## Recognizing the PLLs

These are the 21 permutation cases for the last layer and how I recognize them. In general, if you have any blocks, you can easily recognize the case by aligning the blocks with the faces they match. If you do not have any blocks, you either have an E permutation (easily recognized by the corners not being solved) or an EPLL (edge permutation), which can easily be distinguished.

### Corners Only

In the A permutations, I first AUF (adjust the U-face) until the "corner block" is permuted. By corner block, I mean that there is a corner and the two edges adjacent to it belong adjacent to it. Since this is very similar to the V permutation, I check to see that the two stickers next to the corner block are not opposite (if they are, then this is the V permutation).

Name | Diagram | Angle1 | Angle2 | Angle3 | Angle4 | Comments |

Aa | Look for the corner block. With the corner block at the front-left, the right most sticker will be opposite the other two in the front. The stickers on the left face are not opposite. | |||||

Ab | Look for the corner block. With the corner block at the front-left, the right most sticker will be not opposite the other two in the front. Instead, the opposite stickers are on the left face. | |||||

E | Other than the cases with all corners solved, this is the only case in which there are no blocks. Therefore, it is pretty easy to recognize. |

### Edges Only

In each of these cases, all of the corners are solved.

Name | Diagram | Angle1 | Angle2 | Angle3 | Angle4 | Comments |

Ua | When the solved face is in the back, the opposite colors are on the right side. When the solved face is in the front, the opposite colors are on the left side. | |||||

Ub | When the solved face is in the back, the opposite colors are on the left side. When the solved face is in the front, the opposite colors are on the right side. | |||||

H | All of the corners are solved and there are no solved faces, and the edges that need to be swapped are opposite colors. | |||||

Z | All of the corners are solved and there are no solved faces, but the edges that need to be swapped are not opposite colors. |

### Swapping Two Adjacent Corners & Two Edges

In these cases, you could have a solved block of 2, 3, or 4 pieces.

Name | Diagram | Angle1 | Angle2 | Angle3 | Angle4 | Comments |

Ja | In this J permutation, a face is
complete solved and the solved portion wraps around to the right side
of the cube. Thus, the left two stickers on that face match. |
|||||

Jb | In this J permutation, a face is complete solved and if you look to the right of that face, the two right stickers on that face match. | |||||

T | This is the only case with blocks on opposite sides. The edge sticker on the left face is opposite to the corners. I typically recognize this case by looking at any of those three sides. | |||||

Rb | There is a solved block and when you AUF, the corner opposite that block is also solved. If you look at the solved corners, the block is on the left. | |||||

Ra | There is a solved block and when you AUF, the corner opposite that block is also solved. If you look at the solved corners, the block is on the right. | |||||

F | This case has a solved face but no other blocks. |

### Cycling Three Corners & Three Edges

Though these look the trickiest to recognize, they are actually quite simple. I first AUF to solve the 1x1x2 block. Then, I rotate the cube such that the two corners that share the same color on the same face are on the left side. Then, based on whether the block is at the back, front, far part of the right, or close part of the right, I know whether to apply Gc, Ga, Gb, or Gd, respectively.

Name | Diagram | Angle1 | Angle2 | Angle3 | Angle4 | Comments |

Ga | The two corners with the same color are on the left face but the block is on the front face. | |||||

Gb | The two corners with the same color are on the left face but the block is on the back part of the right face. | |||||

Gc | The two corners with the same color are on the left face but the block is on the back face. | |||||

Gd | The two corners with the same color are on the left face but the block is on the front part of the right face. |

### Permutations Of Two Diagonal Corners & Two Edges

In each of these cases, two diagonal corners need to swap.

Name | Diagram | Angle1 | Angle2 | Angle3 | Angle4 | Comments |

V | This looks like an A permutation except the stickers adjacent to the corner block are opposite colors on both faces instead of just one. | |||||

Na | Every face looks the same. On each face, the two right stickers are the same color and the left sticker is opposite that color. | |||||

Nb | Every face looks the same. On each face, the two left stickers are the same color and the right sticker is opposite that color. | |||||

Y | There are two blocks in this case and they are on adjacent faces. The corner that is adjacent to each of these blocks is opposite the color of these blocks. |