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Date: Sun, 18 Jan 1998 23:59:30 -0500
From: michael reid <reid@math.brown.edu>
To: cube-lovers@ai.mit.edu
Subject: Re:  Face Turns Nine Moves from Start
Cc: jbryan@pstcc.cc.tn.us

jerry writes about strong local maxima in the face turn metric.
he says that superflip is such a position, but pons asinorum is not.
there are some other positions with a high degree of symmetry that are
also strong local maxima, for example

     pons asinorum  composed with  superflip
     superfliptwist
     supertwist

and some of the  T-symmetric positions that may not have standard names

     #1.  B  U  L' F' U  R  U2 D2 F' L  U' B' L  D  R2 L2 B2
     #4.  D' R' U  B' D' R' L  F  L  B' R' F  B' U  L  D' F  U' D2
     #5.  B2 L  U' L  D  R' L' D2 R  U  L' B2 U  R2 U2 F2 U
     #6.  D' L  F' B' L  F2 B2 U  R  L' U  D' L  F' R2 L2 F2 U' D2
     #9.  U  F2 D  B' U' B2 R  B2 D' F2 U' D2 B2 L' U2 B  D2
    #11.  D' F2 U2 B2 R  F' L  U' F2 B  R' F' D  L2 D  R2 F2 U' F2

and there might be more among the  H-symmetric  and  T-symmetric
positions (i can't tell right now without doing more searching).

yes, strong local maxima in the face turn metric are probably quite rare.
in the quarter turn metric, any global maximum is necessarily a local
maximum, because of parity considerations.  however, in the face turn
metric, a global maximum is a local maximum, but it may not be a strong one!
so the only strong local maxima we have here are found as a result of
(lots of) computer searching.

i look forward to seeing your 2 strong local maxima at distance 9f from
start.

mike