Permutation of the Last Layer

These are the 21 permutation cases for the last layer and the algorithms I use for them. These algorithms appear EXACTLY as I perform them when I am solving the last layer, in speedcubing notation with rotations included in the algorithm. It should be noted that these are the algorithms that I find easiest to perform. However, you may find other algorithms better-suited for your own hands, so it is recommended to try many different algorithms for the same situation to find which one works best for your own style of cubing.

In each diagram, the edges that are being swapped or moved are denoted by the red arrows, while the corners that are being swapped are moved are shown with blue arrows.

If you'd like to know how I recognize PLLs, check out my PLL Recognition page. For a printable page of these algorithms, visit my printable page. Please note that you will need Adobe Reader to access and print the printable page.

Corners Only

Name Diagram Algorithm Comments
Aa x (R' U R') D2 (R U' R') D2 R2 This is a basic corner 3-cycle. It is one of my favorite and fastest algorithms. Perform the D2s with the left hand and everything else with the right.
Ab x R2 D2 (R U R') D2 (R U' R)
[y'] x (L U' L) D2 (L' U L) D2 L2
This is just the inverse of the other A perm.  It is performed in a very similar manner.
E x' (R U') (R' D) (R U R' D') (R U R' D) (R U') (R' D') This alg is just two orientations performed consecutively.

Edges Only

Name Diagram Algorithm Comments
Ua (R U' R U) (R U) (R U') (R' U' R2)
[y2] (R2 U' (R' U' R U) (R U) (R U' R)
This is just a simple 3-edge cycle. It is almost as fast as the corner cycles. I solve this case with the bar at the front or the back.
Ub (R2 U) (R U R' U') (R' U') (R' U R')
[y2] (R' U R' U') (R' U') (R' U) (R U R2)
This is the inverse of the other U perm. I place my hands slightly differently for this algorithm. I solve this case with the bar at the front or the back.
H (M2' U) (M2' U2) (M2' U) M2' This is extremely easy to recognize and can be performed VERY quickly. The M'2 is actually performed as (M'M') with rapid pushing at the back face of the M layer with the ring and then middle fingers.
Z (M2' U) (M2' U) (M' U2) (M2' U2) (M' U2) The Z permutation is performed very similarly to the H perm. The last U2 is not necessary if you account for it before the algorithm.

Swapping Two Adjacent Corners & Two Edges

Name Diagram Algorithm Comments
Ja (R' U L') U2 (R U' R') U2 (L R U') I perform the R of the [R L] a split second after I start the L so that I can immediately perform the U' to AUF when the L face has been moved to where it belongs.
Jb (R U R' F') (R U R' U') (R' F) (R2 U') (R' U') This is the same as the T perm with the last four moves instead performed at the beginning.
T (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F') This is the T permuation. It is long but definitely very fast and easy. It can be performed in almost one swift motion without any readjusting of the fingers. Note that it is a combination of two easy orientations.
Rb (R' U2) (R U2) (R' F R U R' U') (R' F' R2 U') This is a pretty straightforward alg that flows pretty nicely.
Ra R U R' F' R U2 R' U2 R' F R U R U2 R' U' You could also just mirror Rb, but this alg is more right hand friendly. Notice the similarity with the Jb permutation.
F R' U' F' (R U R' U') (R' F) (R2 U') (R' U' R U) (R' U R) This is a T permutation with a 3 move setup in the beginning and a cancellation of one of those moves at the end.

Cycling Three Corners & Three Edges

Name Diagram Algorithm Comments
Ga (R2' Uw) (R' U R' U' R Uw') R2' y' (R' U R) This alg has a pretty decent flow to it and can be performed almost in one motion until the rotation.
Gb (R' U' R) y (R2' Uw R' U) (R U' R Uw' R2') This is the inverse of Ga. Note how similar they look. I perform this one almost exactly the same way.
Gc (R2' Uw' R U') (R U R' Uw R2) (Fw R' Fw') You could rotate and insert the pair instead of performing the last three moves as shown.
Gd (R U R') y' (R2' Uw' R U') (R' U R' Uw R2) This is just the inverse of Gc. I execute it very similarly because most of the moves overlap in the same manner.

Permutations Of Two Diagonal Corners & Two Edges

Name Diagram Algorithm Comments
V (R' U R' Dw') (R' F' R2 U') (R' U R' F) (R F) This is one of my least favorite permutations because the flow just isn't there.
Na (z) D (R' U) (R2 D' R D U') (R' U) (R2 D' R U' R) This alg could also be performed using <R,U,L> if you don't do the rotation, but this way is faster with practice.
Nb (z) U' (R D') (R2' U R' D U') (R D') (R2' U R' D R') This is just the mirror of the other N permutation.
Y (F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F') This is very quick and can be performed without any adjustments of where the fingers are. It is just a combination of two quick orientations.