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Date: Wed, 8 Dec 1993 23:39:35 EST
From: "Jerry Bryan"
To: "Cube Lovers List"
Subject: That's all the 48-Fold Symmetries
The two patterns I just posted are the only two for which the size
of the equivalence class is 48. The next size up is 72, and there
are twelve patterns whose equivalence class size is 72. Things
become less interesting as the equivalence class size increases because
they are less symmetrical overall. Also, there are more patterns.
Finally, these things take a good deal of time to chase down.
Therefore, I am going to stop chasing down "pretty patterns"
for now unless somebody is just dying to see the patterns whose
equivalence class size is 72.
Finally, nobody really answered an earlier question, but is the
following true: 1) Mirror-Image-of-Start is 12 q-turns from
Start, and a sequence is known (Dan Hoey sent me a well-known
sequence), 2) All-Edges-Flipped is 9 q-turns from Start, and a
sequence is known, and 3) Mirror-Image-of-Start-and-All-Edges-Flipped
(the antipodal of Start) is 15 q-turns from Start, and a sequence
is *not* known? If this is true, then I will start working on
the 15 move sequence.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) (304) 293-5192
Associate Director, WVNET (304) 293-5540 fax
837 Chestnut Ridge Road BRYAN@WVNVM
Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU
If you don't have time to do it right today, what makes you think you are
going to have time to do it over again tomorrow?