Hmm, yeah I was wondering, do the top 5x5BLDers reorient?
I know that Mike and I both do. I think Mats does as well, and I don't know about Spef, Chester, Tim Sun, aronpm, or the others.
And about my question I'm reffering to just orienting the cube to get lots of centers solved (like one would do with the 4x4), and then from there switch the central most centers. I might have it wrong and I don't be planning on doing this anytime soon, just curious.
Considering the central centers to be pieces, there are 24 different ways that they can be permuted. Half of these cases are "parity" cases, or better said half of the cases are odd permutations of the centers. The half that are even permutations of the centers (i.e. no parity) can be solved with 4 move commutators.
I only re-orient to the even parity cases, as I don't know a quick or efficient center parity alg (which will necessarily have to change the parity of central edges as well).
The way I recognize is to split the unsolved cases into two groups. The first group I consider to be the "three cycles" and the second group the "double swaps", the third group is the solved case alone or no reorienting.
There are 8 "three cycle" cases, and they are the following:
U -> F -> R (and so also D -> B -> L)
U -> F -> L (also D -> B -> R)
U -> R -> F (D -> L -> B)
U -> R -> B (D -> L -> F)
U -> B -> R (D -> F -> L)
U -> B -> L (D -> F -> R)
U -> L -> F (D -> R -> B)
U -> L -> B (D -> R -> F)
To solve a three cycle case I only use M and E turns. I must bring the U center down to either the F or B face via the M layer. But before doing that, I must move the face it is supposed to go to onto either the F or B face with an E layer turn. The way I know which face to turn the E layer to, is to turn it to the one that is the other piece in the cycle.
For example let's do the case: U -> R -> B (D -> L -> F)
To me this case is only U -> R -> B, and I never pay attention to the 3 cycle on the other side of the cube.
I know that the U center must move to the R face, but I have to bring the U center down to either F or B only. I know that I need to bring it down to the B face, because B is the other location in the three cycle.
So first I must move the R center to the B face by doing the turn E. Now I bring the U center down to the B face by doing M'. Lastly I just undo in the proper order to make this a commutator, so then follow with E' M
This makes that case E M' E' M
Every other case is done in a similar way.
The "double swap" cases could also be called the "double turn" cases. There are 3 of these. They make one of the M, E, or S slices appear to be a double turn away from solved. To solve this you use a strategy very similar to a half slice-plane for 3x3x3 BH edges. Let's look at the case:
(U <-> D) and (F <-> B)
This is basically the centralmost centers being an M2 away from solved. To solve this I swap the F and B centers on the E slice by doing E2. Then I bring the U and D centers into the E layer by doing M. Interchange the U and D centers (now on the F and B faces) by doing E2. Then undo my M layer turn with M'.
The whole commutator is E2 M E2 M'
The same idea for the other two double swap, or "double turn," cases.
Chris
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