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 Post subject: Centre Twisting algs
PostPosted: Thu Feb 28, 2013 1:53 pm 
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Does anybody know any 3x3 centre twisting algs?

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 Post subject: Re: Centre Twisting algs
PostPosted: Thu Feb 28, 2013 2:04 pm 
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You can twist a single center 180 degrees with a special construction that makes use of a 2-2 swap conjugate + center twist which when applied twice cancels the 2-2 swap and leaves just the center twist:
[[R:[L:U2]] U]x2

If you want to twist two centers by 90 degrees each, there is a simple [3,1] commutator:
[[R'&2:U'&2],U]


The [[...[...[...[...:A]]]] A]xN construction is very powerful for twisting individual pieces. A few months ago Daniel Kwan and I (DKwan) spent a lot of time examining these. I plan on making a long post and video series about them sometime.

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 Post subject: Re: Centre Twisting algs
PostPosted: Thu Feb 28, 2013 4:10 pm 
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Here is what I do: find two centers that are twisted and place them on the top and front. Note which direction the center on the top needs to turn(clockwise or counterclockwise). Then do the dots pattern so that the top center moves to the front(M E M' E') turn the front front face the direction that you remembered then undo the pattern. Finally, undo the F turn that you performed. In full the alg for twisting the top center clockwise and the front counterclockwise is M E M' E' F E M E' M' F'. Twisting opposite centers uses the same concept, but replaces M E M' E with M E2 M' E2.

To twist the U center 180 degrees just do (R U' R' U') 5 times.

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 Post subject: Re: Centre Twisting algs
PostPosted: Fri Mar 08, 2013 4:02 am 
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I have a comprehensive list. Will post later :roll:

Per

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 Post subject: Re: Centre Twisting algs
PostPosted: Sat Mar 23, 2013 3:08 pm 
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For 180 r u r' u. Repeat until solved.

For 90. I do a t perm then resolve and hope its solved or 180 hahaha


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 Post subject: Re: Centre Twisting algs
PostPosted: Sat Mar 23, 2013 3:57 pm 
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bmenrigh wrote:
If you want to twist two centers by 90 degrees each, there is a simple [3,1] commutator:
[[R'&2:U'&2],U]


I'm having trouble figuring out what exactly that means. Could you write it out in normal notation?

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 Post subject: Re: Centre Twisting algs
PostPosted: Sat Mar 23, 2013 9:17 pm 
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Location: chicago, IL area U.S.A
Without any notation, the way I do it is put the center I need twisted 180 degrees, on the bottom. I turn the right side a quarter turn, turn the bottom a quarter turn, then turn the right side back to the original position. Then continue the bottom one in the same direction as before. Repeat this until it's solved.
I was proud of myself, I actually figured this one out on my own and saw that others had come up with it independently.

-d


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 Post subject: Re: Centre Twisting algs
PostPosted: Sun Mar 24, 2013 5:52 am 
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Joined: Fri May 06, 2005 10:13 am
Location: Norway
Here is one that rotates 4 centers by 180 degrees:

F2 R2 L2 F2 U D' R2 F2 B2 R2 U'

Written with slice moves it becomes:

(F2 MR2 B2 MU)2

Applet:

Center 4-twist (F2,R2,B2,L2) (8 btm).

Most center twisting algorithms are best understood when written with slice turn notation :wink:

Per :solved:

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 Post subject: Re: Centre Twisting algs
PostPosted: Sun Mar 24, 2013 6:10 am 
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Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
BN wrote:
bmenrigh wrote:
If you want to twist two centers by 90 degrees each, there is a simple [3,1] commutator:
[[R'&2:U'&2],U]
I'm having trouble figuring out what exactly that means. Could you write it out in normal notation?
In Gelatinbrain notation R&2 is the slice between L and R turned clockwise as R turns.
R'&2 is the same slice turned anti clockwise.
Correspondingly U&2 is the inner slice below U.
In former WCA notation (2010) R'&2 is equal to M (M is the slice under L turned into the same direction as L and
U'&2 = E (E is in WCA notation the slice above D turned as D turns.
So this [[R'&2:U'&2],U] translates to [[M:D],U] which is the commutator / conjugate notation of
the eight moves M D M' U M D' M' U'
If you use the former WCA notation for Big Cubes slices you would write r' u' r U r' u r U'.

EDIT: In WCA notation 2013 it would become Rw' R Uw' U Rw R' U Rw' R Uw U' Rw R' U'
If I use brackets for slice moves it becomes (Rw' R) (Uw' U) (Rw R)' U (Rw' R) (Uw U') (Rw R') U'
When I wanted to respond to BN's question yesterday, I wanted to quote the WCA notation. I found that simple slice moves do no longer exist and wrote about this here.

Honestly, I hope that WCA will change this back!!!

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 Post subject: Re: Centre Twisting algs
PostPosted: Sun Mar 24, 2013 10:42 am 
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Joined: Sat Jan 28, 2006 6:04 am
Location: Switzerland
See Herbert Kociemba's page Cubes with Twisted Centers.
It's a comprehensive list of 73 algorithms to twist the centers of a 3x3x3.

The algorithms are optimized both in Face Turn Metric and Slice Turn Metric.
... for the later metric they are still written in the former WCA notation. :wink:


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