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Algorithm for orientating flipped middle layer pieces

Submitted by ZMRGZ on Wed, 08/15/2007 - 23:36.
Does anyone know any algorithms for flipping incorrectly orientated middle layer edge pieces? I looked all over the internet but couldn't find any...
THANKS!!!
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Submitted by kuddelmuddel on Tue, 09/25/2007 - 12:00.
take a look at www.kuddelmuddel-cube.2page.de
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RU'R'UF'U2FU2F'UF to flip a s

Submitted by blahness on Mon, 09/03/2007 - 22:36.
RU'R'UF'U2FU2F'UF to flip a single edge piece.
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Re: RU'R'UF'U2FU2F'UF to flip a s

Submitted by Bruce Norskog on Tue, 09/04/2007 - 21:53.
As far as the bottom two layers are concerned, yes, RU'R'UF'U2FU2F'UF has no effect except to flip one of the edges (RF) in the middle layer. Of course, it has a lot of side effects on the top layer. Unfortunately, ZMRGZ didn't specify what part of the cube was expected to be left intact, and what part (if any) was allowed to be changed. If ZMRGZ's intent with the question was simply to finish two layers, then this would be fine way to do that.

By the way, a web search for "F2L" should give several sites that have an "algorithm" for this case of no side effects in the bottom two layers except for flipping a middle-layer edge.
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Re: Algorithm for orientating flipped middle layer pieces

Submitted by Bruce Norskog on Sat, 08/25/2007 - 18:43.

It shouldn't be hard to find web sites that have such sequences. I assume that by "middle layer" you mean the layer between the top and bottom layers.

If you want two edges flipped, with everything else unchanged, there are a number of ways to do that. If you only care about the middle layer between the top and bottom layers, then there are two cases: two edges on the same face to be flipped (such as FL and FR) and two diagonally opposed edges (such BL and FR).

There is a sequence that has been called "Rubik's maneuver" that flips the UF and UB edges, but if you have two edges from the middle layer (but on the same face) to orient, you need to reorient the cube so that the two edges are at UF and UB. (Or you could translate the moves appropriately.) "Rubik's maneuver" is:
M' U M' U M' U2 M U M U M U2

M means to move the inner layer between the L and R faces such that the front face center moves down to the bottom face. M' means to do the inverse of that (so that the front face center moves to the top face). For more on notation, see http://www.speedcubing.com/moves.html.

You could also use a commutator such as the following to flip FL and FR:
(R' S R2 S2 R') F2 (R S2 R2 S' R) F2

S means to move the inner layer between the F and B faces such that the top face center moves to the right face. Of course, S' means to do the inverse of that, and S2 means to do a half-turn of the same layer.

Cube Explorer can be used to find optimal face turn metric. I get this sequence (for FR and FL):
U F L' U F' L U' D F' R U' F R' D'

For diagonally opposite edges, you could do use Rubik's maneuver (with appropriate cube orientation) to flip FL and FR. That will flip one of them correct and mis-orient another. Then the two that are mis-oriented can be fixed by another Rubik's maneuver. Or you could turn a side face a half-turn so that the two bad edges are on the same face. Then a single Rubik's maneuver can be used to orient them, followed by the same side face being turned a half-turn again to restore the positions of the cubies.

For BL and FR, I get the optimal sequence from Cube Explorer:
U2 R F' U R' F U2 D2 B' L U' B L' D2

(While these sequences are longer than the earlier ones, the earlier ones use inner layer turns which count as two moves in the face-turn metric.)

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Sequences with Cube Explorer

Submitted by Herbert Kociemba on Sun, 08/26/2007 - 13:21.
A maybe not so well known feature of Cube Explorer is that you get another sequence if you press the "solve optimal" button again in the main window. In principle you get as many sequences as you want doing this way.
If the optimal solution is not longer as 14-15 moves there is another "trick" which works even better. You undefine (grey out) just one edge with right mouseclicks in the facelet editor (for example the UF edge). Then the solver for incomplete cubes is invoked which outputs all sequences in a seperate window.
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