9-cube

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|9-cubeEnneract |- |bgcolor=#ffffff align=center colspan=2|280pxOrthogonal projectioninside Petrie polygonOrange vertices are doubled, yellow have 4, and the green center has 8 |- |bgcolor=#e7dcc3|Type||Regular 9-polytope |- |bgcolor=#e7dcc3|Family||hypercube |- |bgcolor=#e7dcc3|Schläfli symbol|| {4,37} |- |bgcolor=#e7dcc3|Coxeter-Dynkin diagram|| |- |bgcolor=#e7dcc3|8-faces||18 {4,36} 25px |- |bgcolor=#e7dcc3|7-faces||144 {4,35} 25px |- |bgcolor=#e7dcc3|6-faces||672 {4,34} 25px |- |bgcolor=#e7dcc3|5-faces||2016 {4,33} 25px |- |bgcolor=#e7dcc3|4-faces||4032 {4,32} 25px |- |bgcolor=#e7dcc3|Cells||5376 {4,3} 25px |- |bgcolor=#e7dcc3|Faces||4608 {4} 25px |- |bgcolor=#e7dcc3|Edges||2304 |- |bgcolor=#e7dcc3|Vertices||512 |- |bgcolor=#e7dcc3|Vertex figure||8-simplex 25px |- |bgcolor=#e7dcc3|Petrie polygon||octadecagon |- |bgcolor=#e7dcc3|Coxeter group||C9, [37,4] |- |bgcolor=#e7dcc3|Dual||9-orthoplex 25px |- |bgcolor=#e7dcc3|Properties||convex, Hanner polytope |} In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.

It can be named by its Schläfli symbol {4,37}, being composed of three 8-cubes around each 7-face. It is also called an enneract, a portmanteau of tesseract (the 4-cube) and enne for nine (dimensions) in Greek. It can also be called a regular octadeca-9-tope or octadecayotton, as a nine-dimensional polytope constructed with 18 regular facets.