Commutators for r/l edges on big cubes

[dbeyer]

Here is a really sweet algorithm that Chris and I love:

x-center cycle: Urb -> Dbr -> Ulf
Notice how the Urb is directly above the Dbr?
Now the Ulf is opposite of the Urb on the U face?

This trick is applicable to corners as well.
We call this a columns case:
Urb is the focus point.
Both the Ulf and Dbr have positional relationships with the Urb.
Opposite on the face, and Directly beneath.

Now drop the Opposite x-center out of the U layer.


Setup: l2
Urb and Dbr aren't interchangeable quite yet.
Perhaps:
U' will give the interchangeability.:

Setup: l U'* corrected
Commutator: b2 rF'r' b2 rFr'
=> l U' b2 rF'r' b2 rFr' U l'
12 moves, not bad. Now there is a cancelation that most will miss out on

Why not: l2 U as the setup?
Now Urb and Dbr are interchangeable on the r slice.
So now the commutator would be: Ul2U' r2 Ul2U' r2

Writing it all out: l2 U Ul2U' r2 Ul2U' r2 U' l2 => l2 U2l2U' r2 Ul2U' r2 U' l2
Now like I said before, Chris and I used to use this alg, which we thought was just friggin fast. One of our sub-goals is to use quarter turns rather than double turns. We then further analyzed it, and I realized, (maybe only two weeks ago) that you can actually turn the l slice a quarter turn rather than a double turn.

l U2l'U' r2 UlU' r2 U' l'

I bet you can blaze right through that now can't ya?

 

[Mike Hughey]

Mike Hughey liked the corner commutator system, I think he's learning it right now.

Very slowly; I'm not making as much progress as I'd like. But I am making a bit of progress on it.

I doubt I'll be able to use it at all at the US Open yet.

But I definitely like it. I want to switch, but I'm not sure how fast it will happen.

Oh, and Daniel, that columns algorithm above is very nice.

 

[joey]

I want corner comms. UBL please. Or does UBR have finger friendlier algs?

btw, I'm calling my method G^-1.

 

[Stefan]

Setup: l2 U'
Commutator: b2 rF'r' b2 rFr'

That doesn't do what you want.

Thanks for the other alg, I'll use that for the U2 method so solving one D center doesn't take me ten seconds anymore. I should've seen that myself, but was too dumb.

 

[cmhardw]

I want corner comms. UBL please. Or does UBR have finger friendlier algs?

btw, I'm calling my method G^-1.

Joey,

I also use UBL as my corner buffer, but we decided to standardize BH to have UBR as the buffer. We figured that, in general, us UBL corner buffer users are weirdos and that more often people would use UBR ;-)

(BH corners) http://dbeyer.110mb.com/BHcorners.txt

(reflecting to UBL buffer) http://www.speedcubing.com/chris/algconversion.html

I'm sure you already know how to reflect algs, so I am not implying that you need the above page. But if others who don't know are also reading this post, then I include it for completeness.

Chris

P.S. Should we read G^-1 as "G inverse" ? I assume the G is for Gouly ;-)

 

[joey]

Joey,

I also use UBL as my corner buffer, but we decided to standardize BH to have UBR as the buffer. We figured that, in general, us UBL corner buffer users are weirdos and that more often people would use UBR ;-)

Well, I'm trying to move to non-fixed buffer anyway

(BH corners) http://dbeyer.110mb.com/BHcorners.txt

(reflecting to UBL buffer) http://www.speedcubing.com/chris/algconversion.html

Hmm, I think dbeyer already sent me this, but at the time there were some problems with it, I'll check it now though. Hand pick some nice algs for ugly cases!

P.S. Should we read G^-1 as "G inverse" ? I assume the G is for Gouly ;-)

Well, that's how it would read properly. But really G^-1 is my method, my alg-set, so I only need one setup move per cycle. It's not as hardcore as BH, nor is it full commutators. Nor have I really found all the algs I need for it yet.

 

[blah]

Now we look to see if we can find a solution that uses quarter turns rather than double turns.

