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If you have a Rubik's cube where all the edges flip on each

quarter-turn, you can solve it by using bifocals when it's odd.

I noticed this while drawing a Hasse diagram of the subgroups of M. It

turns out that M has a similar automorphism, where the odd elements are

reflected through the center of the cube.

If anyone wants the Hasse diagram, I can send it--it takes about 30

minutes to draw in the lines, for which directions are included.

If you know whether there are other outer automorphisms of M, please

let me know.

Dan