Pandiagonal Magic Cube
Alternate name
Definition
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.... 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 explicitly construct a pandiagonal perfect magic cube of order 9. Planck (1950; cited in Gardner 1988) constructed a perfect pandiagonal magic cube.
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