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 Post subject: 4x4 Center PermutationPosted: Wed Sep 07, 2011 8:03 pm

Joined: Sat Aug 22, 2009 3:27 pm
Location: California
I'm having two permutation problems on my rhombic dodec 4x4
does anyone know the algs for em?

 Attachments: 4x4 parity 002.JPG [ 2.38 MiB | Viewed 1357 times ] 4x4 parity 001.JPG [ 2.41 MiB | Viewed 1357 times ]

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 Post subject: Re: 4x4 Center PermutationPosted: Wed Sep 07, 2011 8:13 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Do you know any center 3-cycles? That situation can be solved with 3-cycles.

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 Post subject: Re: 4x4 Center PermutationPosted: Wed Sep 07, 2011 11:17 pm

Joined: Fri Jan 07, 2011 2:37 pm
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 PermutationPosted: Thu Sep 08, 2011 1:04 pm

Joined: Tue Mar 24, 2009 12:52 pm
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 Post subject: Re: 4x4 Center PermutationPosted: Thu Sep 08, 2011 11:47 pm

Joined: Sat Aug 22, 2009 3:27 pm
Location: California
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

_________________
Wazzaaaaaa!

hey look ^

Rest In Peace Frank

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 Post subject: 4x4 Center PermutationPosted: Fri Sep 09, 2011 12:32 am

Joined: Tue Mar 24, 2009 12:52 pm
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 PermutationPosted: Tue Sep 13, 2011 8:23 pm

Joined: Sat Aug 22, 2009 3:27 pm
Location: California
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

_________________
Wazzaaaaaa!

hey look ^

Rest In Peace Frank

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 Post subject: Re: 4x4 Center PermutationPosted: Tue Sep 13, 2011 8:47 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
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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Prior to using my real name I posted under the account named bmenrigh.

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 Post subject: Re: 4x4 Center PermutationPosted: Wed Sep 14, 2011 10:48 pm

Joined: Fri Jan 07, 2011 2:37 pm
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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