A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect 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.... There is no pandiagonal semiperfect magic cube of order 3. The order 4 and 5 magic cubes shown above are pandiagonal semiperfect magic (Benson and Jacoby 1988, pp. 15-23 and 30).
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