Rubik's Group

Author

Eric W. Weisstein
November 9, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/RubiksGroup.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RubiksGroup.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Figure

(from tutorial/PermutationGroups)

These are the six basic rotations:

rot1=Cycles[{{1,3,8,6},{2,5,7,4},{9,48,15,12},{10,47,16,13},{11,46,17,14}}];
rot2=Cycles[{{6,15,35,26},{7,22,34,19},{8,30,33,11},{12,14,29,27},{13,21,28,20}}];
rot3=Cycles[{{1,12,33,41},{4,20,36,44},{6,27,38,46},{9,11,26,24},{10,19,25,18}}];
rot4=Cycles[{{1,24,40,17},{2,18,39,23},{3,9,38,32},{41,43,48,46},{42,45,47,44}}];
rot5=Cycles[{{3,43,35,14},{5,45,37,21},{8,48,40,29},{15,17,32,30},{16,23,31,22}}];
rot6=Cycles[{{24,27,30,43},{25,28,31,42},{26,29,32,41},{33,35,40,38},{34,37,39,36}}];
RubiksGroup=PermutationGroup[{rot1,rot2,rot3,rot4,rot5,rot6}];

GroupOrder[RubiksGroup]

superflip=Cycles[{{2,47},{4,10},{7,13},{5,16},{20,19},{21,22},{28,34},{18,44},{25,36},{45,23},{42,39},{31,37}}];

GroupElementQ[RubiksGroup,superflip]