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Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist,[4] and cubes of orders five and six were first discovered by Walter Trump and Christian Boyer on November 13 and September 1, 2003, respectively.[5] A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875, an article was published in the Cincinnati Commercial newspaper on the discovery of a perfect magic cube of order 8 by Gustavus Frankenstein. Perfect magic cubes of orders nine and eleven have also been constructed.
The first perfect cube of order 10 was constructed in 1988 (Li Wen, China).[6]
In recent years[when?], an alternative definition for the perfect magic cube was proposed by John R. Hendricks. By this definition, a perfect magic cube is one in which all possible lines through each cell sum to the magic constant. The name Nasik magic hypercube is another, unambiguous, name for such a cube. This definition is based on the fact that a pandiagonal magic square has traditionally been called 'perfect', because all possible lines sum correctly.[7]
Gabriel Arnoux constructed an order 17 perfect magic cube in 1887. F.A.P.Barnard published order 8 and order 11 perfect cubes in 1888.[6]
