9-cube
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.
| 9-cube Enneract | |
|---|---|
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 | {4,37} |
| Coxeter-Dynkin diagram | |
| 8-faces | 18 {4,36} |
| 7-faces | 144 {4,35} |
| 6-faces | 672 {4,34} |
| 5-faces | 2016 {4,33} |
| 4-faces | 4032 {4,3,3} |
| Cells | 5376 {4,3} |
| Faces | 4608 {4} |
| Edges | 2304 |
| Vertices | 512 |
| Vertex figure | 8-simplex |
| Petrie polygon | octadecagon |
| Coxeter group | C9, [37,4] |
| Dual | 9-orthoplex |
| Properties | convex, Hanner polytope |
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.
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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.