# What's your favorite commutator?



## Cyrus C. (Sep 6, 2011)

I'd have to say mine is [R U R' U', M'], what's yours?


----------



## Rubiks560 (Sep 6, 2011)

My favorite is [D, R U R']. I like it because it's the first commutator I really understood, also I think it's quite cool and useful.Another one I like is [L2, U R2 U'], though.


----------



## aronpm (Sep 6, 2011)

R':[U,R'DR]


----------



## DavidWoner (Sep 6, 2011)

F R U R' U' F'


----------



## Forte (Sep 6, 2011)

[R2 F2 R2 U2 M' , U]

^^ props to Stefan


----------



## nccube (Sep 6, 2011)

[R U2 R', D2]


----------



## Cubenovice (Sep 6, 2011)

U2 M' U2 M

R U R' U' R U R' U' R U R' U' D2 R U R' U' R U R' U' R U R' U' D2

and offcourse:
R2 D R' U2 R D' R' U2 R' Headlights OLL
r U R' U' r' F R F Chameleon OLL
F' r U R' U' r' F R Bowtie OLL


----------



## Sa967St (Sep 6, 2011)

[R' D R, U']


----------



## Stefan (Sep 6, 2011)

Forte said:


> [R2 F2 R2 U2 M' , U]



That's what I was going to post...


----------



## Forte (Sep 7, 2011)

Stefan said:


> That's what I was going to post...



It's so cooool


----------



## Rubiks560 (Sep 7, 2011)

DavidWoner said:


> F R U R' U' F'



Thats conjugate nub


----------



## aronpm (Sep 7, 2011)

Rubiks560 said:


> Thats conjugate nub


 
[FRF',FUF']


----------



## DavidWoner (Sep 7, 2011)

Rubiks560 said:


> Thats conjugate nub


 
c:[a,b]=[c:a,c:b] nub 



Cubenovice said:


> R U R' U' R U R' U' R U R' U' D2 R U R' U' R U R' U' R U R' U' D2



I think you mean R U R' U' R U R' U' R U R' U' D2 U R U' R' U R U' R' U R U' R' D2 but it cancels to R U R' U' R U R' U' R U R' D2 R U' R' U R U' R' U R U' R' D2


----------



## Cool Frog (Sep 7, 2011)

Cubenovice said:


> R U R' U' R U R' U' R U R' U' D2 R U R' U' R U R' U' R U R' U' D2


 x U' R':[U2:R'DR]


aronpm said:


> R':[U,R'DR]


 less than 3

R:[M': U' R' U]


----------



## Phlippieskezer (Sep 7, 2011)

4x4 (With a conjugate):

l' r' u2 r D r' u2 r D' l

Also known as
l'[r' u2 r, D]

:3


----------



## cmhardw (Sep 7, 2011)

[U R2 U' R2 U', B2] (Per Special)


----------



## Weston (Sep 7, 2011)

Forte said:


> [R2 F2 R2 U2 M' , U]
> 
> ^^ props to Stefan


WHOAaldjsfasu;fjilasdf;idasfj;ijiIOWWOW


----------



## Ranzha (Sep 7, 2011)

y:[R':U]:[D2,[R:U']]
y:[R' U R: [D2, R U' R']]
y (R' U R) (D2 R U' R') (D2 R U R2' U' R) y'
Lovin' it.


----------



## cuBerBruce (Sep 7, 2011)

[(R' D)3 S, U2]


----------



## cuber952 (Sep 7, 2011)

Rubiks560 said:


> My favorite is [D, R U R']. I like it because it's the first commutator I really understood, also I think it's quite cool and useful.Another one I like is [L2, U R2 U'], though.


 Im going to take a random guess and say that Cyrus told you to post this.


----------



## Rubiks560 (Sep 7, 2011)

cuber952 said:


> Im going to take a random guess and say that Cyrus told you to post this.


 
You have guessed correctly.


----------



## Lucas Garron (Sep 7, 2011)

I'm pretty fond of [R U R2, R U R'], but not because I execute it as a commutator.



Cool Frog said:


> x U' R':[U2:R'DR]


 


Ranzha V. Emodrach said:


> y:[R':U]:[D2,[R:U']]



Is ambiguous notation fashionable these days?

I suppose the missing outer brackets are clear if you conjugate by only one move, but it's not quite as safe.


