Superflip


The superflip or 12-flip is a Rubik's Cube configuration in which all 20 of the movable subcubes are in the correct permutation, and the eight corners are correctly oriented, but all twelve of the edges are oriented incorrectly. It has been shown that the shortest path between a solved cube and the Superflip position requires 20 moves under the usual half-turn metric, and that no position requires more .
Under the more restrictive quarter-turn metric, only 90° face turns are allowed, so 180° turns count as two "moves". In those terms, the Superflip requires 24 moves, and is not maximally distant from the solved state. Instead, when Superflip is composed with the "four-dot" or "four-spot" position, in which four faces have their centers exchanged with the centers on the opposite face, the resulting position may be unique in requiring 26 moves under QTM.

Solution

This is one possible sequence of moves to generate the Superflip, recorded in Singmaster notation. It is the minimal 20 moves in the half-turn metric, though it requires 28 quarter turns:
U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2
One of solutions in 24 quarter turns is:
R' U2 B L' F U' B D F U D' L D2 F' R B' D F' U' B' U D'
There is another solution by using slice moves. It can be solved in 16 moves in the slice-turn metric and there are 32 quarter turns:
M2 U' R2 D' S M2 U M' U2 F2 D' S M2 U' R2 U'