421 Polytope
| 421 | |
|---|---|
| Type | Uniform 8-polytope |
| Family | k21 polytope |
| Schläfli symbol | {3,3,3,3,32,1} |
| Coxeter symbol | 421 |
| Coxeter-Dynkin diagram | |
| 7-faces | 19440 total: 2160 411 17280 {36} |
| 6-faces | 207360: 138240 {35} 69120 {35} |
| 5-faces | 483840 {34} |
| 4-faces | 483840 {33} |
| Cells | 241920 {3,3} |
| Faces | 60480 {3} |
| Edges | 6720 |
| Vertices | 240 |
| Vertex figure | 321 polytope |
| Petrie polygon | 30-gon |
| Coxeter group | E8, |
| Properties | convex |
The 421 is composed of 17,280 7-simplex and 2,160 7-orthoplex facets. Its vertex figure is the 321 polytope.
For visualization this 8-dimensional polytope is often displayed in a special skewed orthographic projection direction that fits its 240 vertices within a 30-gonal regular polygon (called a Petrie polygon). Its 6720 edges are drawn between the 240 vertices. Specific higher elements (faces, cells, etc.) can also be extracted and drawn on this projection.
As its 240 vertices represent the root vectors of the simple Lie group E8, the polytope is sometimes referred to as the E8 polytope.
Read more about this topic: 4 21 Polytope