8-simplex

{| class="wikitable" align="right" style="margin-left:10px" width="250" ! style="background:#e7dcc3;" colspan="2"|Regular enneazetton(8-simplex) |- | style="background:#fff; text-align:center;" colspan="2"|280pxOrthogonal projectioninside Petrie polygon |- | style="background:#e7dcc3;"|Type||Regular 8-polytope |- | style="background:#e7dcc3;"|Family||simplex |- | style="background:#e7dcc3;"|Schläfli symbol|| {3,3,3,3,3,3,3} |- | style="background:#e7dcc3;"|Coxeter-Dynkindiagram|| |- | style="background:#e7dcc3;"|7-faces||9 7-simplex 25px |- | style="background:#e7dcc3;"|6-faces||36 6-simplex 25px |- | style="background:#e7dcc3;"|5-faces||84 5-simplex 25px |- | style="background:#e7dcc3;"|4-faces||126 5-cell 25px |- | style="background:#e7dcc3;"|Cells||126 tetrahedron 25px |- | style="background:#e7dcc3;"|Faces||84 triangle 25px |- | style="background:#e7dcc3;"|Edges||36 |- | style="background:#e7dcc3;"|Vertices||9 |- | style="background:#e7dcc3;"|Vertex figure||7-simplex |- | style="background:#e7dcc3;"|Petrie polygon||enneagon |- | style="background:#e7dcc3;"|Coxeter group|| A8 [3,3,3,3,3,3,3] |- | style="background:#e7dcc3;"|Dual||Self-dual |- | style="background:#e7dcc3;"|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, with suffix -on. Jonathan Bowers gives it the acronym ene.