#cube
Commutator and Conjugates.
Not to confuse anyone, both are the same thing. If you turn a piece a little bit before applying a commutator than it's called conjugate. Or whatever. Who cares?
|| When needed?
At last stage when you might want to fix the last 5 corners or edges.
|| How much does it help?
You can move a single piece to its desired location.
|| Won't it destroy the rest?
No. But you have to sacrifice another piece you select from a different layer. So basically you are moving three pieces. The one you want to bring to location that's two pieces. And a 3rd piece, a helper.
|| How does it work?
Turn 1:
Turn any layer of the cube to see if a piece finds it's perfect location. Even if that means the rest of the pieces are getting replaced. Count this as bottom layer.
Turn 2:
Now make a perpendicular turn to take this piece to the top layer.
Turn 3:
Next turn the top layer to place any other piece from the top layer into its location.
Turn 4:
Now undo the parallel turn (turn 2) to restore the bottom layer.
Turn 5:
Undo turn 1 to fully restore the bottom layer.
Turn 6:
This one is interesting. Make the parallel turn again on the restored bottom. Turn 2 from above.
Turn 7:
Undo turn 3 so that our piece returns to it's location.
Turn 8:
Undo turn 6. The parallel turn.
Done.
Example :
B' R T R'
B R T' R'
There's more to it like making sure all three pieces are perfectly aligned when turning is finished, but that will lead to too much searching. Just make sure you are placing one piece in it's correct location and the 3rd piece is a dirty piece -- and that should do it.