Cubeathon · Printable reference
PLL — all 21 cases
Permutation of the Last Layer · 21 of 21 cases · notation: cubeathon.com/notation
3×3 · CFOP · PLL · Intermediate · Algorithms
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PLL algorithms: all 21 cases.
PLL is the last step of the CFOP method. The top face is already one colour (that was OLL); PLL moves the last-layer pieces into their places without flipping any of them, and the cube is solved.
There are 21 cases. Every algorithm on this page is checked by Cubeathon's cube simulator: it leaves the first two layers and the top colour untouched, and each diagram is computed from the algorithm itself.
New to PLL? Start with 2-look PLL: six of these algorithms solve every case in two steps. Then add the rest a few at a time, beginning with the cases that come up most in your solves.
Notation: how to read R, U, F, M, x… · Just starting? Learn 2-look OLL and PLL first
The complete set: all 21 PLL cases.
- 3×3
- CFOP
- PLL
- Intermediate
- Recognition
Press Play on any case to watch it solved on a 3D cube.
Play it on the cube
No case selected
Yellow on top, green in front: the case is set up first, then the algorithm plays one move at a time. Drag the cube to look around it.
See it. Name it. Recall it.
21 cases, shuffled. Recognise each one from the diagram, say the algorithm, then check yourself. Misses come back until you have them.
Recognising the cases
Look at the side stickers of the top layer. Two matching corner stickers on one side are called headlights; three matching stickers are a solid bar; two matching neighbours are a block.
Count the headlights first. Headlights on all four sides means only edges move (Ua, Ub, H, Z). Headlights on exactly one side points to T, Ja, Jb, Ra, Rb, the A perms or the G perms. No headlights anywhere means the corners swap diagonally (V, Y, Na, Nb) or it's the E perm.
Each case below says how to recognise it and how to hold it. The diagram shows the exact starting position for the algorithm next to it. Sides are described as you face them.
The corners are already in place; three or four edges move.
Ua Permutation
Three edges cycle anticlockwise (seen from above)
Spot it: A solid bar on one side, headlights on the other three.
Hold it: Bar at the back. The front edge belongs on the right.
R U' R U R U R U' R' U' R2Ub Permutation
Three edges cycle clockwise (seen from above)
Spot it: A solid bar on one side, headlights on the other three.
Hold it: Bar at the back. The front edge belongs on the left.
R2 U R U R' U' R' U' R' U R'H Permutation
Opposite edges swap in two pairs
Spot it: Headlights on all four sides; each side's middle sticker matches the opposite side.
Hold it: Any angle.
M2 U M2 U2 M2 U M2Z Permutation
Neighbouring edges swap in two pairs
Spot it: Headlights on all four sides; each side's middle sticker matches a neighbouring side.
Hold it: The front edge belongs on the left (front and left swap, back and right swap).
M2 U M2 U M' U2 M2 U2 M'
The edges are already in place; the corners move.
Aa Permutation
Three corners cycle; the edges are already solved
Spot it: Headlights on one side and a solved 2×2 block in a corner.
Hold it: Headlights at the back, solved block at the front left.
x R' U R' D2 R U' R' D2 R2 x'Ab Permutation
Three corners cycle the other way; the edges are already solved
Spot it: Headlights on one side and a solved 2×2 block in a corner.
Hold it: Headlights on the right, solved block at the front left.
x R2 D2 R U R' D2 R U' R x'E Permutation
Corners swap in two pairs; the edges are already solved
Spot it: No headlights and no blocks anywhere, yet every edge matches its centre.
Hold it: The front corners show the colours of the left and right sides.
x' R U' R' D R U R' D' R U R' D R U' R' D' x
Two neighbouring corners swap, along with two edges.
T Permutation
Two neighbouring corners and two opposite edges swap
Spot it: Headlights on one side, and a block of two on each of the sides next to it.
Hold it: Headlights on the left.
R U R' U' R' F R2 U' R' U' R U R' F'F Permutation
Two neighbouring corners and two opposite edges swap
Spot it: A solid bar on one side; nothing else matches.
Hold it: Bar on the left.
R' U' F' R U R' U' R' F R2 U' R' U' R U R' U RJa Permutation
Two neighbouring corners and two neighbouring edges swap
Spot it: A solid bar on one side; each other side shows a block of two on its left half.
Hold it: Bar on the left.
x R2 F R F' R U2 r' U r U2 x'Jb Permutation
Two neighbouring corners and two neighbouring edges swap
Spot it: A solid bar on one side; each other side shows a block of two on its right half.
Hold it: Bar at the back.
R U R' F' R U R' U' R' F R2 U' R'Ra Permutation
Two neighbouring corners and two neighbouring edges swap
Spot it: Headlights on one side; a block of two on one of the sides next to it.
Hold it: Headlights on the left, a block on the left half of the front.
R U' R' U' R U R D R' U' R D' R' U2 R'Rb Permutation
Two neighbouring corners and two neighbouring edges swap
Spot it: Headlights on one side; a block of two on one of the sides next to it.
Hold it: Headlights on the left, a block on the right half of the back.
R2 F R U R U' R' F' R U2 R' U2 R
Two opposite corners swap, along with two edges.
V Permutation
Two opposite corners and two neighbouring edges swap
Spot it: No headlights; a solved 2×2 block in one corner.
Hold it: Solved block at the back left.
R' U R' U' y R' F' R2 U' R' U R' F R FY Permutation
Two opposite corners and two neighbouring edges swap
Spot it: No headlights; two separate blocks of two on neighbouring sides.
Hold it: Blocks on the left half of the front and the right half of the right side.
F R U' R' U' R U R' F' R U R' U' R' F R F'Na Permutation
Two opposite corners and two opposite edges swap
Spot it: Every side shows a block of two on its right half.
Hold it: The front and back edges already match their centres.
R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'Nb Permutation
Two opposite corners and two opposite edges swap
Spot it: Every side shows a block of two on its left half.
Hold it: The front and back edges already match their centres.
R' U R U' R' F' U' F R U R' F R' F' R U' R
Three corners and three edges cycle at the same time.
Ga Permutation
Three corners and three edges cycle
Spot it: Headlights on one side and a single block of two elsewhere.
Hold it: Headlights on the left, a block on the right half of the front.
R2 U R' U R' U' R U' R2 U' D R' U R D'Gb Permutation
Three corners and three edges cycle
Spot it: Headlights on one side and a single block of two elsewhere.
Hold it: Headlights on the left, a block on the right half of the right side.
R' U' R U D' R2 U R' U R U' R U' R2 DGc Permutation
Three corners and three edges cycle
Spot it: Headlights on one side and a single block of two elsewhere.
Hold it: Headlights on the left, a block on the left half of the back.
R2 U' R U' R U R' U R2 U D' R U' R' DGd Permutation
Three corners and three edges cycle
Spot it: Headlights on one side and a single block of two elsewhere.
Hold it: Headlights on the left, a block on the left half of the right side.
R U R' U' D R2 U' R U' R' U R' U R2 D'
How to practice PLL
Learn a case by watching it on the cube, then set it up yourself: run the algorithm backwards (reverse the order, invert each move) and solve it. Repeat until you no longer look at the notation.
Drill recognition separately from execution: the drill shows a random case and asks you to name it. Then time full 3×3 solves: every solve ends in a PLL, so each one is a free recognition test.