# Message #1840

From: Andrew Gould <agould@uwm.edu>

Subject: RE: [MC4D] Re: State graph of MC2D

Date: Wed, 03 Aug 2011 13:06:00 -0500

oops, speaking of link problems, if you click the link, it doesn’t give you

a left side. Copy & paste http://kociemba.org/cube.htm. Also, by

‘rotations’ and ‘reflections’ I mean applying them to the whole puzzle.

–

Andy

From: 4D_Cubing@yahoogroups.com [mailto:4D_Cubing@yahoogroups.com] On Behalf

Of Andrew Gould

Sent: Wednesday, August 03, 2011 12:54

To: 4D_Cubing@yahoogroups.com

Subject: RE: [MC4D] Re: State graph of MC2D

Hi David,

Herbert Kociemba (part of the cube20.org group) used this ‘reducing by

symmetries’ to solve god’s number is 20. It cut the number of states they

had to solve by a factor of about 39.7. So it’s quite practical. He didn’t

call it ‘recoloring’ though….

He defined a ‘symmetry’: a combination of rotations or a combination of

rotations with a reflection. Each symmetry, S has a unique inverse S’, and

the double inverse, S’’ = S. Two states, j and k are then said to be

equivalent if there exists a symmetry such that j = SkS’. I look at it as

conjugating by symmetries only.

For details, go to http://kociemba.org/cube.htm, then on the left side under

‘The Mathematics behind Cube Explorer’, click ‘Equivalent Cubes and

Symmetry’.

–

Andy