Hmmmm, a little inconsistent (sp?) with the notation there.
I usually only use U when quoting the processes of others.
I'm going to try tackling the 1152-fold symmetry idea
When looking for CD-type processes I find it helps to think
in terms of distinct states you pass through in approaching
the goal state. Sort of like factoring a composite pattern
into simpler ones you add together.
Rotating the cube in space definitely helps too.