | |
| Uniform index | 8 9 10 | |
The omnitruncated 5-cell is composed of 120 vertices, 240 edges, 150 faces (90 squares and 60 hexagons), and 30 cells. The cells are: 10 truncated octahedra, and 20 hexagonal prisms. Each vertex is surrounded by four cells: two truncated octahedra, and two hexagonal prisms, arranged in two chiral irregular tetrahedral vertex figures.
Coxeter calls this Hinton's polytope after C. H. Hinton, who described it in his book The Fourth Dimension in 1906. It forms a uniform honeycomb which Coxeter calls Hinton's honeycomb.
Read more about this topic: Runcinated 5-cell