To sum up everything we know:

1) A Symetric position is a local maximum.
2) A maximally distant state is a local maximum.
3) If Plummer's cross is 28 Qs away from home, then it is a local maximum.

All the other implications that have been flying around are unproven
as far as I know. I welcome PROOFS of anything else that I might not
be aware of. The volume of air-headed speculation on this subject has
reached the point where the MC mailer is so overloaded with gubbish
that a "CUBE-LOVERS Digest" is being considered. Now that is just
plain silly given that NORMALLY we only get one or two pieces of mail
a week through this list. If you don't understand why one of the
three facts above are true, DON'T send mail to the whole list! Look
through the old mail (they are all explained there) or send JUST ME a
question, and I will try and answer it.