A Pantriagonal Diagonal magic cube
is a magic cube
that is a combination Pantriagonal magic cube
and Diagonal magic cube
. All main and broken triagonals must sum correctly, In addition, it will contain 3m order m simple magic squares
in the orthogonal planes, and 6 order m pandiagonal magic squares
in the oblique planes.
A proper pantriagdiag magic cube contains exactly 7m2 + 6m lines that sum to m(m3 + 1)/2.
For short, I will reduce this unwieldy name to PantriagDiag.
This is number 4 in what is now 6 classes of magic cubes. So far, very little is known of this class of cube. The only ones constructed so far are order 8 (not associated and associated). Is order 8 the smallest possible for this type of cube?
This cube was discovered in 2004 by Mitsutoshi Nakamura.
Magic cube classes
- http://homepage2.nifty.com/googol/magcube/en/ : Mitsutoshi Nakamura’s Magic Cubes and Tesseracts
- http://members.shaw.ca/hdhcubes/ : Harvey Heinz All about cubes