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hypercubes
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| Plural form of hypercube. |
| A geometrical figure in four or more dimensions which is analogous to a cube in three dimensions. |
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In geometry, a Hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). 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 * * * * * * n * * * * * {\displaystyle {\sqrt {n}}} * . * An n-dimensional hypercube is also called an n-cube or an n-dimensional cube. The term "measure polytope" is also used, notably in the work of H. S. M. Coxeter (originally from Elte, 1912), but it has now been superseded. * The hypercube is the special case of a hyperrectangle (also called an n-orthotope). * A unit hypercube is a hypercube whose side has length one unit. Often, the hypercube whose corners (or vertices) are the 2n points in Rn with each coordinate equal to 0 or 1 is called "the" unit hypercube. |