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
Magic cube classes Frost referred to all but the simple class as Nasik cubes. <br>The smallest normal diagonal magic cube is order 5. See Diagonal magic cube. Minimum correct summations required = 3"m" + 6"m" + 4 All 4m pantriagonals must sum correctly (that is 4 one-segment, 12("m"-1) two-segment, and 4("m"-2)("m"-1) three-segment). There may be some simple AND/OR pandiagonal magic squares, but not enough to satisfy any other classification. <br>The smallest normal pantriagonal magic cube is order 4. See Pantriagonal magic cube. <br>Minimum correct summations required = 7"m". All pan-"r"-agonals sum correctly for "r" = 1 and 3. A cube of this class