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Pantriagonal Magic Cube
{{no footnotes, date=December 2014 A pantriagonal magic cube is a magic cube where all 4''m''2 pantriagonals sum correctly. There are 4 one-segment pantriagonals, 12(''m'' − 1) two-segment pantriagonals, and 4(''m'' − 2)(''m'' − 1) three-segment pantriagonals. This magic cube classes, class of magic cubes may contain some Magic_square#Classification_of_magic_squares, simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications. The magic constant for magic cubes is ''S'' = ''m''(''m''3 + 1)/2. A proper pantriagonal magic cube has 7''m''2 lines summing correctly. It contains ''no'' magic squares. The smallest pantriagonal magic cube has order 4. A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square – instead of the ability to move a ''line'' from one edge to the opposite edge of the square with it remaining magic, you can move a ''plane'' from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 to the same number, the so-called magic constant of the cube, denoted ''M''3(''n''). It can be shown that if a magic cube consists of the numbers 1, 2, ..., ''n''3, then it has magic constant :M_3(n) = \frac. 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. Alternative definition In recent years, an alternative definition f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
