A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly. There are 4 one-segment, 12(m − 1) two-segment, and 4(m − 2)(m − 1) three-segment pantriagonals. This class of magic cubes may contain some simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications.
The constant for magic cubes is S = m(m3 + 1)/2.
A proper pantriagonal magic cube has 7m2 lines summing correctly. It contains no magic squares.
Order 4 is the smallest pantriagonal magic cube possible. A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square. Only, instead of the ability to move a line from one edge to the opposite edge of the square with it remaining magic, you can move a plane from one edge to the other.
Famous quotes containing the word magic:
“The magic of photography is metaphysical. What you see in the photograph isn’t what you saw at the time. The real skill of photography is organised visual lying.”
—Terence Donovan (b. 1936)