6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
| 6-cube Hexeract | |
|---|---|
Orthogonal projection inside Petrie polygon Orange vertices are doubled, and the center yellow has 4 vertices | |
| Type | Regular 6-polytope |
| Family | hypercube |
| Schläfli symbol | {4,34} |
| Coxeter diagram | |
| 5-faces | 12 {4,3,3,3} |
| 4-faces | 60 {4,3,3} |
| Cells | 160 {4,3} |
| Faces | 240 {4} |
| Edges | 192 |
| Vertices | 64 |
| Vertex figure | 5-simplex |
| Petrie polygon | dodecagon |
| Coxeter group | B6, [34,4] |
| Dual | 6-orthoplex |
| Properties | convex, Hanner polytope |
It has Schläfli symbol {4,34}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets.
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