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A semiperfect magic cube, also called an Andrews Cube, is a Magic Cube for which the cross-section diagonals do not sum to the Magic Constant.
See also Magic Cube, Perfect Magic Cube
References
Gardner, M. ``Magic Squares and Cubes.'' Ch. 17 in Time Travel and Other Mathematical Bewilderments.
New York: W. H. Freeman, pp. 213-225, 1988.