Superflip

The superflip or 12-flip is a Rubik's Cube configuration in which all 20 of the movable subcubes (or "cubies") are in the correct permutation, and the eight corners are correctly oriented, but all twelve of the edges are oriented incorrectly ("flipped"). It has been shown[1] that the shortest path between a solved cube and the Superflip position requires 20 moves under the usual half-turn metric (HTM, in which rotating a face 180° counts as a single move), and that no position requires more (although there are many other positions that also require 20 moves).

A computer graphic of the Superflip pattern

Under the more restrictive quarter-turn metric (QTM), only 90° face turns are allowed, so 180° turns count as two "moves". In those terms, the Superflip requires 24 moves,[2] 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.[3]

Solution

This is one possible sequence of moves to generate the Superflip (starting from a solved Rubik's cube), 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 (but 22 half turns) is:[4][5]

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'

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See also

References
  1. Rokicki, Tomas. "God's Number is 20". Cube 20.
  2. The first algorithm is one of several 24 qtm solutions
  3. Rokicki, Tomas. "God's Number is 26 in the Quarter-Turn Metric". Cube 20.
  4. Joyner 2008, p.100
  5. Michael Reid (2005-05-24). "M-symmetric positions". Rubik's cube page. Archived from the original on 2015-07-06.

Further reading
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