On 10/11/95 at 22:56:15 email@example.com said:
> The four rotations are i, b, bb, and bbb, where we use lower case
> letters to simulate Frey and Singmaster's script notation for rotations.
> For example, b is the whole cube rotation consisting of grasping
> the Back face and rotating the whole cube (not just the Back face)
> clockwise by 90 degrees.
The reflections are similarly rrv, rrbv, ttv, and ttbv, where t and r
are the whole-cube rotations by the Top and Right faces, and v is the
I am not quite sure why it took me so long to figure out that
Q2-conjugation was the appropriate symmetry when generating G
without B and B'. With the wisdom if hindsight, it is perhaps
because the Q2 subgroup of M could be described as fixing the
B and F face centers, and I was thinking only in terms of fixing
the B face center. Obviously, you cannot fix the B face center
without also fixing the F face center. Thus, it is clear that
Q2-conjugation is also the appropriate symmetry when generating
G without F and F'.
Q1 and Q3 are subgroups of M which are conjugate with Q2 in Dan's
taxonomy of subgroups of M. Q1 fixes the T and D face centers, and
would be the appropriate symmetry when generating G without T and T',
or without D and D'. Q3 fixes the R and L face centers, and would be
the appropriate symmetry when generating G without R and R', or without
L and L'.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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