7-cube
In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.
| 7-cube Hepteract | |
|---|---|
Orthogonal projection inside Petrie polygon The central orange vertex is doubled | |
| Type | Regular 7-polytope |
| Family | hypercube |
| Schläfli symbol | {4,35} |
| Coxeter-Dynkin diagrams |
|
| 6-faces | 14 {4,34} |
| 5-faces | 84 {4,33} |
| 4-faces | 280 {4,3,3} |
| Cells | 560 {4,3} |
| Faces | 672 {4} |
| Edges | 448 |
| Vertices | 128 |
| Vertex figure | 6-simplex |
| Petrie polygon | tetradecagon |
| Coxeter group | C7, [35,4] |
| Dual | 7-orthoplex |
| Properties | convex, Hanner polytope |
It can be named by its Schläfli symbol {4,35}, being composed of 3 6-cubes around each 5-face. It can be called a hepteract, a portmanteau of tesseract (the 4-cube) and hepta for seven (dimensions) in Greek. It can also be called a regular tetradeca-7-tope or tetradecaexon, being a 7 dimensional polytope constructed from 14 regular facets.
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