Magic Cube Collection

F. Poyo(

I have collected several magic cubes. Most of the magic cubes shown below are perfect magic cubes.

As long as I know, I can mention the followings:

  1. 4n-type cube has general algorithm (at least reported by Andrew.)
  2. I have an algorithm to construct arbitrary prime order complete magic cube (N>6).
  3. My generic algorithm for m-dimensional (Nm hyper magic cube covers arbitrary odd number order N except N=5 (as a particular case m=3).
  4. There is well known algorithm to construct 5x5x5 and 3x3x3 magic cube (reported by Andrew.)
  5. 6x6x6 complete magic cube and 10x10x10 magic cube are reported in Japanese book.
  6. Since we have 6x6x6 and 10x10x10 magic cubes, we can obtain 6(2m+1) and 10(2m+1) ordered magic cubes by the multiplication method. Therefore, it is conjectured that we can obtain 18x18x18 30x30x30 magic cubes, though they are 4n+2 type.
Since 2 may have potentiality to exhaust listing up some category of (complete) magic cubes, it is important, but in order to give one magic cube, 2 is not necessary. The algorithms 1, 2, 4 cover 4n type, 4n+1 type and 4n+3 type. We do not have 14x14x14, (18x18x18:we have theoretically), 22x22x22, and 4n+2 type (thus, n>2) magic cubes.

Here are the examples.

Mathemusement : Magic Squares and Magic Cubes