nLab hypercube

Idea

A hypercube is a cube in higher dimension.

Regarded as a topological space, the $n$-dimensional hypercube for $m \in \mathbb{N}$ is $[0,1]^n$, the $n$-fold Cartesian product of the standard interval with itself.

Properties

Example

The symmetry group of the $n$-dimensional hypercube is the wreath product $C_2 \wr Sym(n)$ of the cyclic group of order 2 with the symmetric group on $n$ elements.

Related concepts

• hyperplane

References

See also:

• Wikipedia, Hypercube