Rubik's Cube techniques

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Any two corners A and B can be twisted in opposite directions using a commutator. The basic strategy is as follows:

1. Use any sequence X to twist corner A in place, without regard for any destruction it does to the rest of the cube.
2. Use sequence Y to move cornerB to take the place of corner A.
3. Apply X^-1. This will twist corner B in the reverse direction to A.
4. Apply Y^-1. This will move corners B and A back to their original positions.

Note that it is impossible to twist two corners (and only two corners) in the same direction as this violates the laws of the cube.

Below are some examples of corner twists:

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