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
Floppy Cube 4); this means they can now be permutated in 12!/(12-4)! different ways. The corners still cannot be flipped; their orientation continues to be fully dependent on their position. All of these positions are attainable: there is no parity constraint, regardless of whether the edge pieces can twist on their own or not. The full number is therefore: This number is significantly larger than the number of combinations on the Floppy Cube. The God's Number for this puzzle is also considerably larger than that of the Floppy Cube: 13 (when edges can twist on their own) or 15 (when they cannot).