Commutator for 3 cycle corner permutation

[mande]

Does anybody know a commutator for a 3 cycle corner permutation (that keeps the orientation fixed)?

 

[tikva]

Yes. In fact, I haven't seen an A-perm which isn't a conjugate with a commutator.

For example my ccw A-perm that doesn't touch DFL, but cycles all others on F face is

R2 U2 R D R' U2 R D' R,

which is actually:
R' R' U2 R D R' U2 R D' R,

or shorter:
[R' U2 R, D]^R'.

Pure commutator would be much longer, though.

 

[mande]

Conjugating with commutator is fine, I actually wanted a pure commutator (if possible, a short one)

 

[tikva]

Ok, here is one inspired by F2L pair switching aspect of half-N-perm:

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

It cycles DBR -> DFR -> DFL.

You can write it as a commutator within a commutator:

[[R U' F, U2], D'].

 

[blade740]

Yes. In fact, I haven't seen an A-perm which isn't a conjugate with a commutator.

r U r' U' r' F r2 U' r' U' r U r' F'

 

[tikva]

Yes. In fact, I haven't seen an A-perm which isn't a conjugate with a commutator.

r U r' U' r' F r2 U' r' U' r U r' F'

You forgot your first U there
it's
U r U r' U' r' F r2 U' r' U' r U r' F'.

Actually that's yet another conjugate with a commutator:

[r' U r U r' U', r' F r U']^r

 

[Lucas Garron]

(that keeps the orientation fixed)?

Please hide, fast. Stefan might find this thread at any moment.

Anyhow, I'd like to see someone write (R'URU'R2F'U'FURFR'F'R2*y2)*2 as a comm.

 

[tikva]

(that keeps the orientation fixed)?

Please hide, fast. Stefan might find this thread at any moment.

Although he didn't use the most precise terms, everyone understood he meant A-perm.

Anyhow, I'd like to see someone write (R'URU'R2F'U'FURFR'F'R2*y2)*2 as a comm.

I'll give it a try once... (maybe write a program?)

 

[mande]

Well, i didn't really mean an A perm, I wanted any general 3 cycle of corners (needn't be all on the same layer)
I asked particularly about the orientation because I know that the commutator R'D'R U R'DR U' does a 3 cycle of corners, but doesn't keep orientation fixed.

 

[joey]

(that keeps the orientation fixed)?

Please hide, fast. Stefan might find this thread at any moment.

Although he didn't use the most precise terms, everyone understood he meant A-perm.

Not actually what Lucas meant

QUOTE=mande;106574]Well, i didn't really mean an A perm, I wanted any general 3 cycle of corners (needn't be all on the same layer)
I asked particularly about the orientation because I know that the commutator R'D'R U R'DR U' does a 3 cycle of corners, but doesn't keep orientation fixed.[/QUOTE]

Wow, thanks for this explanation. You've now explained something completely different than what was first thought.

I'll give you a clue, I know one, [R2, (find this bit your self)]. Good luck.

 

[mande]

Wow, thanks for this explanation. You've now explained something completely different than what was first thought.

I'll give you a clue, I know one, [R2, (find this bit your self)]. Good luck.

Ooh, thanks for the hint...I don't know whether I've used it or not though. I just realised that I use a commutator [R2DR2D'R2 , U2] for a 3 cycle of corners during my BLD solves .

 

[badmephisto]

btw i've derived a way to do this about halfway through my commutators tut on youtube
http://www.youtube.com/watch?v=7yZoDi_B1lI

idea is that basically you can use your f2l knowledge to create this commutator just using logic... of course, if you need it to be quick too, thats a different story

 

[mande]

btw i've derived a way to do this about halfway through my commutators tut on youtube
http://www.youtube.com/watch?v=7yZoDi_B1lI

idea is that basically you can use your f2l knowledge to create this commutator just using logic... of course, if you need it to be quick too, thats a different story

even i wanted the commutators so that i could develop a bit of group theory related to the cube for a lecture that i had to give.

 

[Lucas Garron]

I think j`ey wants me to post this:
[R' U L' D2 L U' R, U]
Also try:
[R' D F' D2 F D' R, U]

 

[Swordsman Kirby]

[R2,[F:L]] and variants.