Mathematical Definition via Wikipedia:
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.
An n-dimensional hypercube is also called an n-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polytope" is also used, notably in the work of H.S.M. Coxeter (originally from Elte, 1912), but it has now been superseded.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 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.