From cube-lovers-errors@mc.lcs.mit.edu  Mon Aug 18 13:49:17 1997
Return-Path: <cube-lovers-errors@mc.lcs.mit.edu>
Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP
	id NAA02319; Mon, 18 Aug 1997 13:49:16 -0400 (EDT)
Precedence: bulk
Errors-To: cube-lovers-errors@mc.lcs.mit.edu
Mail-from: From kociemba@hrz1.hrz.th-darmstadt.de Sun Aug 17 03:43:15 1997
Message-Id: <33F6AA41.3C98@hrz1.hrz.th-darmstadt.de>
Date: Sun, 17 Aug 1997 09:37:37 +0200
From: Herbert Kociemba <kociemba@hrz1.hrz.th-darmstadt.de>
To: cube-lovers@ai.mit.edu
Subject: Re: isoglyphs
References: <199708170235.WAA07984@sun30.aic.nrl.navy.mil>

[Mike Reid wrote:]
> >  ...
> > 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.
> 

Dan Hoey wrote:

>...
> I've done some analysis by facets on these three cases, which is too
> messy to describe, but which leads me to the conclusion that the above
> position is the only isoglyph of its pattern, implying the conclusion
> that there is no chiral form.

There are two more isoglyphs of this pattern,

B2 D . R D' B2 F' R2 U' B' R' U F R'  (13)
D2 R D2 L B2 R' B2 . D' R F D' L' F' D2 L'  (15)

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

--Herbert