----------



## Ranzha (Sep 7, 2011)

Lucas Garron said:


> Is ambiguous notation fashionable these days?


 
I was just fooling around, don't worry xD


----------



## qqwref (Sep 7, 2011)

The Niklas family, by so much.

There's the basic form of [L', U R U'], but so much can be done. The U/U' can be swapped; either of the L' and R moves can be done to any angle (clockwise, counterclockwise, or 180); and either of the L' and R moves can be done on any L and R slice, as long as the two slices aren't the same.

Oh yeah, and it also works on other puzzles such as minxes. <3


----------



## 5BLD (Sep 7, 2011)

[M' U M, E']


----------



## aronpm (Sep 7, 2011)

qqwref said:


> The Niklas family, by so much.
> 
> There's the basic form of [L', U R U'], but so much can be done. The U/U' can be swapped; either of the L' and R moves can be done to any angle (clockwise, counterclockwise, or 180); and either of the L' and R moves can be done on any L and R slice, as long as the two slices aren't the same.
> 
> Oh yeah, and it also works on other puzzles such as minxes. <3


 I might be wrong but I think you just described all the 8-move 3-cycle corner commutators


----------



## Tim Major (Sep 7, 2011)

[R'UR,D']
I do a cool to execute fingertrick.


----------



## irontwig (Sep 7, 2011)

[R2:[R F R', u2]] 
You might want to AFF.


----------



## Rpotts (Sep 7, 2011)

[R U2 R', E']


----------



## Cubenovice (Sep 7, 2011)

DavidWoner said:


> I think you mean R U R' U' R U R' U' R U R' U' D2 U R U' R' U R U' R' U R U' R' D2 but it cancels to R U R' U' R U R' U' R U R' D2 R U' R' U R U' R' U R U' R' D2



Nono, I really mean R U R' U' R U R' U' R U R' U' D2 R U R' U' R U R' U' R U R' U' D2 
I like how I can just keep spamming the Sexy move, no need to invert it.

It is my special Per Special


----------



## qqwref (Sep 7, 2011)

aronpm said:


> I might be wrong but I think you just described all the 8-move 3-cycle corner commutators


And a whole bunch of center ones, and a whole bunch of bigcube edge ones ;D


----------



## irontwig (Sep 7, 2011)

qqwref said:


> And a whole bunch of center ones, and a whole bunch of bigcube edge ones ;D


 
Well, they're basically the same thing just using different slices. imo corner comms are the most basic since they only use outer layers.


----------



## Zane_C (Sep 7, 2011)

Some comms I enjoy are:
- x [R' D2 R, U] and [R' U R, D']
- I also like doing U2 and D2 simultaneously at the end of: U2 [R2 U R2 U' R2, D2]

- [R U' R', E]. It's fast, and something easy to use when explaining commutators.
- [U R U', M']


----------



## Joël (Sep 7, 2011)

One of my favourites: [R' D R2 d' R, U2]


----------



## porkynator (Sep 7, 2011)

Definetly [M', U2]


----------



## TMOY (Sep 7, 2011)

The single corner twist.


Spoiler



[(twist the corner in place), (pop the corner and apply a x2 y rotation to it)]


----------



## lucarubik (Sep 7, 2011)

niklas
I also like U R B' M2 B R' B' M2 B U'


----------



## Kirjava (Sep 7, 2011)

I don't really have a favourite, but I like the construction X Y X' Z Y' Z' because of stuff like this;

[F2 r2: [R U R' U', M2]]
[l': [r l, R U R' U']]

on 4x4x4.


----------



## Stefan (Sep 7, 2011)

[sexy, lexy] (cause Uperm for 3x3x3 and Aperm for megaminx)
[R' L' U2 R L, U] (first part "turns U upside down" so you're kinda doing U' twice)


----------



## Mike Hughey (Sep 7, 2011)

I know this is a boring one, but I went for a long time doing commutators without knowing about one particular class of 8 move commutators, and once I discovered them, they became my favorite:
[M D M', U]

I find myself going out of my way to do commutators like this even when something better exists, just because for some strange reason they seem particularly elegant to me.


----------



## RyanReese09 (Sep 7, 2011)

I love all my commutators the same .

Though probably Aperm. Simple and fast.


