5-cube
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
| 5-cube penteract (pent) | ||
|---|---|---|
| Type | uniform 5-polytope | |
| Schläfli symbol | {4,3,3,3} | |
| Coxeter diagram | ||
| 4-faces | 10 | tesseracts |
| Cells | 40 | cubes |
| Faces | 80 | squares |
| Edges | 80 | |
| Vertices | 32 | |
| Vertex figure | 5-cell | |
| Coxeter group | B5, [4,33], order 3840 | |
| Dual | 5-orthoplex | |
| Base point | (1,1,1,1,1,1) | |
| Circumradius | sqrt(5)/2 = 1.118034 | |
| Properties | convex, isogonal regular, Hanner polytope | |
It is represented by Schläfli symbol {4,3,3,3} or {4,33}, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge. It can be called a penteract, a portmanteau of the Greek word pénte, for 'five' (dimensions), and the word tesseract (the 4-cube). It can also be called a regular deca-5-tope or decateron, being a 5-dimensional polytope constructed from 10 regular facets.
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