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Subject: Local Maxima Revisited
From: mark.longridge@canrem.com (Mark Longridge)
Message-Id: <60.656.5834.0C18F5BD@canrem.com>
Date: 	Mon, 27 Dec 1993 00:58:00 -0500
Organization: CRS Online  (Toronto, Ontario)

                Some thoughts on Local Maxima
                -----------------------------

   I have verified that the position I call "6 H order 2 type 2"
is a local maximum.

p175 6 H order 2 type 2  T2 B2 L2 T2 D2 L2 F2 T2              (8)

A rare example of a pattern with symmetry level 2, perhaps even
the only one of this type, and also the most symmetric of the
6 H patterns.

Nothing new here, as this was noted formerly by David Singmaster
in one of the Cubic Circulars and by Jim Saxe & Dan Hoey in the
archives.

Somewhat more interesting is the conclusion that the pattern
4 H order 2, or H's on the F,R,B,L faces (oriented like the
letter H) is also a local maximum, at least in the square's
group.

p160 4 H order 2 Type 2  B2 D2 (L2 R2 F2) ^2 T2 F2           (10)