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