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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.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 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?