What is a “perfect” magic cube?
The terminology used in this web site for the “perfect” multimagic cubes, is the most commonly used: a perfect magic cube is a magic cube with the additional property of each square being magic (every diagonal is magic, not just the triagonals). Definition used for example by Martin Gardner (Scientific American, January 1976), by William H. Benson and Oswald Jacoby (Magic Cubes: New Recreations, 1981), and also by Clifford A. Pickover (The Zen of Magic Squares, Circles and Stars, 2002). It is also used in the Eric Weissteins World of Mathematics at http://mathworld.wolfram.com/PerfectMagicCube.html. For multimagic cubes, it means for example that each square of the 32nd-order perfect bimagic cube is bimagic, and that each square of the 256th-order perfect trimagic cube is trimagic. There is another definition of a “perfect” cube, with supplemental properties of pandiagonality to get, defined by John R. Hendricks. The above “perfect” cubes are then no more called perfect, but “diagonal”
