This article is about the mathematical concept. For the flashbulb cartridges, see Magicube. For the puzzle, see Rubik's Cube.
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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.
In mathematics, a magiccube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such...
A pantriagonal magiccube is a magiccube where all 4m2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(m − 1) two-segment pantriagonals...
Every magiccube may be assigned to one of six magiccube classes, based on the cube characteristics. This new system is more precise in defining magic cubes...
In mathematics, a perfect magiccube is a magiccube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section...
In recreational mathematics, a pandiagonal magiccube is a magiccube with the additional property that all broken diagonals (parallel to exactly two of...
P-multimagic cube is a magiccube that remains magic even if all its numbers are replaced by their k th powers for 1 ≤ k ≤ P. 2-multimagic cubes are called...
simulated by the MagicCube4D software. There have been many different shapes of Rubik type puzzles constructed. As well as cubes, all of the regular...
simple magiccube is the lowest of six basic classes of magiccubes. These classes are based on extra features required. The simple magiccube requires...
inlaid magic squares and other three dimensional magic figures like magic spheres and magic cylinders in Theory of magic squares and of magiccubes (1888)...
In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magiccubes, that is, an n × n × n × ... × n array of integers...
In a magiccube, a broken space diagonal is a sequence of cells of the cube that follows a line parallel to a space diagonal of the cube, and continues...
mean of the divisors of 5005, which is the magic constant of a 10 × 10 {\displaystyle 10\times 10} magiccube. 5005 is also the tenth non-unitary convolution...
Pan-3-Agonal MagicCube, Journal of Recreational Mathematics 5:1:1972, pp 51–54. First published mention of pan-3-agonals Hendricks, J. R., Magic Squares to...
the Rubik's Cube. His Notes on Rubik's "MagicCube" which he began compiling in 1979 provided the first mathematical analysis of the Cube as well as providing...
Professor's CubeMagicCube Postponed to 28–31 December 2020 and later canceled due to the COVID-19 pandemic. "WCA Regulations | World Cube Association"...
O'Shea Jackson Sr. (born June 15, 1969), known professionally as Ice Cube, is an American rapper, songwriter, actor, and film producer. His lyrics on N...
1980 book Notes on Rubik's "MagicCube". The same idea was adopted by James G. Nourse in his The Simple Solution to Rubik's Cube which became the bestselling...
magic cubes. Number shapes on a triangular grid divided into equal polyiamond areas containing equal sums give polyiamond magic constant. The magic constant...
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