Pandiagonal magic cube
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In a Pandiagonal magic cube, ALL 3m planar arrays must be pandiagonal magic squares. The 6 oblique squares are always magic. Several of them MAY be pandiagonal magic.
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 pandiagonal magic squares and 6 simple magic squares (one or two of these MAY be pandiagonal). A Perfect magic cube has 9m pandiagonal magic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main traigonals suming correctly. (NO broken triagonals sum correct.)
Order 7 is the smallest possible pandiagonal magic cube.
[edit] See also
[edit] References
- J.R.Hendricks, Magic Squares to Tesseracts by Computer, Self-published 1999. ISBN 0-9684700-0-9
- J.R.Hendricks, Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999. ISBN 0-9684700-4-1
- Harvey Heinz: All about magic cubes
