Pandiagonal magic cube
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In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions.
In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares. A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main space diagonals summing correctly (no broken space diagonals have the correct sum.)
The smallest pandiagonal magic cube has order 7.
See also
[edit | edit source]References
[edit | edit source]- Hendricks, J.R; Magic Squares to Tesseracts by Computer, Self-published 1999. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Hendricks, J.R.; Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999. Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Harvey Heinz: All about magic cubes
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