On 12/07/93 at 20:13:08 hoey@aic.nrl.navy.mil said:

My (very cheap) guess for where we will find the other two M-symmetric
positions is opposite to Jerry Bryan's. On a cube with faces, the
central reflection of the edges with respect to the faces is Pons
Asinorum, which has the easy 12-qt tight lower bound we've seen before
(or if not, you can of course get it from me with email). I'm
guessing that this bound happens to be tight on the cube without
faces, as well. But I have no proof of this guess, and I'm very
grateful we won't have to settle for guesses for very long.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil

Dan Hoey is correct. Mirror-Image-of-Start is at level 12.
Edges-Flipped is at level 9. Mirror-Image-of-Start-and-Edges-Flipped
is at level 15. And, of course, Start is at Level 0. This exhausts
the list of configurations with order-24 symmetry.

I am still thinking about the easiest way to extract sequences of
operators from my data base. I gather from Dan's comments that a
12-qt operator is known for Mirror-Image-of-Start. Are operators
known for the other two cases? This is going to be sufficiently
time-consuming that I don't want to try to find operators that
are already known.

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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?