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From: Dan Hoey <Hoey@aic.nrl.navy.mil>
To: kociemba@hrz1.hrz.th-darmstadt.de
Cc: cube-lovers@ai.mit.edu
In-Reply-To: <33F6AA41.3C98@hrz1.hrz.th-darmstadt.de> (message from Herbert
	Kociemba on Sun, 17 Aug 1997 09:37:37 +0200)
Subject: Re: isoglyphs

Herbert Kociemba asks:

> Could someone tell me, what chiral and achiral exactly mean?

"Chirality" is Lord Kelvin's word for "handedness" as in "appearing in
two mirror-image varieties."

A "chiral isoglyph" is one in which the handedness of the glyph is
taken into account in testing for isoglyphy,* so that the glyph
appears only in one variety.  Neither Mike's original isoglyph nor the
                                                       *..     ..*
two you found are chiral isoglyphs--they all have both *** and *** .
                                                       ***     ***

Mike used "achiral" for an isoglyph that fails to be a chiral
isoglyph, though I would tend to use "non-chiral".  I would rather use
"achiral" for a situation that lacked chirality, as in an isoglyph of
a mirror-symmetric glyph.

[* Thanks to Allan Wechsler for inventing the word "isoglyphy".  His
   alternate term, "isoglyphism", is still looking for a good use. ]

Dan
Hoey@AIC.NRL.Navy.Mil