Magic Hypercube

In Mathematical, a magic Hypercube is generalization '' K '' - dimensional of a magic square , a magic Cube and a magic Tesseract, i.e., a whole number of arranged in a reason for size N × N × N ×… × N such as the numbers of each pile (along each axis) as of the principal diagonals is equal to a single number, which one calls the magic Constante of a magic Hypercube, noted $M\_k\; (N)\; \backslash ,$. It can be shown that if a magic hypercube is consisted of numbers 1,2,…, N ^K , then it has the magic constant

$M\_k\; (N)\; =\; \backslash \; frac\; \{1\}\; \{2\}\; N\; (n^k+1)$

If, moreover, the numbers of each Plane section diagonal give also the magic constant of the magic hypercube, the hypercube is called a perfect magic Hypercube; otherwise, it is called a semi-perfect magic Hypercube. The number N is called the order of the magic hypercube.

The hypercubes with dimensions five, six, seven and eight of order three were built by J.R. Hendricks. Marián Trenkler showed the following theorem: A magic hypercube p - dimensional of order N exists if and only if p > 1 and $n\; \backslash \; 2\; \backslash ,$ or p = 1. Demonstration rises a construction from a magic hypercube.

The computer programming language R includes a module, library (magic) , which can create magic hypercubes of any dimension (with multiple N of 4).

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