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hypercube
Also 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}.
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Article
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.