Simple magic cube

An example of a 3 × 3 × 3 simple magic cube.

A simple magic cube is the lowest of six basic classes of magic cube. These classes are based on extra features required.

The simple magic cube requires only the basic features a cube requires to be magic. Namely; all lines parallel to the faces, and all 4 triagonals sum correctly.^[1] i.e. all 1-agonals and all 3-agonals sum to

$S={\frac {m(m^{3}+1)}{2}}.$

No planar diagonals (2-agonals) are required to sum correctly, so there are probably no magic squares in the cube.

See also

• Magic square
• Magic cube classes

References

1. Pickover, Clifford A. (2002). The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures Across Dimensions. Princeton University Press. p. 400. ISBN 9780691070414.

External links

• Aale de Winkel - Magic hypercubes encyclopedia
• Harvey Heinz - large site on magic squares and cubes
• Christian Boyer - Multimagic cubes
• John Hendricks site on magic hypercubes