Editing Pandiagonal magic cube

{{Short description|Magic cube with extra constraints}}
{{notability|date=April 2012}}

In [[recreational mathematics]], a '''pandiagonal magic cube''' is a [[magic cube]] with the additional property that all [[broken diagonal]]s (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of [[diagonal magic cube]]s (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize [[pandiagonal magic square]]s to three dimensions.

In a pandiagonal magic cube, all 3''m'' planar arrays must be [[panmagic square]]s. The 6 oblique squares are always [[magic square|magic]]. Several of them may be panmagic squares.
A '''proper pandiagonal magic cube''' has exactly 9''m''<sup>2</sup> lines plus the 4 main [[space diagonal]]s summing correctly (no broken space diagonals have the correct sum.)

The smallest pandiagonal magic cube has order 7.

==See also==
*[[Magic cube classes]]

==References==
*Hendricks, J.R; ''Magic Squares to Tesseracts by Computer'', Self-published 1999. {{ISBN|0-9684700-0-9}}
*Hendricks, J.R.; ''Perfect n-Dimensional Magic Hypercubes of Order 2n'', Self-published 1999. {{ISBN|0-9684700-4-1}}
*[http://members.shaw.ca/hdhcubes/  Harvey Heinz: All about magic cubes]

[[Category:Magic squares]]


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