Hypercube

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 .

This article is about the mathematical concept. For the film, see Cube 2: Hypercube. For the computer architecture, see Connection Machine. For internetwork topology, see Hypercube internetwork topology. For the four-dimensional object known as "the" hypercube, see Tesseract.
Perspective projections
Cube (3-cube) Tesseract (4-cube)

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.

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.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.