On Fri, Aug 31, 2012 at 9:03 AM, Chris Smith <[email protected]> wrote: > David, could you entertain a question here: > > I wrote a routine to generate permutations of an nxn Rubik's cube. I > enter into a PermutationGroup the permutation of the faces after these > standard rotations: > > 1) cw rotation of cube from front > 2) cw rotation of cube from top > 3) n//2 + n%2 cw slice rotations from the front (e.g. just the front > 1/nth of the cube, then the 2/nth slice of the cube, ..., until the > middle or the one before the middle).
In the "odd" cases, the center cubie of each face should be fixed. This fixes an orientation of the cube in space. In the "even" cases, I'm not sure how to fix an orientation. > > I checked with an appropriately numbered tissue box that the right > permutations are being returned. And these seem like they should be a > sufficient basis for obtaining any orientation of the cube. But when I > check the order I find: > >>>> from sympy.combinatorics import * >>>> for i in range(1, 4): > ... print i, RubikGroup(i).order() > ... > 1 24 > 2 88179840 > 3 1038048078587756544000 When you fix an orientation, this should be 4.3x10^19, roughly. >>>> RubikGroup(4).order() > 43252003274489856000 This is 4.3x10^19, roughly. Did you define RubikGroup(4) to be the 3x3 Rubik's cube group? > (and if I use the generators my routine generates, recursion error > prevents the order from being computed) > > Is there any easy way that you can explain to me why the 3x3's order > is larger than the 4's when giving those particular permutations? > > Is this just a suboptimal group? What permutations make the optimal > group? With the code I have I can construct the permutation for any > sequence of turns that should be in the optimal group. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
