Pocket Cube court affirmed the judgment that Rubik's 2×2×2 Pocket Cube infringed Nichols's patent, but overturned the judgment on Rubik's 3×3×3 Cube. Any permutation of the eight corners is possible (8! positions), and seven of them can be independently rotated (3 positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles
Pantriagonal magic cube Pantriagonal magic cube A pantriagonal magic cube is a magic cube where all 4"m" 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"("m" + 1)/2. A proper pantriagonal magic cube has 7"m" 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