HyperCube

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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, at right angles to each other.

An n-dimensional hypercube is also called an n-cube. The term "measure polytope" (which is apparently due to Coxeter; see Coxeter 1973) is also used but it is rare.

The hypercube is the special case of a hyperrectangle (also called an 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 coordinates equal to 0 or 1 is called "the" unit hypercube.

A point is a hypercube of dimension zero. If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one. If one moves this line segment its length in a perpendicular direction from itself; it sweeps out a two-dimensional square. If one moves the square one unit length in the direction perpendicular to the plane it lies on, it will generate a three-dimensional cube. This can be generalized to any number of dimensions. For example, if one moves the cube one unit length into the fourth dimension, it generates a 4-dimensional unit hypercube (a unit tesseract).

The 1-skeleton of a hypercube is a hypercube graph.

Από: http://en.wikipedia.org/wiki/Hypercube