4x4 LL Commutators Tutorial

[jms_gears1]

So i hope that this post Helps someone.

Ive noticed while looking through the forum that not very many people understand 4x4+ commutators and i thought that maybe i would give a tutorial a shot so here goes.

Before i start i would like to say that if you use the Reduction method, then there is no real need to learn this, because these mainly apply to the K4 type method where you only pair up the cross, then you do F3L, and then LL.

On a solved Cube Do this:

r f' D' f U2 f' D f U2 r

Now before i explain commutators you should understand what orbitals are.

There are two diffrent types of orbitals: Left and Right and rather than explain in text look at your cube.

The three cycled edge pieces are in the Right orbital, Which is to say they are all the right edge of the face, and if they were in the left orbital they would be the left edge of the face.

there are two basic types of commutators ones that cycle in the same orbitral and ones that cycle pieces from diffrent orbitals.

the first im going to show you is Same orbital Commutators:

Now to see how the commutators work.

Using the scrable above you can see that the FUr edge needs to go back to the RUb edge slot, and that the RUb edge needs to go to the LUf edge slot, and the LUf edge needs to go to the FUr slot.

So we will denote the cycle as: FUr->RUb->LUf

The first step in the commutator is to move the first piece to get swapped into the D layer, meaning the FUr edge needs to be moved into the D layer.

The obvious move is: r'

Now what you want to do is to move the target postion into the D layer, so for this case the RUb edge slot should be moved into the D layer.

the move to do this is: b'

Terminology: the Second Slice you moved is called the Working Slice

now that you have the RUb edge slot on the D layer and the RUb piece on the D layer you position the piece into the slot with a D move.

The move here would be: D

Notice that when you Move D it kicks the edge piece already in the position out, that piece goes into the next slot.

Now you move move the working slice back up so that you can position another Edge Slot in the working slice by moving the U layer:

The move here is: b

Remember that edge we kicked out earlier?
well now we find the place where it goes and we use a U move to rotate that slot into the Working Slice this case the LUf edge slot into the b slice

The move here is: U2

We move the Second edge slot that sould now be in the b layer into the D layer. So the LUf edge slot should now be in the RUb postion and we need to move it into the D layer.

the move here is: b'

Now we Use a D turn to put the remaining two edges into place.

The move here is: D'

return the working slice to the U layer.

Move here is: b

then fix the last edge with: U2 and r

so the final Commutator is:
r' b' D b U2 b' D' b U2 r

same explanation not spread out so much:

what just happend was you targeted a piece you wanted to move and found the location that the piece goes to, you moved the target piece into the D layer and then the target position into the D layer.

You then postioned the piece into the Right slot using a D turn as well as kicked a piece out of place and left it on the D layer.

You then moved the Slot and the piece together back into the U layer and postioned the slot of the piece you kicked out into the working slice then you moved that slot into the D layer.

Now you move the edge piece you kicked out into the Slot and kicked out another piece but this time that piece goes back to the original target piece completeing the cycle.

finally you move the Slot back into the top layer Fixed the U layers rotation and brought the original slice back up into the U layer finishing the Commutator.

im about to pass out ill finish the diffrent orbital Commutator tutorial tommorrow. Hope this helps.

Please kindly tell me if i have grammatical errors that make this hard to read/understand im half asleep writing this so i probablly missed some things...

 

[jms_gears1]

So now we move on to edge pieces in Diffrent orbitals.

To recognize if an edge is in a diffrent orbital you just have to see if there is an unoriented edge. The edge appears as if its unoriented but in actuallity its just in the wrong place, because with the 4x4 you cant have orientation errors. If you dont understand try taking a piece from your cube and putting it back flipped.

the first step in fixing this is finding a move that will put the piece into the right orbital on the D layer and then you proceed as if it was a normal commutator.

preform this on a solved cube: R2 r' D' r U' r' D r U R2

the cycle here is RUf->LUf->FUr

if you look at the cube you see two pieces flipped, these are the pieces that are in the wrong orbital.

Now will be a good time to state a couple rules for Commutators:

1. a double face turn, ie: F2 put the two edges into the D layer on the F face as well as switch thier orbital.

2. a single inner slice turn ie: r' leaves a piece in its own orbital on the D layer.

3. If you put a piece into a diffrent orbital another piece will also be switched at the end of the Commutator.

4.The double face turn should always be the first turn, and should be applied to the piece thats on its own orbital.

