[next] [prev] [up] Date: Mon, 17 Aug 81 11:34:00 -0400 (EDT)
[next] [prev] [up] From: Allan C. Wechsler <ACW@MIT-AI >
~~~ ~~~ [up] Subject: 12q relations.
I12-1	FR' F'R   UF' U'F    RU' R'U
I12-2	FR' F'R   UF' F'L    FL' U'F
I12-3	FR' F'R   UF' UL'    U'L FU'

I can't believe I'm the first person to notice this:

Suppose we only know I12-1 and I12-2.  Then we have

I12-1'			U'RUR'F'U (FR'F'RUF')'
(I12-1')(I12-2)		U'RUR'F'U (FR'F'RUF')' (FR'F'RUF') F'LFL'U'F
Reduce:			U'RUR'F'U F'LFL'U'F
Conjugating by (U'RUR'F'U)', we get 
			F'LFL' U'FU'R UR'F'U
But this is just the RL mirror image of
			FR'F'L UF'UL' U'LFU'

This is exactly I12-3. So there are really only two independent 12q
identities, and the third can be deduced from them.


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