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> there was never any response to this, but i'll give my solution

anyway.

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 .mike

Brilliant.

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 <-