Ok so if you remember we need to do a double face turn to put one of the edges into the D layer, and it has to be done on the face with the edge piece that is in its own orbital. if you look at the cube two of the pieces are in the Right orbital and the RUf edge is in the left orbital. Therefore we need to apply the double turn to that piece.

Move: R2

Now that the piece is in the D layer we need figure out what the working slice is, The working slice if you remember is the slice that is the first edges target which happens to be the LUf edge slot so we move that into the D layer.

Move: f'

Now we insert the edge into the Target position with a D turn, take note of the edge that is in there previous to actually turning the D layer.

Move: D2

Now move the working slice back into the U layer.

Move: f

Now we locate the edge slot the edge we kicked out goes into, in this case the FUr Edge slot. We move this Slot into the working slice.

Move: U

Now move the slot into the D layer so that we can position the new edge into its position.

Move: f'

Now we use a D move so that we can position the remaining two edges into their correct slots.

Move: D2

Now we move the working slice back into the U layer.

Move: f

now we correct the U layer and undo the setup move for the commutator

Moves: U' R2

Full Commutator
R2 f' D2 f U f' D2 f U' R2

I hope this tutorial helps someone im probablly going to eventually make a vid about commutators as it helps some people to have the visual representation.

 

[trying-to-speedcube...]

I understand what you are trying to accomplish, but you might want to check the scramble(s). I tried the first one, and first, it also destroys centers. The cycle does work, but it's confusing because of the centers being unsolved.

if you look at the cube you see two pieces flipped, these are the pieces that are in the wrong orbital.

There's no orientation on a 4x4.

Also, the second example you gave isn't optimal. If you want people to "understand" commutators, you shouldn't give them a step-by-step plan to construct them. You shouldn't say that a piece "has to" go to the D-layer, because it isn't necessary. The optimal solution for the second example is Fw' U' F U f U' F' U F.

 

[jms_gears1]

I understand what you are trying to accomplish, but you might want to check the scramble(s). I tried the first one, and first, it also destroys centers. The cycle does work, but it's confusing because of the centers being unsolved.

do you know a better way to do 4x4 commutators? not a challenge just that this was how i learned it and its worked for me so far.

if you look at the cube you see two pieces flipped, these are the pieces that are in the wrong orbital.

There's no orientation on a 4x4.

I know its easier to see the pieces im talking about when i explained it this way

Also, the second example you gave isn't optimal. If you want people to "understand" commutators, you shouldn't give them a step-by-step plan to construct them. You shouldn't say that a piece "has to" go to the D-layer, because it isn't necessary. The optimal solution for the second example is Fw' U' F U f U' F' U F.

a commutator doesnt have to be optimal in fact often times im pretty sure they arnt the optimal alg for that situation. if i want them to understand should i not explain how to set commutators up so that they can understand what i did? Im not sure i follow your logic

 

[zosomaniac]

http://www.youtube.com/watch?v=zgKoHu_H2IQ

http://www.youtube.com/watch?v=j_HBREynswY&feature=channel

i do not know to embed.Sorry

 

[Stefan]

The optimal solution for the second example is Fw' U' F U f U' F' U F.

That's nine moves. You can do it in eight.

 

[Robert-Y]

y' x' U' R U r U' R' U r'

 

[trying-to-speedcube...]

I understand what you are trying to accomplish, but you might want to check the scramble(s). I tried the first one, and first, it also destroys centers. The cycle does work, but it's confusing because of the centers being unsolved.

do you know a better way to do 4x4 commutators? not a challenge just that this was how i learned it and its worked for me so far.

Yes, intuitively, without a step-by-step plan. Instead of saying "Do move A so X does Y, then do move B so Y does Z", you should give no more than the fact that a commutator is A B A' B' and some important stuff about constructing a successful commutator.

However, this is just my way of teaching; in my opinion it's good to have people not totally understand what you're saying, because they will think about it more; that way, people will understand it better. You can teach your way, but in my opinion people won't really "understand" it.

if you look at the cube you see two pieces flipped, these are the pieces that are in the wrong orbital.

There's no orientation on a 4x4.

I know its easier to see the pieces im talking about when i explained it this way.

I think it only raises confusion.

