Editing Diagonal magic cube

{{Short description|Magic cube with extra constraints}}
The class of '''diagonal magic cubes''' is the second of the six [[magic cube classes]] (when ranked by the number of lines summing correctly), coming after the [[simple magic cube]]s.

In a diagonal magic cube of order ''m'',<ref group = "notes" >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. </ref> 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'' [[Magic_square#Classification_of_magic_squares|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<sup>2</sup>  + 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''<sup>2</sup> correct lines and 9''m'' [[pandiagonal magic square]]s.

==See also==
*[[Magic cube classes]]
==Notes==
{{Reflist|group = notes}}

==External links==
*New definition:
**[http://members.shaw.ca/hdhcubes/cube_perfect.htm#Definitions Harvey Heinz’s magic cubes]
**[http://www.magichypercubes.com/Encyclopedia/ Aale de Winkel’s Magic Encyclopedia]
*Old definition:
**[https://web.archive.org/web/20050205173640/http://cboyer.club.fr/multimagie/index.htm Christian Boyer’s Multimagic cubes]
**[https://www.trump.de/magic-squares/magic-cubes/cubes-1.html Walter Trump’s Search for the smallest ‘perfect’ cube]

[[Category:Magic squares]]