| 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°.