In answer to the question by Dan Hoey, I printed out the unique
antipodal of the 3x3x3 edges -- the one configuration that is
15 moves from Start using only q-turns on the edges of the 3x3x3.

It is really quite extraordinary and wonderful. I already knew
that there were only four equivalence classes with 24 elements.
Well, two of them are Start itself and its antipodal. Without
further ado:

   *6*              *6*
   6*6              3*4
   *6*              *1*
   *2*              *5*
   2*2              3*4
   *2*              *2*
*3**1**4*        *1**1**1*
3*31*14*4        5*23*42*5
*3**1**4*        *6**6**6*
   *5*              *2*
   5*5              3*4
   *5*              *5*

Start          Antipodal

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan)              (304) 293-5192
Associate Director, WVNET                  (304) 293-5540 fax
837 Chestnut Ridge Road                     BRYAN@WVNVM
Morgantown, WV 26505                        BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are
going to have time to do it over again tomorrow?