Date: 17 August 1981 11:34-EDT
From: Allan C. Wechsler <ACW at MIT-AI>
Subject:  12q relations.
To: CUBE-LOVERS at MIT-AI


    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.