nLab hypercube

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Contents

Contents

Idea

A hypercube is a cube in higher dimension.

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

Properties

Example

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

References

See also:

Last revised on January 27, 2025 at 14:09:04. See the history of this page for a list of all contributions to it.