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Date: Sat, 16 Aug 1997 11:25:08 +0200
From: Herbert Kociemba <kociemba@hrz1.hrz.th-darmstadt.de>
To: cube-lovers@ai.mit.edu
Subject: Re: isoglyphs
References: <199708150145.VAA22661@life.ai.mit.edu>

michael reid wrote:
> 
> dan's idea of glyph patterns, especially isoglyphs is quite interesting.
> herbert has given all the "continuous" isoglyphs.  i spent some time
> looking for other isoglyphs, and was surprised at how many exist.
> herbert, how did you find those?  is that part of your pattern generator?
> if your program can also find all "discontinuous" isoglyphs, then i guess
> there's not much point in trying to do it by hand.

With the pattern generator it's indeed very easy to find the isoglyphs. 
I restricted myself to continuous isoglyphs, because I had the most
interest in them an because the number is quite limited. There are many,
if you do not use the "continuous" condition. By the way, Mike, it would
be nice to complete the chapter "continous isoglyphs" by computing the
shortest generators for them with your program. This hopefully should
not take too long, because most of the generators seem to be rather
short.

Here are for example the (not necessarily continuous) isoglyphs, which
built the "snake patterns". There are 13 of them:

R2 B' U2 B' . D' F' U D' L B' F L D R2 D F2  (16)
D' B2 F2 D' U L2 . F' L R' F' D U' R D B2 R  (16)
R L2 B2 R' . D' L' D B2 F L2 U' L U' F'  (14)
B2 U2 F2 D2 F2 U . R' F' L2 U2 L R U' L2 F2 L' F  (17)
D B2 L2 D2 . F' D2 L B2 D F2 U2 F U2 R' D2  (15)
D2 R D2 F2 L U2 . B R' D R2 D' R B D2 L U2 L'  (17)
U' B2 R2 U2 . F' D2 L' F2 U' F2 D2 F U2 R' U2  (15)
D2 B2 L B2 F2 L' . U B F' L F2 L' B' F D2 U'  (16)
D2 U' B2 D2 U2 L2 U2 . B' U2 L F2 U B2 D2 B D2 R' U2  (18)
U2 R' F2 R' D2 F2 . B U' L' U' B D L' F2 D'  (15)
U' F2 D R2 U L2 U2 . B' U B' U R D' L F' R D2  (17)
U2 F2 D F2 L2 U2 . F' U2 L F2 D B2 D2 F D2 R' F2  (17)
D2 F2 D2 U2 R D2 U2 R' . U R L' B D2 B' R' L D2 U'  (18)


P.S.: I could not hold what I promised, the Cube Explorer 1.5 version
(which for example has the "continuous" feature) still is not ready....

--Herbert