6-polytopes

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|6-cubeHexeract |- |bgcolor=#ffffff align=center colspan=2|280pxOrthogonal projectioninside Petrie polygonOrange vertices are doubled, and the center yellow has 4 vertices |- |bgcolor=#e7dcc3|Type||Regular 6-polytope |- |bgcolor=#e7dcc3|Family||hypercube |- |bgcolor=#e7dcc3|Schläfli symbol|| {4,34} |- |bgcolor=#e7dcc3|Coxeter diagram|| |- |bgcolor=#e7dcc3|5-faces||12 {4,3,3,3} 25px|class=skin-invert |- |bgcolor=#e7dcc3|4-faces||60 {4,3,3} 25px|class=skin-invert |- |bgcolor=#e7dcc3|Cells||160 {4,3}

In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and 7 5-simplex 5-faces. Its dihedral angle is cos−1(1/6), or approximately 80.41°.