| bgcolor=#e7dcc3 colspan=2 | 9-cube Enneract | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection inside Petrie polygon Orange vertices are doubled, yellow have 4, and the green center has 8 | |
| Type | Regular 9-polytope | |
| Family | hypercube | |
| Schläfli symbol | ||
| Coxeter-Dynkin diagram | ||
| 8-faces | 18 | |
| 7-faces | 144 | |
| 6-faces | 672 | |
| 5-faces | 2016 | |
| 4-faces | 4032 | |
| Cells | 5376 | |
| Faces | 4608 | |
| Edges | 2304 | |
| Vertices | 512 | |
| Vertex figure | ||
| Petrie polygon | octadecagon | |
| Coxeter group | C9, [3<sup>7</sup>,4] | |
| Dual | ||
| Properties | convex, Hanner polytope |
It can be named by its Schläfli symbol, 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.
It is a part of an infinite family of polytopes, called hypercubes. The dual of a 9-cube can be called a 9-orthoplex, and is a part of the infinite family of cross-polytopes.
Cartesian coordinates for the vertices of a 9-cube centered at the origin and edge length 2 are
(±1,±1,±1,±1,±1,±1,±1,±1,±1)while the interior of the same consists of all points (x0, x1, x2, x3, x4, x5, x6, x7, x8) with −1 < xi < 1.
Applying an alternation operation, deleting alternating vertices of the 9-cube, creates another uniform polytope, called a 9-demicube, (part of an infinite family called demihypercubes), which has 18 8-demicube and 256 8-simplex facets.