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Mail-from: From reid@math.brown.edu Fri Aug 15 19:48:02 1997
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Date: Fri, 15 Aug 1997 19:49:54 -0400
From: michael reid
To: cube-lovers@ai.mit.edu
Subject: Re: isoglyphs
perhaps i am missing something, but doesn't
D2 R2 U2 D2 R2 U D (12q, 7f)
produce an isoglyph of type 4D ?
are there any isoglyphs of type 21 or 23 ? i haven't found any.
each has three possible patterns:
... .*. .*.
*** .** ***
*** , *** and *.* ,
.*. ... ...
.*. **. .*.
*.* , *.* and *** .
i hadn't even considered chiral versus achiral isoglyphs. indeed,
all the "continuous" isoglyphs given by herbert are chiral.
achiral isoglyphs certainly exist, for example
D2 R2 U' B' L B U B L F2 R D' L2 U2 B2 D (22q, 16f)
of type 11; pattern
*..
***
***
and others can be derived from this. i suspect that there is no
chiral form of this isoglyph, but i'm not absolutely certain.
another interesting note is that the inverses of the "continuous"
isoglyphs are also isoglyphs; in fact the same pattern, perhaps in
a different orientation. however, there is at least one (probably
more) isoglyph whose inverse is not an isoglyph. instead of giving
it right here, i'll challenge other readers to find it/them.
mike