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
Soma cube oriented to fill just that one remaining corner, and orienting it such that it fills zero corners will obviously not make a cube. Therefore, the "T" must always fill two corners, and there is only one orientation (discounting rotations and reflections) in which it does that. It also follows from this that in all solutions, five of the remaining six pieces will fill their maximum number of corners and one piece will fill one fewer than its maximum (this is called the deficient piece). Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6