As demonstrated in [1], it is possible to generalise the familiar 3-dimensional cube to n dimensions for each n > 0. We present here a fascinating link between a geometrical aspect of these 'n-dimensional hypercubes' and the normal distribution.

In what follows we shall identify with n-dimensional space, and use n-D to denote ‘;n-dimensional’. For the sake of mathematical convenience we initially consider n-D hypercubes of edge length 1 unit whose 2n vertices are situated in at all possible n-tuples (c1, c2, ... , cn), where ck is equal either to 0 or 1, . We denote these mathematical objects by Cn, n = 0,1,2,3, .... Our results, however, can easily be generalised to hypercubes of any edge length, and situated anywhere in .