If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square (Kraitchik 1942, pp. 143 and 189-191). (Only the rows, columns, and main diagonals must sum to the same constant for the usual type of magic square.) The terms diabolic square (Gardner 1961, pp. 135-137, p. 24; Madachy 1979, p. 87), pandiagonal square, and Nasik square are sometimes also used. No panmagic squares exist of order 3 or any order 4k + 2 for k an integer. The Siamese method for generating magic squares produces panmagic squares for orders 6k ± 1 with ordinary vector (2, 1) and break vector (1, -1).
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