Also, the second example you gave isn't optimal. If you want people to "understand" commutators, you shouldn't give them a step-by-step plan to construct them. You shouldn't say that a piece "has to" go to the D-layer, because it isn't necessary. The optimal solution for the second example is Fw' U' F U f U' F' U F.

a commutator doesnt have to be optimal in fact often times im pretty sure they arnt the optimal alg for that situation. if i want them to understand should i not explain how to set commutators up so that they can understand what i did? Im not sure i follow your logic

Okay, of course it doesn't have to be optimal, but don't you think (almost) always having a setup to D somehow throws out the idea that what you're doing is "understanding"? Of course, if that's your algorithm to construct a commutator, I don't have any objection against that, but I think it kind of stops the idea of everything being intuitive?

Sorry if I sound harsh or hating; I try to hang on to constructive critisism as much as I can

And I should have found that 8-mover, thanks Stefan for pointing that out.

 

[mrCage]

So i hope that this post Helps someone.

Ive noticed while looking through the forum that not very many people understand 4x4+ commutators and i thought that maybe i would give a tutorial a shot so here goes.

Before i start i would like to say that if you use the Reduction method, then there is no real need to learn this, because these mainly apply to the K4 type method where you only pair up the cross, then you do F3L, and then LL.

On a solved Cube Do this:

r f' D' f U2 f' D f U2 r

Now before i explain commutators you should understand what orbitals are.

There are two diffrent types of orbitals: Left and Right and rather than explain in text look at your cube.

The three cycled edge pieces are in the Right orbital, Which is to say they are all the right edge of the face, and if they were in the left orbital they would be the left edge of the face.

there are two basic types of commutators ones that cycle in the same orbitral and ones that cycle pieces from diffrent orbitals.

the first im going to show you is Same orbital Commutators:

Now to see how the commutators work.

Using the scrable above you can see that the FUr edge needs to go back to the RUb edge slot, and that the RUb edge needs to go to the LUf edge slot, and the LUf edge needs to go to the FUr slot.

So we will denote the cycle as: FUr->RUb->LUf

The first step in the commutator is to move the first piece to get swapped into the D layer, meaning the FUr edge needs to be moved into the D layer.

The obvious move is: r'

Now what you want to do is to move the target postion into the D layer, so for this case the RUb edge slot should be moved into the D layer.

the move to do this is: b'

Terminology: the Second Slice you moved is called the Working Slice

now that you have the RUb edge slot on the D layer and the RUb piece on the D layer you position the piece into the slot with a D move.

The move here would be: D

Notice that when you Move D it kicks the edge piece already in the position out, that piece goes into the next slot.

Now you move move the working slice back up so that you can position another Edge Slot in the working slice by moving the U layer:

The move here is: b

Remember that edge we kicked out earlier?
well now we find the place where it goes and we use a U move to rotate that slot into the Working Slice this case the LUf edge slot into the b slice

The move here is: U2

We move the Second edge slot that sould now be in the b layer into the D layer. So the LUf edge slot should now be in the RUb postion and we need to move it into the D layer.

the move here is: b'

Now we Use a D turn to put the remaining two edges into place.

The move here is: D'

return the working slice to the U layer.

Move here is: b

then fix the last edge with: U2 and r

so the final Commutator is:
r' b' D b U2 b' D' b U2 r

same explanation not spread out so much:

what just happend was you targeted a piece you wanted to move and found the location that the piece goes to, you moved the target piece into the D layer and then the target position into the D layer.

You then postioned the piece into the Right slot using a D turn as well as kicked a piece out of place and left it on the D layer.

You then moved the Slot and the piece together back into the U layer and postioned the slot of the piece you kicked out into the working slice then you moved that slot into the D layer.

Now you move the edge piece you kicked out into the Slot and kicked out another piece but this time that piece goes back to the original target piece completeing the cycle.

finally you move the Slot back into the top layer Fixed the U layers rotation and brought the original slice back up into the U layer finishing the Commutator.

im about to pass out ill finish the diffrent orbital Commutator tutorial tommorrow. Hope this helps.

Please kindly tell me if i have grammatical errors that make this hard to read/understand im half asleep writing this so i probablly missed some things...

Aew you sure you really know what an orbital is? There is no way you can cycle pieces (edges) from different otbitals, unless you are doing parallell cycles or something

Per

 

[jms_gears1]

Aew you sure you really know what an orbital is? There is no way you can cycle pieces (edges) from different otbitals, unless you are doing parallell cycles or something

Per

yep. if you do a double face turn i.e. F2 it switches its orbital in the bottom layer. Try it.