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Date: Sat, 16 Aug 1997 11:25:02 +0200
From: Herbert Kociemba <kociemba@hrz1.hrz.th-darmstadt.de>
To: cube-lovers@ai.mit.edu
Subject: Re: isoglyphs
References: <199708152344.TAA05912@life.ai.mit.edu>

michael reid wrote:

> perhaps i am missing something, but doesn't
> 
>      D2 R2 U2 D2 R2 U D   (12q, 7f)
> 
> produce an isoglyph of type 4D ?

That's right, and it is the only one which exists of this type. But it
is no continuous isoglyph.
> 
> are there any isoglyphs of type 21 or 23 ?  i haven't found any.
> each has three possible patterns:
> 
> ...     .*.         .*.
> ***     .**         ***
> ***  ,  ***   and   *.* ,
> 
> .*.     ...         ...
> .*.     **.         .*.
> *.*  ,  *.*   and   *** .

Here are generators for all isoglyphs of your second pattern:
D2 R2 B2 L2 U2 F2 U2 B2 R2 U2 R2 U2  (12)
U2 R2 F2 R2 U2 B2 D2 B2 L2 U2 R2 U2  (12)
U2 L2 F2 R2 U2 B2 D2 B2 R2 U2 R2 U2  (12)
D2 L2 B2 L2 U2 F2 U2 B2 L2 U2 R2 U2  (12)

and here for the fifth:
D2 R2 F2 L2 U2 B2 D2 F2 L2 U2 L2 U2  (12)
U2 R2 B2 R2 U2 F2 U2 F2 R2 U2 L2 U2  (12)
U2 L2 B2 R2 U2 F2 U2 F2 L2 U2 L2 U2  (12)
D2 L2 F2 L2 U2 B2 D2 F2 R2 U2 L2 U2  (12)

For the others, no isoglyphs exist.

--Herbert