8-cube
In geometry, an 8-cube is an eight-dimensional hypercube. It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells, 1120 tesseract 4-faces, 448 5-cube 5-faces, 112 6-cube 6-faces, and 16 7-cube 7-faces.
| 8-cube Octeract | |
|---|---|
Orthogonal projection inside Petrie polygon | |
| Type | Regular 8-polytope |
| Family | hypercube |
| Schläfli symbol | {4,36} |
| Coxeter-Dynkin diagrams |
|
| 7-faces | 16 {4,35} |
| 6-faces | 112 {4,34} |
| 5-faces | 448 {4,33} |
| 4-faces | 1120 {4,32} |
| Cells | 1792 {4,3} |
| Faces | 1792 {4} |
| Edges | 1024 |
| Vertices | 256 |
| Vertex figure | 7-simplex |
| Petrie polygon | hexadecagon |
| Coxeter group | C8, [36,4] |
| Dual | 8-orthoplex |
| Properties | convex, Hanner polytope |
It is represented by Schläfli symbol {4,36}, being composed of 3 7-cubes around each 6-face. It is called an octeract, a portmanteau of tesseract (the 4-cube) and oct for eight (dimensions) in Greek. It can also be called a regular hexdeca-8-tope or hexadecazetton, being an 8-dimensional polytope constructed from 16 regular facets.
It is a part of an infinite family of polytopes, called hypercubes. The dual of an 8-cube can be called an 8-orthoplex and is a part of the infinite family of cross-polytopes.
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