Now I really don't get this. I, with my limited knowledge of commutators and very limited brainspace to keep track of too many things, like double turns way more than quarter turns, so I always try to setup my commutators for double turns if possible (even if it means one more setup move, no kidding, no exaggeration), because I'm much less prone to mistakes when I do double turns. I think I need to illustrate what I mean with an example: (I only use commutators for centers)

Check out this cycle: Ubl > Fur > Rdb

There are 2 commutators I 'see' instantly (though there are probably more that I don't).

Commutator 1: F rU2r' d' rU2r' d F'
Commutator 2: R' rUr' u rU'r' u' R

Obviously, the main difference is how I do my setup moves (the commutators themselves are pretty much the same). I'd pick Commutator 1 over Commutator 2 any day, because then I'd only have to keep track of one thing (F), because I don't have to bother about the direction of the U turn since it's a U2 either way. For Commutator 2, I'd have to keep track of two things (R' and U), and I execute my commutator much slower because I want to make sure I don't make a stupid mistake. So in fact for me, a quarter turn is not only more dangerous, but also slower than a double turn (I use a double trigger) in practice. For C1, I can execute the whole thing smoothly non-stop in practice, but for C2, I just have to pause before each U turn.

If you're wondering why the u and d turns are not double turns, well, I don't really know why, but I just have less of a problem keeping track of the slice turns, it's more the direction of the face turns that bugs me. But I'd still pick a double slice turn over a quarter one any day, I just don't 'need' it as badly as a double face turn, so if I have a choice of making my face turn a double or my slice turn a double, I'd pick face.

Here's why I'd rather do one more setup move than keep track of whether it's a clockwise or counterclockwise turn: In my head, I see 8-move commutators as one 'unit' and setup moves as another (let's call them 'memory compartments' A and B respectively). (Is this bad? It's quick for processing information though, at least I think it is.)

Case 1: If setup moves are needed, I'd always setup the commutator to involve at least one double turn (preferably face rather than slice).
Case 2: If I 'see' a commutator that doesn't need setup moves, then I'll just do that commutator without setup moves, even if it means there are no double turns.

Analysis: By doing what I do for case 1, I only use one memory compartment: B. If I do one less setup move and a quarter turn in my commutator, I use both memory compartments A and B. Somehow, I don't know why, the amount of information stored in each memory compartment isn't as important as the number of memory compartments used. For case 2, without a setup move, I'm only using memory compartment A; with a setup move, I'm using both A and B. And I think using only one memory compartment is a good tradeoff for a double turn. Somehow, slice turns are not involved in any of the memory compartments, as I've said, I've got less of a problem with these.

This is just what I feel after less than a week of big cube BLD So it might be pretty worthless information that leads people in the wrong direction, I dunno. But just out of curiosity, has anyone ever thought of it this way before?

 

[deadalnix]

Il do the same. If a solution existe without setup, i choose this one.

 

[Mike Hughey]

@Chris: When I'm practicing BH, I use UBL as my corner buffer as well, so I always have to adjust your algorithms correspondingly when I'm practicing. I chose that simply because that corresponds to the piece I label "A" and start with on 5x5x5 X centers.

It looks like UBL isn't as weird as you think it is.


@Blah: When I was starting out (and for quite many months, actually), I preferred double turns over quarter turns as well. In fact, I think I mentioned that in my "How I solve centers on a 4x4x4" post. But with experience, I've gotten where I prefer quarter turns. I suspect that's just something that happens with practice. It gets where you see the whole thing at once, so it's not extra information any more to remember which direction to go. But I totally sympathize with your perspective. I still probably occasionally make mistakes with quarter turn moves that I wouldn't make with double turn moves. (I think I remember one from just last week.)

Oh, and I'm sure my double triggers are a lot slower than yours, which probably has something to do with it. I really stink at double triggers.

 

[deadalnix]

Chris, you make me smarter again !

I just understand what you mean by doing the corners like X centers. It's sometime more complicated for set-ups but very clever !

