Magic Cube Classes - Another Definition and A Table

Another Definition and A Table

Proper: A Proper magic cube is a magic cube belonging to one of the six classes of magic cube, but containing exactly the minimum requirements for that class of cube. i.e. a proper simple or pantriagonal magic cube would contain no magic squares, a proper diagonal magic cube would contain exactly 3m + 6 simple magic squares, etc. This term was coined by Mitsutoshi Nakamura in April, 2004.

Notes for table

1. For the diagonal or pandiagonal classes, one or possibly 2 of the 6 oblique magic squares may be pandiagonal magic. All but 6 of the oblique squares are ‘broken’. This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2_D square; broken oblique squares are 2-D in a 3-D cube.
2. The table shows the minimum lines or squares required for each class (i.e. Proper). Usually there are more, but not enough of one type to qualify for the next class.