Need commutator that rotates centers 180 degrees on D face.

[cuber786]

Hello all, I am very bad with making commutators. So can someone please give me a commutator for this case?:

1.)rotate centers on D face 180 degrees (So top left center on D switches with bottom right,etc).

I also need a commutator for this case:
2) Rotate centers on U face counterclockwise(So bottom left center on U would then be bottom right,etc).

Thanks in advance.

Edit: Oh crap My bad I forgot to mention that this was for 4x4. Sorry about that

 

[ShadenSmith]

Rotate the D center 180 degrees?

x2 (2 T-Perms) x2



I think you're asking for the wrong thing. I'm not sure what exactly you're asking, actually. It sounds like something for a >3 cube because you mentioned centers, but without specifying I really have no idea. More specific please?

 

[cuber786]

oops I meant for the 4x4 sorry.

 

[ThePizzaGuy92]

in that case...

x2 (2 T-Perms) x2

lol

 

[masterofthebass]

or...

x2 RL U2 R'L' U RL U2 R'L' U x2

There's also a nicer one:

(R' U' R U')*5

 

[ConnorCuber]

or...

x2 RL U2 R'L' U RL U2 R'L' U x2

There's also a nicer one:

(R' U' R U')*5

In the second you for got x2 surrounding the alg

 

[deadalnix]

(RLD2R'L'D)2 is the simpliest.

 

[Stefan]

You guys are all missing the point. He explicitly said he needs commutators and you're not giving him any.

Here's one (lower case meaning inner slice only): [ r l u2 r' l', U ]

That was trivial, now someone please find a pure single-center rotation commutator for the 3x3 or prove that it's impossible. I just thought about it for a bit and am not sure.

 

[TMOY]

For the 3^3 it's impossible. That's because the trivial permutation is even; if you start and end on the solved state you will always have performed an even number of quarter-turns inbetween.
For the 4^3 it's impossible too, for similar parity reasons: the permutations of corners and center pieces must always have the same parity.

 

[Stefan]

TMOY, I'm obviously allowing 180 degrees turns. Try again.

 

[AvGalen]

You guys are all missing the point. He explicitly said he needs commutators and you're not giving him any....

That's because he didn't specify why he needed commutators. Everyone seemed to assume (and I think rightfully) that he didn't really need commutators.

Maybe the topic starter can explain why he needs commutators.

(and I personally do x2 (2*J-Perm) x2 instead of x2 (2*T-Perm) x2

 

[Stefan]

Everyone seemed to assume [...] that he didn't really need commutators.

Yeah I assumed that as well. I think what he needed was someone to make him aware he's misusing terminology.

Now c'mon, solve my riddle. That's much more interesting than providing yet another trivial "well the way I do it" answer.

 

[TMOY]

OK, I've got a solution for the 4^3. Lowercase letters are still inner-slice moves:
[l u r u r' u l', U]

Edit: For the 3^3 it is actually impossible. Say you have a commutator [A, B]. If A rotates the centers on themselves a given number of times, A' will execute the same rotations backwards, not necessarily on the same centers if you allow double layer and slice moves, but the overall sum will always be zero. Same for B and B'. So you cannot perform a 180 degree rorarion on one single center using only a commutator.

 

[cubeRemi]

TMOY, I'm obviously allowing 180 degrees turns. Try again.

2 faces, 180:

(M2U2M2U2) (S) (U2M2U2M2) (S')

I did not found a comm. for just one face (yet).

 

[AvGalen]

Everyone seemed to assume [...] that he didn't really need commutators.

Yeah I assumed that as well. I think what he needed was someone to make him aware he's misusing terminology.

Now c'mon, solve my riddle. That's much more interesting than providing yet another trivial "well the way I do it" answer.

First time you said "now someone please find..."
Second time you said "Try again."
Now you say: "Now c'mon, solve my riddle"

First you go out and do the Smith experiment

 

[Stefan]

Ok thanks TMOY, that's a good explanation and I agree with it (just adding that counting the rotations ought to be done modulo 4 (or modulo 360 degrees)).

 

[cubeRemi]

and this sort of commutator: A B C A B C, A B C B C A ore A B C A C B

ABCDEFGABCDEFG

what is the fewest number of letters needed?

Remi

 

[deadalnix]

I don't know any commutator technique that can perform changes on only one piece :S

I'm not sure it is possible.

 

[Stefan]

I don't know any commutator technique that can perform changes on only one piece

Just to prove there are puzzles where it's possible: On a 1x1x3 do [ E, x2 ]

On a 3x3x3 we now know it's impossible because its centers are out of the question and all other pieces can't be changed alone anyway. It also easily extends to all NxNxN cubes (except 1x1x1). Don't know about other puzzles.

 

[TMOY]

I don't know any commutator technique that can perform changes on only one piece :S

Pop a corner and hold it with the stickers backwards, twist it clockwise, fix the pop, twist the corner counterclockwise.