| bgcolor=#e7dcc3 colspan=2 | 10-cube Dekeract | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection inside Petrie polygon Orange vertices are doubled, and central yellow one has four | |
| Type | Regular 10-polytope e | |
| Family | hypercube | |
| Schläfli symbol | ||
| Coxeter-Dynkin diagram | ||
| 9-faces | 20 | |
| 8-faces | 180 | |
| 7-faces | 960 | |
| 6-faces | 3360 | |
| 5-faces | 8064 | |
| 4-faces | 13440 | |
| Cells | ||
| Faces | ||
| Edges | 5120 segments | |
| Vertices | ||
| Vertex figure | ||
| Petrie polygon | icosagon | |
| Coxeter group | C10, [3<sup>8</sup>,4] | |
| Dual | ||
| Properties | convex, Hanner polytope |
It can be named by its Schläfli symbol, being composed of 3 9-cubes around each 8-face. It is sometimes called a dekeract, a portmanteau of tesseract (the 4-cube) and deka- for ten (dimensions) in Greek, It can also be called an icosaronnon or icosa-10-tope as a 10 dimensional polytope, constructed from 20 regular facets.
It is a part of an infinite family of polytopes, called hypercubes. The dual of a dekeract can be called a 10-orthoplex or decacross, and is a part of the infinite family of cross-polytopes.
Cartesian coordinates for the vertices of a dekeract centered at the origin and edge length 2 are
(±1,±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, x9) with −1 < xi < 1.
Applying an alternation operation, deleting alternating vertices of the dekeract, creates another uniform polytope, called a 10-demicube, (part of an infinite family called demihypercubes), which has 20 demienneractic and 512 enneazettonic facets.