 

[blah]

I've decided to make my life easier, now I don't care about pairs anymore, I'll use commutators only if I hit an r/l slice edge 'directly', i.e. if it's the second part of my pair (indirect), I'll do the first part normally with r2 then I'll pair the slice piece and the first part of my next pair together, and do them as a commutator. Though I still memorize in pairs to facilitate of memorization, not execution. I don't know why but I'm just not comfortable with inverse commutators How do I cure this disease?

Any major disadvantage to doing this rather than the approach I described in the first post of this thread? (i.e. if any one of the next two pieces is an r/l-slice piece I'll do a commutator)

 

[cmhardw]

I don't know why but I'm just not comfortable with inverse commutators How do I cure this disease?

For BH, Daniel and I define a commutator to be ABA'B' where A is the "insertion" part of the alg, and B is the "interchanging" part of the alg.

So for example: r' d r U2 r' d' r U2 is a commutator for x-centers where,
A = r' d r
B = U2

Notice that A is 3 moves (sometimes 5, or 4) and that B is 1 move. B is always one move, which is a way to think about a freestyle commutator (a commutator where the B part of the alg, the interchange move, is exactly 1 turn in HTM).

So to do the inverse of a commutator, you are simply executing the commutator as BAB'A'

What this means is, interchange first, then do the insertion part. So in my head, when applying a commutator (ABA'B') I first picture the insertion move, and how that affects the main/interchanging slice. After applying the insertion move, I imagine in my head how the interchanging move affects the pieces on the main slice, then I apply the interchanging move. After that I stop visualizing anything, and just do the inverse of the insertion move, followed by the inverse of the interchanging move.

So in essence, the first 2 parts of any commutator are very visual, and I picture everything about the 3 pieces affected. The last 2 parts of the alg are 100% abstract, with no visualization. I simply invert the previously applied sequences in the correct order. To do the inverse of a commutator, simply interchange first while picturing how this affects your 3 pieces. Then, picture the insertion move, and apply it. Then, in the abstract sense only, apply the inverse of the interchange move, followed by the inverse of the insertion move.

Simple, when thought of this way at least.

Chris

 

[deadalnix]

I think in the same way !

But I never use 5 moves A. Maximum 4, and set-up if needed.

So you have a list of the wing alg like for corners ? (even if the list isn't finish, it give an idea).

 

[cmhardw]

I think in the same way !

But I never use 5 moves A. Maximum 4, and set-up if needed.

So you have a list of the wing alg like for corners ? (even if the list isn't finish, it give an idea).

If you don't use 5 move A algs, you might want to consider it, at least for 1 case. What do you do for Ubl->Dfl->Ufr ?

I use:
A: U' f2 U f2 U
B: l2

There is another alg, that Daniel found, which is very fast but I am absolutely mystified as to how it works. If I don't understand an alg, I'm afraid to use it in a BLD solve. I understand how that 5 move A works as the insertion alg, so I prefer the above alg.

As for the list for x-centers, yes I am about 30%-40% done writing it. Daniel and I are splitting up the job of writing up all the algs, and x-centers are my responsibility. I'm still working on it, but with work and practicing for Nationals I honestly haven't worked on the list at all in about a week.

Chris

 

[deadalnix]

I will not do this alg because Ubl and Ufr are interchangables centers. Theyre is need to do this kind of cycles.

But As I said, i user set-ups, and if I have tu solve this, I wil probably set up with r'F' and then [l2,UrU']. It's not shorter, but easier to do. And useless !

 

[blah]

What do you do for Ubl->Dfl->Ufr ?

Setup: r' D2
A: l F2 l'
B: b2

Is this bad? Or worse, plain weird?
It's the same number of moves as whatever you're doing, though it's much harder to perform on a real cube.

And useless !

Uh-huh... Wait, uh-huh?

 

[dbeyer]

I made the correction to the algorithm. I guess I copy and pasted or something. Anyway, it should be l (or l' for that matter) U' then a commutator on the F or B face, (which ever one you decide to put the Ulf on).

The point is though, to see the 11 mover.

Here is another solution its the Conjugated Cyclic Shift.

l2D b2 D'lDl' b2 lD' l
Later,
DB