6-cube

{| 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} 25px|class=skin-invert |- |bgcolor=#e7dcc3|Faces||240 {4} 25px|class=skin-invert |- |bgcolor=#e7dcc3|Edges||192 |- |bgcolor=#e7dcc3|Vertices||64 |- |bgcolor=#e7dcc3|Vertex figure||5-simplex |- |bgcolor=#e7dcc3|Petrie polygon||dodecagon |- |bgcolor=#e7dcc3|Coxeter group||B6, [34,4] |- |bgcolor=#e7dcc3|Dual||6-orthoplex 25px|class=skin-invert |- |bgcolor=#e7dcc3|Properties||convex, Hanner polytope |} In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

It has Schläfli symbol {4,34}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets.