magic tesseract

In mathematics, a magic tesseract is the 4-dimensional generalization of a magic square and magic cube, that is, a number of integers arranged in an n × n × n × 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 tesseract, denoted M₄(n). It can be shown that if a magic tesseract consists of the numbers 1, 2, ..., n⁴, then it has magic constant

M_4(n) = \frac{1}{2}n(n^4+1)

The number n is called the order of the magic tesseract.

Perfect magic tesseract

If, in addition, the numbers on every cross section diagonal also sum up to the tesseract's magic constant, the tesseract is called a perfect magic tesseract; otherwise, it is called a semiperfect magic tesseract. The smallest known perfect magic tesseract is of order 16; its magic constant is 524296, and it was discovered by retired meteorologist John R. Hendricks from British Columbia with the help of Cliff Pickover at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York after about ten hours of computing time on an IBM Intellistation computer system.

Magic Tesseract

Perfect magic tesseract

See also