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 Post subject: 4x4 Center Permutation
PostPosted: Wed Sep 07, 2011 8:03 pm 
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I'm having two permutation problems on my rhombic dodec 4x4
does anyone know the algs for em?


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 Post subject: Re: 4x4 Center Permutation
PostPosted: Wed Sep 07, 2011 8:13 pm 
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Do you know any center 3-cycles? That situation can be solved with 3-cycles.

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 Post subject: Re: 4x4 Center Permutation
PostPosted: Wed Sep 07, 2011 11:17 pm 
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bmenrigh wrote:
Do you know any center 3-cycles? That situation can be solved with 3-cycles.

r' d' r U r' d r U' is a is a three-cycle of centers. It involves pieces in the U and R layers. (This may or may not help in this situation.)


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 Post subject: 4x4 Center Permutation
PostPosted: Thu Sep 08, 2011 1:04 pm 
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Look here:
http://twistypuzzles.com/forum/viewtopic.php?f=8&t=17715&p=241755#p241755
http://twistypuzzles.com/forum/viewtopic.php?p=249831#p249831


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 Post subject: Re: 4x4 Center Permutation
PostPosted: Thu Sep 08, 2011 11:47 pm 
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is there no easy way to simply rotate the center?
'cause if not I already know how to switch pieces
thanks for the input either way guys

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 Post subject: 4x4 Center Permutation
PostPosted: Fri Sep 09, 2011 12:32 am 
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Quote:
is there no easy way to simply rotate the center?

Ок.
Variant 2.
1) Simply to rotate the centres;
2) 3-cycle of the central elements.


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 Post subject: Re: 4x4 Center Permutation
PostPosted: Tue Sep 13, 2011 8:23 pm 
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pytlivyj_1 wrote:
Quote:
is there no easy way to simply rotate the center?

Ок.
Variant 2.
1) Simply to rotate the centres;
2) 3-cycle of the central elements.

I know how to do a 3-cycle, I was simply asking if there was an algorithm that was faster

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 Post subject: Re: 4x4 Center Permutation
PostPosted: Tue Sep 13, 2011 8:47 pm 
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mitchblahman wrote:
I know how to do a 3-cycle, I was simply asking if there was an algorithm that was faster

Sure there is but there is also "Newton's law of twisty puzzles" which states "for every rotation of a piece there is an equal and opposite rotation elsewhere". This holds true for all commutators and also whenever twist is preserved for the piece type which is the case for most puzzle's pieces including the 3x3x3 / 4x4x4 centers. Little known fact: Sir Isaac Newton was a twisty puzzle genius.

If you want to rotate a group of 4 centers clockwise and another group of 4 centers on a different face counter-clockwise then you can use what I have been terming an "orientation changing commutator" which using Gelatinbrain's 3x3x3 notation looks like:

[F&2, U'&2, F'&2], U, [F&2, U&2, F'&2], U'

From your original picture this would help you a great deal. It would solve all 4 centers on one face and solve 1 center on the other face leaving you with a single 3-cycle (or possibly 2-2 swap) rather than a bunch of 3-cycles.

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 Post subject: Re: 4x4 Center Permutation
PostPosted: Wed Sep 14, 2011 10:48 pm 
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For anyone referencing this thread in the future, I'll give an algorithm that cycles three center pieces on one face. In normal 4x4x4 notation, it is ( r f ' r ' f ) F ( f ' r f r ' ) F ( r f ' r ' f ) F2 ( f ' r f r ' ). On the front face, this moves three center pieces counter-clockwise around the lower-left piece. The lower-left piece does not move.


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