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| 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 |
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.
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.