Magic cube

An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.

In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal, the so-called magic constant of the cube, denoted M3(n).[1][2] If a magic cube consists of the numbers 1, 2, ..., n3, then it has magic constant (sequence A027441 in the OEIS)

If, in addition, the numbers on every cross section diagonal also sum up to the cube's magic number, the cube is called a perfect magic cube; otherwise, it is called a semiperfect magic cube. The number n is called the order of the magic cube. If the sums of numbers on a magic cube's broken space diagonals also equal the cube's magic number, the cube is called a pandiagonal magic cube.

  1. ^ W., Weisstein, Eric. "Magic Cube". mathworld.wolfram.com. Retrieved 2016-12-04.{{cite web}}: CS1 maint: multiple names: authors list (link)
  2. ^ "Magic Cube". archive.lib.msu.edu. Retrieved 2021-04-20.