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6-cube
6-dimensional hypercube / From Wikipedia, the free encyclopedia
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.
More information 6-cube Hexeract ...
6-cube Hexeract | |
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![]() 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 |
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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.