2_21 Polytope
| 221 polytope | |
|---|---|
| Type | Uniform 6-polytope |
| Family | k21 polytope |
| Schläfli symbol | {3,3,32,1} |
| Coxeter symbol | 221 |
| Coxeter-Dynkin diagram | |
| 5-faces | 99 total: 27 211 72 {34} |
| 4-faces | 648: 432 {33} 216 {33} |
| Cells | 1080 {3,3} |
| Faces | 720 {3} |
| Edges | 216 |
| Vertices | 27 |
| Vertex figure | 121 (5-demicube) |
| Petrie polygon | Dodecagon |
| Coxeter group | E6, order 51840 |
| Properties | convex |
The 221 has 27 vertices, and 99 facets: 27 5-orthoplexes and 72 5-simplices. Its vertex figure is a 5-demicube.
For visualization this 6-dimensional polytope is often displayed in a special skewed orthographic projection direction that fits its 27 vertices within a 12-gonal regular polygon (called a Petrie polygon). Its 216 edges are drawn between 2 rings of 12 vertices, and 3 vertices projected into the center. Higher elements (faces, cells, etc.) can also be extracted and drawn on this projection.
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