> there was never any response to this, but i'll give my solution
I am working on an engine to search optimal paths for < U, F, R > but
it's not done yet. It's certainly within the bounds of computibility:
Size (u_f_r) = 170,659,735,142,400 (hmmm, 170 trillion maybe not!)
let X = U2 F R' F2 R F2 R F2 R' F U2 .
then X produces two two-cycles of corner-edge pairs. the commutator
[ X , C_UFR ] produces "cube in a cube" in 22 face / 32 quarter turns
and only turns the faces U, F and R.
the notation C_UFR refers to a rotation of the whole cube, and
[ a, b ] denotes the commutator a b a^-1 b^-1 .
Although harder to remember, X + ( X * C_UFR) will do.
U2 F1 R3 F2 R1 F2 R1 F2 R3 F1 U2 F2 R1 U3 R2 U1 R2 U1 R2 U3 R1 F2 (22 f, 32 q)
-> Mark <-