7-simplex

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|Regular octaexon(7-simplex) |- |bgcolor=#ffffff align=center colspan=2|280pxOrthogonal projectioninside Petrie polygon |- |bgcolor=#e7dcc3|Type||Regular 7-polytope |- |bgcolor=#e7dcc3|Family||simplex |- |bgcolor=#e7dcc3|Schläfli symbol|| {3,3,3,3,3,3} |- |bgcolor=#e7dcc3|Coxeter-Dynkindiagram|| |- |bgcolor=#e7dcc3|6-faces||8 6-simplex 25px |- |bgcolor=#e7dcc3|5-faces||28 5-simplex 25px |- |bgcolor=#e7dcc3|4-faces||56 5-cell 25px |- |bgcolor=#e7dcc3|Cells||70 tetrahedron 25px |- |bgcolor=#e7dcc3|Faces||56 triangle 25px |- |bgcolor=#e7dcc3|Edges||28 |- |bgcolor=#e7dcc3|Vertices||8 |- |bgcolor=#e7dcc3|Vertex figure||6-simplex |- |bgcolor=#e7dcc3|Petrie polygon||octagon |- |bgcolor=#e7dcc3|Coxeter group|| A7 [3,3,3,3,3,3] |- |bgcolor=#e7dcc3|Dual||Self-dual |- |bgcolor=#e7dcc3|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°.

== Alternate names == It can also be called an octaexon, or octa-7-tope, as an 8-facetted polytope in 7-dimensions. The name octaexon is derived from octa for eight facets in Greek and -ex for having six-dimensional facets, and -on. Jonathan Bowers gives an octaexon the acronym oca.