Main Page | See live article | Alphabetical index In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the sum of the numbers on each row, each column, each pillar and the four main space diagonals is equal to a single number, the so-called magic constant of the cube, denoted M3(n). It can be shown that if a magic cube consists of the numbers 1, 2, ..., n³, then it has magic number (Sloane's A027441) 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 cube. See also Magic square Perfect magic cube Semiperfect magic cube Bimagic cube Trimagic cube Multimagic cube Magic tesseract External links MathWorld: Magic Cube This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.