2_31 Polytope
| Gosset 231 polytope | |
|---|---|
| Type | Uniform 7-polytope |
| Family | 2k1 polytope |
| Schläfli symbol | {3,3,33,1} |
| Coxeter symbol | 231 |
| Coxeter-Dynkin diagram | |
| 6-faces | 632: 56 221 576 {35} |
| 5-faces | 4788: 756 211 4032 {34} |
| 4-faces | 16128: 4032 201 12096 {33} |
| Cells | 20160 {32} |
| Faces | 10080 {3} |
| Edges | 2016 |
| Vertices | 126 |
| Vertex figure | 131 |
| Petrie polygon | Octadecagon |
| Coxeter group | E7, |
| Properties | convex |
The 231 is composed of 126 vertices, 2016 edges, 10080 faces (Triangles), 20160 cells (tetrahedra), 16128 4-faces (3-simplexes), 4788 5-faces (756 pentacrosses, and 4032 5-simplexes), 632 6-faces (576 6-simplexes and 56 221). Its vertex figure is a 6-demicube. Its 126 vertices represent the root vectors of the simple Lie group E7.
This polytope is the vertex figure for a uniform tessellation of 7-dimensional space, 331.
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