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
N-dimensional sequential move puzzle the 2D puzzle cannot be scrambled at all if the same restrictions are placed on the moves as for the real 3D puzzle. The moves actually given to the 2D Magic Cube are the operations of reflection. This reflection operation can be extended to higher-dimension puzzles. For the 3D cube the analogous operation would be removing a face and replacing it with the stickers facing into the cube. For the 4-cube, the analogous operation is removing a cube and replacing it inside-out. Another alternate-dimension puzzle is a view achievable in David Vanderschel's Magic Cube 3D. A 4-cube projected on to