The class of diagonal magic cubes is the second of the six
magic cube classes
Every magic cube may be assigned to one of six magic cube classes, based on the cube characteristics.
This new system is more precise in defining magic cubes. But possibly of more importance, it is consistent for all orders and all dimensions of ...
(when ranked by the number of lines summing correctly), coming after the
simple magic cube
A simple magic cube is the lowest of six basic classes of magic cubes. These classes are based on extra features required.
The simple magic cube requires only the basic features a cube requires to be magic. Namely, all lines parallel to the face ...
s.
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 3m
2 + 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 squar ...
s.
See also
*
Magic cube classes
Every magic cube may be assigned to one of six magic cube classes, based on the cube characteristics.
This new system is more precise in defining magic cubes. But possibly of more importance, it is consistent for all orders and all dimensions of ...
Notes
{{Reflist, group = notes
External links
*New definition:
Harvey Heinz’s magic cubesAale de Winkel’s Magic Encyclopedia*Old definition:
Magic squares