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 corner pieces, which can be permutated in 4! different ways. They cannot be flipped; their orientation is fully determined by their location. The whole puzzle also has a parity constraint: the parity of the corner permutation is the same as the parity of the number of flipped edges. This divides the full number by 2. The full number of possible combinations on the Floppy Cube is therefore: In relative terms, this number is extremely low compared to other puzzles like the Rubik's Cube (with over 43 quintillion combinations), the Rubik's Domino (which has just under 410 million combinations), or