Pandiagonal magic cube
In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals have the same sum as each other. Pandiagonal magic cubes are extensions of magic cube">magic square">magic cubes and generalize pandiagonal magic squares to three dimensions.
In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main space diagonals summing correctly
The smallest pandiagonal magic cube has order 7.