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In a Pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares. Gardner called Langman’s pandiagonal magic cube a ‘perfect’ cube, presumably not realizing it was a higher class then Myer’s diagonal magic cube. A diagonal magic cube has 3m plus 6 simple magic squares. A pandiagonal magic cube has 3m panmagic squares and 6 simple magic squares (one or two of these MAY be pandiagonal). A perfect magic cube has 9m panmagic squares. A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main triagonals summing correctly. (NO broken triagonals sum correct.) Order 7 is the smallest possible pandiagonal magic cube. See also * Magic cube classes References * Hendricks, J.R; Magic Squares to Tesseracts by Computer, Self-published 1999. ISBN 0-9684700-0-9 * Hendricks, J.R.; Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999. ISBN 0-9684700-4-1 Retrieved from "http://en.wikipedia.org/"  |
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