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
Helicopter Cube thus jutting outwards like spikes rather than lie flat on the face of the cube. More subtle changes may also be introduced, which are described later. There are four variants of the Helicopter Cube: If the puzzle is only scrambled using 180° twists, then it is obviously solvable using only 180° twists. However, if some jumbling moves were made, even if the puzzle was subsequently returned to cube shape, it may not be possible to solve it using only 180° twists. The reason for this is that using only 180° twists, each face center piece can only be permuted within