| Regular enneazetton (8-simplex) | |
|---|---|
 Orthogonal projection inside Petrie polygon | |
| Type | Regular 8-polytope |
| Family | simplex |
| Schläfli symbol | {3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram |   
|
| 7-faces | 9 7-simplex
|
| 6-faces | 36 6-simplex
|
| 5-faces | 84 5-simplex
|
| 4-faces | 126 5-cell
|
| Cells | 126 tetrahedron
|
| Faces | 84 triangle
|
| Edges | 36 |
| Vertices | 9 |
| Vertex figure | 7-simplex |
| Petrie polygon | enneagon |
| Coxeter group | A8 [3,3,3,3,3,3,3] |
| Dual | Self-dual |
| Properties | convex |
In geometry, an 8-simplex is a self-dual regular 8-polytope. It has 9 vertices, 36 edges, 84 triangle faces, 126 tetrahedral cells, 126 5-cell 4-faces, 84 5-simplex 5-faces, 36 6-simplex 6-faces, and 9 7-simplex 7-faces. Its dihedral angle is cos−1(1/8), or approximately 82.82°.
It can also be called an enneazetton, or ennea-8-tope, as a 9-facetted polytope in eight-dimensions. The name enneazetton is derived from ennea for nine facets in Greek and -zetta for having seven-dimensional facets, and -on.