4 21 Polytope - 421 Polytope

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