F2L Edge piece extraction

(Note) Edge means edge piece, and Corner means corner piece.

1. AUF before pairing up

1) Cross-color face of Corner and Edge are in line -> No AUF is needed.

2) Not in the above case 1), and Edge color and Corner color are same -> move Corner so that its Cross-color face looks at the right or left side.

3) Not in the above case 1), and Edge color and Corner color are different -> move Corner so that its Cross-color face looks at the front or back side.

4) In case Corner color is Cross color and Edge is not flipped -> move Corner in front or back of the slot where Edge is.

5) In case Corner color is Cross color and Edge is flipped -> move Corner above the slot where edge is.

2. Algorithm for pairing up

For above case 1):

A. Edge and Corner colors are same, and they are in a column-> R U’ R’ / R’ U R (L’ U L / L U’ L’)

B. Edge and Corner colors are same, and they are in a row -> F’ U’ F / f’ L’ f (F U F’ / f R f’)

C. Edge and Corner colors are different, and they are in a column-> R U R’ / R’ U’ R (L’ U’ L / L U L’)

D. Edge and Corner colors are different, and they are in a row -> F’ U F / f’ L f (F U’ F’ / f R’ f’)

For above case 2):

A. Edge and Corner are in a column -> R U’ R’ / R’ U R (L’ U L / L U’ L’) (same as case 1-A)

B. Edge and Corner are in a row -> F’ U2′ F / f’ L2′ f (F U2 F’ / f R2 f’)

C. Edge and Corner are in a diagonal -> F’ U’ F / f’ L’ f (F U F’ / f R f’) (same as case 1-B)

For above case 3):

A. Edge and Corner are in a column -> R U2′ R’ / R’ U2 R (L’ U2 L / L U2′ L’)

B. Edge and Corner are in a row -> F’ U F / f’ L f (F U’ F’ / f R’ f’) (same as case 1-D)

C. Edge and Corner are in a diagonal -> R U R’ / R’ U’ R (L’ U’ L / L U L’) (same as case 1-C)

For above case 4):

R’ F R F’ (Sledgehammer) / R B’ R’ B (Back Sledgehammer) (L F L’ F’ / L’ B L B’)

For above case 5):

R U’ R’ / R’ U R (L’ U L / L U’ L’) (same as case 1-A)

That’s all! As you can see, there are many cases, but some of them use the same algorithms, so actually it is not so complicated to memorize them.

Without the above case 4), all algorithms are of 3 moves.