Diagonal magic cube
In a diagonal magic cube of order m, all 6m 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 3m 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 + 6m + 4 correctly summing lines and 3m + 6 simple magic squares.
The new definition perfect magic cube has a total of 13m2 correct lines and 9m pandiagonal magic squares.
NOTE: 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.
See also
External Links
New definition:
http://members.shaw.ca/hdhcubes/cube_perfect.htm#Definitions ; Harvey Heinzs magic cubes.
http://home.wanadoo.nl/aaledewinkel/Encyclopedia/ : Aale de Winkels Magic Encyclopedia
Old definition:
http://cboyer.club.fr/multimagie/index.htm :Christian Boyers Multimagic cubes.
http://www.trump.de/magic-squares/magic-cubes/cubes-1.html ; Walter Trumps Search for the smallest perfect cube.