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hypercube
Sign in to saveAlso known as n-cube, n-eract, octachoron
In geometry, a hypercube is an n-dimensional analogue of a square (two-dimensional|) and a cube (Three-dimensional|); the special case for Four-dimensional space| is known as a tesseract. It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to \sqrt{n}.
~15 min read
Encyclopedic overview
13 sectionsContents
- Construction
- By the number of dimensions
- Vertex coordinates
- Faces
- Graphs
- Related families of polytopes
- {{anchor|Relation to n-simplices}}Relation to (''n''−1)-simplices
- Generalized hypercubes
- Relation to exponentiation
- See also
- Notes
- References
- External links
In geometry, a hypercube is an n-dimensional analogue of a square (two-dimensional|) and a cube (Three-dimensional|); the special case for Four-dimensional space| is known as a tesseract. It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length. A unit hypercube's longest diagonal in n dimensions is equal to \sqrt{n}.
An n-dimensional hypercube is more commonly referred to as an '''n-cube or sometimes as an n-dimensional cube. The term measure polytope' (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes.
Excerpted from Wikipedia’s “hypercube” article, available under the CC BY-SA 4.0 licence.