Hi :-) There's more to commutators than those easy short 4-move algs. When writing like Chris said : X Y X' Y' or P Q P' Q' (not to confuse with turning the cube physically) each of P or Q can be a sequence of several moves. And also conjugates commutators are very useful. A conjugate is like this : C P Q P' Q' C' so u add C before a commutator and inverse C after it. That combined alg gives same net effect on the cube but on different cubies. C server to bring other cubies into the positions affected by P Q P' Q' only.
By making C the inverse of part of P Q P' Q' we achieve a cyclical shift. Ie if we have P = R' and Q = F then P Q P' Q' = R' F R F'. By letting C = R we get C P Q P' Q' C' = R R' F R F' R' = F R F' R'. And so on. It's very interesting and useful to study commutators that make up for instance 3-cycles on corners or edges :-) -Per > --- In [email protected], "undermostfiend" <[EMAIL PROTECTED]> wrote: > > it does thank you > > John, > > --- In [email protected], cmhardw <[EMAIL PROTECTED]> > wrote: > > > > Those are all commutators of the form X Y X' Y' > > > > > R2 E2 R2 E2 > > X=R2 > > Y=E2 > > > > > R2 E R2 E' > > X=R2 > > Y=E > > > > > R2 U2 R2 U2 > > X=R2 > > Y=U2 > > > > The key is that for most of them they are their own inverses. This > > is one key to making quick easy commutators. > > > > Hope this helps some, > > Chris > > > > --- In [email protected], "undermostfiend" > > <[EMAIL PROTECTED]> wrote: > > > > > > R2 E2 R2 E2 > > > > > > R2 E R2 E' > > > > > > R2 U2 R2 U2 > > > > > > i found these out when i was fooling around > > > > > > Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
