A pantriagonal magic cube is a magic cube where all 4m2 pantriagonals sum correctly.
This class of magic cubes may contain some simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications.
A proper pantriagonal magic cube has 7m2 lines summing correctly.
The smallest pantriagonal magic cube has order 4.
A pantriagonal magic cube is the 3-dimensional equivalent of the pandiagonal magic square – 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.