----------



## lucarubik (Sep 7, 2011)

Mike Hughey said:


> I know this is a boring one, but I went for a long time doing commutators without knowing about one particular class of 8 move commutators, and once I discovered them, they became my favorite:
> [M D M', U]
> 
> I find myself going out of my way to do commutators like this even when something better exists, just because for some strange reason they seem particularly elegant to me.


 
I also like this one  also some M2 commutators are great as UB DF LF, for edges my favourtie is that turbo R U R' U', M'


----------



## ben1996123 (Sep 7, 2011)

If I randomly pick up a 3x3, I'll probably do [U R U', M2].


----------



## JonnyWhoopes (Sep 7, 2011)

LOVE ALL THE X Y X' Y'

Really though, I love pretty much all the 8 movers. Specifically for bigcube wings. They make me feel powerful. Heh.


----------



## DavidWoner (Sep 7, 2011)

Cubenovice said:


> Nono, I really mean R U R' U' R U R' U' R U R' U' D2 R U R' U' R U R' U' R U R' U' D2
> I like how I can just keep spamming the Sexy move, no need to invert it.
> 
> It is my special Per Special


 
It's not a commutator though, what you wrote is ABAB or ABAB', not ABA'B'.


----------



## Anthony (Sep 7, 2011)

Joël said:


> One of my favourites: [R' D R2 d' R, U2]


 
[F U' R2 D R', U2]


----------



## Cubenovice (Sep 7, 2011)

DavidWoner said:


> It's not a commutator though, what you wrote is ABAB or ABAB', not ABA'B'.



Can we agree to call it an algorithm that cycles corners?


----------



## Muesli (Sep 7, 2011)

Anthony said:


> [F U' R2 D R', U2]


 
Ooooh s'purteh


----------



## MaeLSTRoM (Sep 7, 2011)

[r' U,M2]2


----------



## StachuK1992 (Sep 7, 2011)

M' U2 M U2 M' U M' U2 M' U2 M
= [[M', U2] M'; U]


----------



## Cool Frog (Sep 7, 2011)

MaeLSTRoM said:


> [r' U,M2]2


 
[r' u M2 u' r, U2]


----------



## MaeLSTRoM (Sep 7, 2011)

Cool Frog said:


> [r' u M2 u' r, U2]


 
hehe. oops....


----------



## antoineccantin (Sep 7, 2011)

M' U M' U M' U M'


----------



## Ollie (Oct 10, 2013)

Bump

These are fun 



Kirjava said:


> I don't really have a favourite, but I like the construction X Y X' Z Y' Z' because of stuff like this;
> 
> [F2 r2: [R U R' U', M2]]
> [l': [r l, R U R' U']]
> ...





Cool Frog said:


> [r' u M2 u' r, U2]


----------



## TDM (Oct 10, 2013)

I don't really have one, but I like being able to write stuff like this as commutators and conjugates:
[F:[R,U]2] [[R,U],M']
I also use [x':[R U R',D]] as an OLL, so I guess that could be my favourite single commutator as it's one of the very few I actually use (I've already said [[R,U],M'] and I hate A perms).


----------



## kcl (Oct 10, 2013)

Probably a perms or the MU U perms


----------



## IcyBlade (Oct 10, 2013)

E perm (two commutators).
Or I guess the A perm, in which I failed to explain to my brother.


----------



## Lucas Garron (Oct 10, 2013)

I'm still a fan of [R U R2, R U R'].


----------



## uberCuber (Oct 10, 2013)

Lucas Garron said:


> I'm still a fan of [R U R2, R U R'].



I saw this thread and came to post Sune


----------



## Cubenovice (Oct 10, 2013)

tie between 
F' r U R' U' r' F R and r U R' U' r' F R F'


----------



## cubernya (Oct 10, 2013)

Lucas Garron said:


> I'm still a fan of [R U R2, R U R'].





uberCuber said:


> I saw this thread and came to post Sune



Funny, I thought the _exact_ same thing


----------



## antoineccantin (Oct 11, 2013)

antoineccantin said:


> M' U M' U M' U M'



wtf is this


----------



## CubeRoots (Oct 11, 2013)

U R U' R'


----------



## Lucas Garron (Oct 13, 2013)

theZcuber said:


> Funny, I thought the _exact_ same thing



Yeah, I've seen some cool commutators, but there's something classic about that Sune decomposition.


