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 number of permutations is reduced to 24!/(4!) arrangements. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given colour. This is raised to the sixth power because there are six colours. This gives a total number of permutations of The expanded number is (approximately trillion or 12 trilliard on the long scale or 12 sextillion on the short scale) To count non-cube positions, we need to count all the possible shapes (ignoring the colours). Counting those shapes is tricky, since sometimes moves are blocked purely due to the shape of the