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[ i sent a similar message several days ago, but it appears to

have gotten lost. my apologies if anyone already got this. ]

i wrote

in the same way, local maxima (within the antislice group) in the

90 degree antislice metric are local maxima in the full cube group

(quarter turn metric).

this isn't necessarily true. one must check that the minimal

maneuvers (within the antislice group) for such positions are

also minimal in the full group.

the position i mentioned

(FB') (RL') (U'D) (R2L2) = [ ... ]

is quickly checked to require 10 quarter turns, so indeed it

is locally maximal.

here's an example i found of a locally maximal position whose

inverse is not locally maximal:

A = B U2 F2 R U' R' B' R' U F2 U2 (15q)

this position has six symmetries, generated by the cube rotation

C_UFR and central reflection. using these symmetries we can

give minimal maneuvers which end with a half turn of any face,

and thus with any of the twelve quarter turns. the same is not

true of its inverse, and we can easily check that there is no

minimal maneuver for A which begins with the quarter turn B'.

equivalently, the position A^-1 B' requires 16 quarter turns.

mike