Date: 22 Aug 1984 18:06-EDT From: Dan Hoey Subject: An outer automorphism of the cube group To: cube-lovers at mit-mc 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