The class of diagonal magic cubes is the second of the six

magic cube classes In mathematics, a magic cube of order n is an n\times n \times n grid of natural numbers satisfying the property that the numbers in the same row, the same column, the same pillar or the same length-n space diagonal, diagonal add up to the same n ...

(when ranked by the number of lines summing correctly), coming after the simple magic cubes. In a diagonal magic cube of order ''m'',Traditionally, ''n'' has been used to indicate the order of the magic hypercube. However, in recent years, due to the increasing emphasis on higher dimension hypercubes, there is a trend to use ''m'' to indicate order and ''n'' to indicate dimension. all 6''m'' of the diagonals in the ''m'' planes parallel to the top, front, and sides of the cube must sum correctly. This means that the cube contains 3''m'' simple magic squares of order ''m''. Because the cube contains so many magic squares, it was considered for many years to be "perfect" (although other types of cubes were also sometimes called a "perfect magic cube"). It is now known that there are three higher classes of cubes. The (proper) diagonal magic cube has a total of 3m² + 6''m'' + 4 correctly summing lines and 3''m'' + 6 simple magic squares. The new definition perfect magic cube has a total of 13''m''² correct lines and 9''m''

pandiagonal magic square A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the squ ...

Notes

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External links

*New definition:
Harvey Heinz’s magic cubes

Aale de Winkel’s Magic Encyclopedia
*Old definition:

Magic squares

See also

Notes

External links