Hypercube (EntityClass, 17)
From Higher Dimensions Database
A hypercube is an n-dimensional polytope which is the dual of that dimension's cross polytope. They exist in all dimensions. They can be represented by the bracketopic string [a_{1}a_{2}...a_{n}] or by the combined Coxeter-Dynkin string x4o(3o)*.
Under the elemental naming scheme, hypercubes are denoted by the geo- prefix, meaning the classical element of "earth".
Number of hypercells in a hypercube
Number of k-cubes in an n-cube: 2^{n-k}n!/(k!(n-k)!)
Hypercubes |
point • digon • square • cube • geochoron • geoteron • geopeton |