Helicopter Cube a 6-member cycle, often referred to as its "orbit". Face center pieces in different orbits cannot be interchanged using only 180° twists. However, jumbling moves are able to permute face center pieces between different orbits, thus leaving the puzzle in a state that cannot be solved by 180° twists alone. Assume that Helicopter Cube is scrambled without jumbling moves (i.e. mixed with only 180 degree twists). Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving 8!×3 combinations. There are
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