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
Multimagic cube Multimagic cube In mathematics, a "P"-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their "k"-th power for 1 ≤ "k" ≤ "P". Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic. A "P"-multimagic cube is said to be semi-perfect if the "k"-th power cubes are perfect for 1 ≤ "k" < "P", and the "P"-th power cube is semiperfect. If all "P" of the power cubes are perfect, the multimagic cube is said to be perfect. The first known