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Pandiagonal Perfect Magic Cube


A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of n plane sections becomes 123...n, 23...n1, 3...n12, ..., or n123... (Benson and Jacoby 1981, p. 4).

Pandiagonal perfect magic cubes are possible for orders 8 and 9, but no smaller orders. They are also not possible for orders 12 or 14, but are possible for all orders that are multiples of 8 and odd orders greater than or equal to 9 (Benson and Jacoby 1981, p. 5). Benson and Jacoby (1981, pp. 76-78) explicitly construct a pandiagonal perfect magic cube of order 9.

Planck (1950; cited in Gardner 1988) constructed a perfect pandiagonal magic cube.


See also

Magic Cube, Nasik Cube, Pandiagonal Semiperfect Magic Cube, Semiperfect Magic Cube

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References

Benson, W. H. and Jacoby, O. Magic Cubes: New Recreations. New York: Dover, 1981.Gardner, M. "Magic Squares and Cubes." Ch. 17 in Time Travel and Other Mathematical Bewilderments. New York: W. H. Freeman, pp. 213-225, 1988.Pickover, C. A. The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions. Princeton, NJ: Princeton University Press, 2002.

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Pandiagonal Perfect Magic Cube

Cite this as:

Weisstein, Eric W. "Pandiagonal Perfect Magic Cube." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PandiagonalPerfectMagicCube.html

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