Difference between revisions of "Superflip"

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(Wrote up some more stuff and added a 16s* solution.)
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[[Image:Superflip.png|frame|The superflip.]]
  
[[Image:superflip.gif|frame|Superflip]]
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The '''superflip''' is a famous position of the [[3x3x3]] where all corners are solved, and all edges are in the correct location but flipped. Despite its symmetry, this is an extremely difficult pattern, which is known to require 20 moves [[HTM]] to solve (in fact it was the first position that was proven to require that many moves). No position has ever been found which requires more moves than this, so many people believe that 20 moves is in fact the maximum number of moves that any 3x3 pattern could take to solve.
  
'''Superflip''' is a position of the Rubik's cube where all edges are flipped in place.
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The superflip also has a few interesting properties because of the way it interacts with the [[Rubik's cube group]]. If you do a [[commutator]] with the superflip and any other algorithm, you will always end up back at the solved state; the superflip is also self-inverse, which means doing it twice will bring you back to the solved state. Also, because the superflip is completely symmetrical but not solved, any move will bring it to a position that is easier to solve.
It is known to require 20 moves to be optimally solved and its symmetry is the reason that some believe it to be the "hardest" scramble of a Rubik's cube.
 
  
 
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One optimal solution in HTM for the superflip is U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2. The superflip also requires a minimum of 24 quarter turns to solve, and a minimum of 16 slice turns. One example of an optimal solution which requires 16 slice turns is S U B2 D2 M D' M2 S U R2 D M2 U B2 U S2.
Scramble: U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2
 

Revision as of 23:23, 26 November 2008

The superflip.

The superflip is a famous position of the 3x3x3 where all corners are solved, and all edges are in the correct location but flipped. Despite its symmetry, this is an extremely difficult pattern, which is known to require 20 moves HTM to solve (in fact it was the first position that was proven to require that many moves). No position has ever been found which requires more moves than this, so many people believe that 20 moves is in fact the maximum number of moves that any 3x3 pattern could take to solve.

The superflip also has a few interesting properties because of the way it interacts with the Rubik's cube group. If you do a commutator with the superflip and any other algorithm, you will always end up back at the solved state; the superflip is also self-inverse, which means doing it twice will bring you back to the solved state. Also, because the superflip is completely symmetrical but not solved, any move will bring it to a position that is easier to solve.

One optimal solution in HTM for the superflip is U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2. The superflip also requires a minimum of 24 quarter turns to solve, and a minimum of 16 slice turns. One example of an optimal solution which requires 16 slice turns is S U B2 D2 M D' M2 S U R2 D M2 U B2 U S2.