Regular octaexon (7-simplex) | |
---|---|
Orthogonal projection inside Petrie polygon | |
Type | Regular 7-polytope |
Family | simplex |
Schläfli symbol | {3,3,3,3,3,3} |
Coxeter-Dynkin diagram | |
6-faces | 8 6-simplex |
5-faces | 28 5-simplex |
4-faces | 56 5-cell |
Cells | 70 tetrahedron |
Faces | 56 triangle |
Edges | 28 |
Vertices | 8 |
Vertex figure | 6-simplex |
Petrie polygon | octagon |
Coxeter group | A7 [3,3,3,3,3,3] |
Dual | Self-dual |
Properties | convex |
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell 5-faces, 28 5-simplex 6-faces, and 8 6-simplex 7-faces. Its dihedral angle is cos−1(1/7), or approximately 81.79°.