----------



## TheNextFeliks (Oct 13, 2013)

[R U R', D]


----------



## antoineccantin (Oct 13, 2013)

CubeRoots said:


> U R U' R'



[U, R]


----------



## Cubo largo (Oct 13, 2013)

2(M' U M U)


----------



## TDM (Oct 13, 2013)

Cubo largo said:


> 2(M' U M U)


Not a commutator, but I tried [M' U M,U] and used it to find this:
[F2:[M' U M,U]2]
which does the same as:
[(M' U)4,y2]


----------



## Cubo largo (Oct 13, 2013)

Why not? FD>UL>UB


----------



## mDiPalma (Oct 13, 2013)

[y, x z x2]


----------



## TDM (Oct 13, 2013)

Cubo largo said:


> Why not? FD>UL>UB


A commutator is not the same as a 3-cycle.


----------



## Cubo largo (Oct 13, 2013)

So what is this? So U2 M' U2 M' is not a commutator? Let me know please I ate to do mistakes in commutators...


----------



## Christopher Mowla (Oct 13, 2013)

Cubo largo said:


> So what is this? So U2 M' U2 M' is not a commutator? Let me know please I ate to do mistakes in commutators...


U2 M' U2 M' isn't a commutator, and (M' U M U)2 is not, neither is M' U M U.


----------



## Cubo largo (Oct 13, 2013)

I'm really sorry. What an error! So I think my preferite is [E2, R U2 R']


----------



## TDM (Oct 13, 2013)

Cubo largo said:


> So what is this? So U2 M' U2 M' is not a commutator? Let me know please I ate to do mistakes in commutators...


U2 M' U2 M' isn't, but U2 M' U2 M and U2 M U2 M' are. They can be written as [U2,M'] and [U2,M].


----------



## Christopher Mowla (Oct 13, 2013)

Cubo largo said:


> I'm really sorry. What an error! So I think my preferite is [E2, R U2 R']


There's no need to ask for an apology. 

When I first started cubing, and I learned M' U2 M U2, I too thought that it might be possible that all 3-cycles are commutators. All 3-cycles of corners, at least (I'm not sure about middle edges, because I haven't proved it yet) can be reached with a single commutator, but as far as actual maneuvers are concerned, as TDM pointed out, this is not the case.

EDIT:
For big cubes, I like mine [U' Rw U2 r2 U2 Rw' U, R'].


----------



## Ollie (Oct 13, 2013)

M' E2 M, U


----------



## elrog (Oct 13, 2013)

I like these 3 the most. The 1st and 3rd combined do the same as the second.
[R, U' M' U]
[R, U' l' U]
[R, U' L' U]

I also like ones like these for FMC though they are hard to find. I am also aware that M moves count as two for FMC though I think they shouldn't.
[U' L' U2 L2 U', R']
[U' L' U2 L U', R2]
[U' M U, M']


----------



## TDM (Oct 13, 2013)

cmowla said:


> [U' Rw U2 r2 U2 Rw' U, R'].


[[U' Rw U2:r2],R']

Can the 4x4 PLL parity alg be written as a commutator?


----------



## Christopher Mowla (Oct 13, 2013)

TDM said:


> Can the 4x4 PLL parity alg be written as a commutator?


If you are specifically talking about the algorithm: r2 U2 r2 Uw2 r2 u2, no. It can be expanded to (r2 U2 r2 U2 r2)(r2 u2 r2 u2), but you probably already know that. However, you could solve that PLL parity case with a single commutator if you wanted to.

You could even solve this or even this with a single commutator using my commutator method, but the commutators created using my method are not going to be something you would use in practice I suspect. In the future, I might be able to make my method create custom commutators and find a way to shorten them, but for now, my method is solely being used to complete the proof of Per's conjecture.

Maybe someone could start a "Request a commutator" thread for which they would ask only for commutators to solve certain positions or to create certain patterns, even if those commutators aren't practical to use in practice.

As I mentioned in the "My Ultimate Commutator Challenge" thread, I can solve any even cube even permutation configuration with a single commutator, and, if I can complete proving middle edges (I've been too busy to spend any time on cubing lately), then the same holds true for odd cubes as well. You could ask for any odd cube size even permutation, and I probably could create a single commutator solution for any position you ask, however (I just didn't technically solve _all_ possible positions yet, but I have the method to solve positions as I need to).


----------

