Pandiagonal magic cube

In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions.

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. A proper pandiagonal magic cube has exactly 9m² lines plus the 4 main triagonals summing correctly. (No broken triagonals have the correct sum.)

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
• Harvey Heinz: All about magic cubes