# Commutators on Skewb?



## some1rational (Sep 10, 2010)

hey guys, (some background) so I've been into the twisty puzzle craze for about 8 months now and since having assistance on learning the 3x3 and 4x4 (via videos and websites mainly) I've been able to tackle all my new puzzles without any help. The most common method I've used to solve all subsequent puzzles has been the use of commutators and conjugates (which I used to solve the mega- & giga- minx, pyraminx, pyraminx crystal, 5x5-7x7).

However, I've kinda of got into a roadblock with the Skewb. Even though it seems pretty simple...the 'deep-cut'-ness has thus far prevented me from finding commutators on the thing and hence I could not solve it on my own. I've been able to solve one face and have developed a commutator to orient the rest of the corners (since they're already in the correct positions once one face is solved) but I cannot seem to find one that allows me to 3-cycle the centers.

Additionally, I can't say that the corner orienting algorithm I've found is (X/ truly /X WRONG) a 'pure' commutator because it also cycles 3 centers, but I'm assuming there must be some algorithm which only cycles the centers without unorienting the corners so I can orient them first then proceed to cycle the centers later.

OK lol, sorry for the long post, my question is, can someone tell me or point to me an algorithm which is a commutator which allows me to swap 3 centers on the Skewb? (that is it swaps two, messes up bottom ; you twist the top then swap another two with the inverse while restoring the bottom...that kind of thing?)

o yea, I've found algorithms that do swap 3 centers online obviously...but I'd rather have a commutator algorithm because I feel it gives me more of an understanding of the puzzle personally.


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## bobthegiraffemonkey (Sep 10, 2010)

As a listener of the cubecast podcast, I taught myself to BLD a skewb using only comms for a laugh (sorry Andrew ).

For 3-cycling centers, try:
[DRF URB DRF' URB DRF URB DRF' URB' DRF URB' DRF', DLF]

Unless I made a mistake noting that down there, it should work 

Matt


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## Stefan (Sep 10, 2010)

some1rational said:


> I can't say that the corner orienting algorithm I've found is truly a commutator because it also cycles 3 centers



That makes no sense.

What's your corner orientation commutator?


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## riffz (Sep 10, 2010)

some1rational said:


> I can't say that the corner orienting algorithm I've found is truly a commutator because it also cycles 3 centers



Just because it affects other pieces doesn't mean it isn't a commutator (hence Stefan's complaint).


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## qqwref (Sep 10, 2010)

"Pure" commutators - which only affect the 3 pieces you're cycling, or the 2 or 3 pieces you're twisting - are very useful, but they aren't always necessary to solve the puzzle. If you can find an impure/non-pure commutator (one which affects those 3 pieces, plus any number of pieces of *different types*) you can often make a working solution that relies on solving pieces in a certain order.

For instance, R U R' U' is a non-pure commutator on the 3x3. It cycles 3 edges, but also affects 4 corners (which is OK because they aren't edges). You can do the edges with this and then solve all the corners later with pure commutators.

Back to the skewb. Hold it with one corner pointing up and one facing towards you; now I'll use U for the top half, R for the corner to the right of the one facing towards you, and L for the corner to the left of it. Now try R U' R' L R' L' R. You can use this sequence plus moves of the bottom half to get a pure center 3-cycle. There might be more efficient ways to do this, but this one should make sense intuitively.


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## some1rational (Sep 13, 2010)

thx qqwref I like that sequence haha, wish I had enough patience to go figure it out myself 

o yea and I feel stupid for not realizing the scope of the definition of 'commutator', my bad stefan (seems so obvious now haha)

EDIT: o and my corner commutator, ok so I don't really know any notation for this thing soo bear with me...so I hold it with the first corner I want to rotate facing directly at me; I bring it 'down' (by twisting the bottom-right adjacent corner actually); then I twist the corner I just brought down (cw or ccw depending on the twist, in my head im twisting 'bottom'); then I bring that corner back 'up' (by twisting the bottom-right adjacent position again)

then I twist the 'top' (which puts the next corner in place for the inverse) and I do the inverse: 'down' -> cw/ccw -> 'up' now all the corners are oriented

but this also cycles the 3-centers surrounding the first corner oriented with the algorithm (in such a way that if you started from a solved skewb, they would cycle in the same direction as the first corner is twisted so that all the colors still match with the first corner)...I hope that made sense, let me know if it needs to be clarified

I think I could potentially solve the whole Skewb possibly with, as you said qqwref, applying this in a specific order; I'll have to try it sometime when I muster up the patience (feel free to correct me if I'm wrong...could be partiy issues applying only the same algorithm over and over, not good enough to tell haha)


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