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Mail-from: From kociemba@hrz1.hrz.th-darmstadt.de Fri Aug  8 09:15:32 1997
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Date: Fri, 08 Aug 1997 15:10:22 +0200
From: Herbert Kociemba <kociemba@hrz1.hrz.th-darmstadt.de>
To: Dan Hoey <Hoey@aic.nrl.navy.mil>, cube-lovers@ai.mit.edu
Subject: Continuous isoglyph patterns
References: <199708052311.TAA13218@sun30.aic.nrl.navy.mil>

Dan Hoey made some proposals concerning 2-colored cube patterns. The
"coninuous"-condition i find especially interesting. I added this
feature to my Cube Explorer program and found exactly 34 continuous
isoglyphs (plus the trivial solution). I don't know if there are any
among them, which have not been described somewhere else before.
Here are generators for the patterns (I searched only about 1 minute for
most generators of the patterns, so there is no claim for the maneuvers
to be optimal):

D F2 D' . R B2 R' D F2 D' R B2 R'  (12)
U . L' D' U B2 D U' L' U'  (9)
U2 L' B2 . F R' D' R2 D B2 F' U L  (12)
D' U . L' R B' F D' U  (8)
R2 D L2 U' B2 D' U2 . R' F' U R B' L' D' F L2 B2 R U'  (19)
F2 L2 U L2 U' F2 D . B L R' D' U' F' D2 F' R2 F R  (18)
B2 U' B2 D' B2 D . L' B2 F' U R D2 R' D' U' F U  (17)
L2 D2 B D2 B' D2 B L2 . D B R D2 F L2 D F' R'  (17)
B2 U' B2 L2 B2 U2 B2 U' D2 . R U R' D' L U F U' D' L  (19)
U R2 D . F' L D2 U2 R' D2 U2 F D' R2 U'  (14)
U B2 . L B F' L2 R' B' F D U2 L' B2 U'  (14)
D' U . F' U L' R B' U F D' U R'  (12)
U' B2 F2 L2 U B2 U' L2 F2 . B' U R' F D' R2 D2 R' F'  (18)
F2 R2 D R2 D U F2 D' . R' D' F L2 F' D R U'  (16)
D U2 R2 D' U' . R D B2 R2 B2 R2 D B2 D2 R U'  (16)
D U2 L2 U R2 U' L2 U . R' B2 L2 F' L2 B' R' F' L D U'  (19)
D2 U F2 D' L2 U R2 B2 . R B2 R2 U2 B' L2 D2 R2 D R' U'  (19)
D2 R B2 R . F L B' F U' R L' U' F' D2 F' L2  (16)
D' B2 F2 D' U L2 . F' L R' F' D U' R D B2 R  (16)
U' R2 F2 U2 . L' D2 B' L2 U' L2 D2 L U2 F' U2  (15)
L2 U2 R' . B' D U' B2 D' R' D L D2 F D U2 L2  (16)
U' F2 U . R U2 R2 U2 R' F' R2 F U' F2 U  (14)
U2 R2 F2 U B2 D' . L' F L' F L' F D B2 U  (15)
D2 R F2 L' D2 R . B D2 F' L2 U' R' D L F D L' D L'  (19)
D' L2 F2 L2 B2 R2 U F2 U2 . L' F R B D R U' L F' U2 F  (20)
B2 L2 R2 U B2 R2 D F2 U' . B F U2 R' B2 L2 D U' B' L' R'  (20)
U B2 U2 L2 U F2 R2 B2 U' L2 D2 F2 U' . B L2 R2 D2 U2 F'  (19)
L2 . R' B2 F2 D2 B2 F2 L2 R2 U2 R'  (11)
D U L2 B2 D U' . F' U F' R F2 R' F D' B2 L2 D' U'  (18)
L2 U' B2 F2 D . R D F' U' R2 B2 U' B D2 B' F' L U'  (18)
D F2 R2 F2 R2 U F2 . R F2 R D2 U' F L' F' L D  (17)
B2 R2 F' U2 D2 L2 R2 B . U' L R B' F U D B2 F2 R' F2  (19)
D' L2 R2 D2 B2 F2 U' . R' B' F D' U L R' F2 D2 U2 F'  (18)
B2 F2 L2 R2 D2 U2  (6)

If you copy and paste the maneuvers from this message to a text file,
you can load them into Cube Explorer and directly watch the results.

The response to my Cube Explorer 1.0 program showed me, that the
userinterface and the terminology of the program are confusing (if not
to say bad) and some features are missing which should be there.
I almost completed Version 1.5 now. When I put it to my homepage in a
few days, I will send another message.

--Herbert