In mathematics, a magic hypercube is the k-dimensional generalization of magic squares, magic cubes and magic tesseracts, that is, a number of integers arranged in an n x n x n x ... x n pattern such that the sum of the numbers on each pillar (along any axis) as well as the main space diagonals is equal to a single number, the so-called magic constant of the hypercube, denoted Mk(n). It can be shown that if a magic hypercube consists of the numbers 1, 2, ..., nk, then it has magic number
Five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks.