You don't nood commutators for it, cycles are sufficient (because there
are so many similar colored beads). If I remember right one useful move
is: turn right ring clockwise two beads, turn left clockwise two beads,
turn right anti-clockwise two beads, turn left anti-clockwise two beads.
Using them properly will solve the rings.

dik
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland
dik@cwi.nl