The first step in finding |B| in <F,U,L,R,D> is to build a little
Start-rooted data base using only the ten generators F, F', U, U', etc.
I was able to search eight levels deep with a "quick and dirty" search.
To search deeper would take a good bit longer. I hope that eight levels
will be enough to calculate |B|. By constructing a companion
B-rooted data base, I should be able to test up to 15 levels deep.
(B is odd, so eight levels deep for each half-depth search only
gets you 15 levels total instead of 16.)

I haven't started the search for B yet, but I thought the
results so far might be of minor interest in their own right. As
I indicated before, these are actual cube positions. I haven't
figured out any way to apply conjugacy classes to this problem.

I find it a little puzzling that the branching factor is not
monotonically decreasing (c.f., level 3 to level 4).

Level         Number of       Local      Branching
              Positions        Max        Factor

0                  1           0
1                 10           0           10.000
2                 77           0            7.700
3                584           0            7.584
4              4,434           0            7.592
5             33,664           0            7.592
6            255,320           0            7.584
7          1,933,936                        7.575
8         14,635,503                        7.568

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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