PLL Edges Tutorial — Rubik's Cube (LBL)
Recap
PLL Corners is done — all four top corners are in place, the top face is all yellow. Now only the four top-edge positions remain. This is the final step of LBL — once done, the cube is solved.
Formulas used here: Ua-perm and Ub-perm (edge 3-cycles, inverses of each other). Advanced/optional: H-perm and Z-perm (M-slice formulas). All only move top edges — the bottom two layers stay intact. Notation: see Fundamentals.
Goal
Done = all four top edges in their correct positions, each edge's side sticker matching the adjacent center. This is the end of LBL — the entire cube is solved.
Tool: U-perm
The U-perm is a 3-cycle of edges: it holds one edge (UB) fixed and cycles the other three. It comes in two directions — Ua (UF→UR→UL) and Ub (UF→UL→UR), inverses of each other. Two formulas handle all edge-permutation cases.
Click the cube below to play: you'll see three outlined edges (UF/UR/UL) cycle, while UB has no outline — it stays still. First Ua (one direction), then Ub (the reverse) — one mechanism, two directions.
- The three outlined edges will be cycled by the U-perm. UB has no outline — it's the anchor, it stays.RU'RURURU'R'U'R2（Ua: 3-edge cycle）
- Ua done: three edges cycled forwardR2URUR'U'R'U'R'UR'（Ub: reverse cycle）
- Ua + Ub: both directions shown
Ua — R U' R U R U R U' R' U' R2 · Ub — R2 U R U R' U' R' U' R' U R'
Recognition
Anchor decision: look at the 4 top edges — is there one whose side sticker matches the adjacent center (= in place = anchor)?
Here are the two cases:
1 edge in place → U-turn it to UB → look at the UF edge's side sticker (it doesn't belong at UF — its side color reveals where it's going): matches R → belongs at UR → Ua (right); matches L → belongs at UL → Ub (left) → solved.
0 edges in place → do any Ua or Ub → an anchor always appears → U-turn it to UB → continue the anchor flow. At most 2×.
Theory: why two formulas are enough
Parity invariant: every face turn is a 4-cycle (4 edges + 4 corners move simultaneously) — an odd edge permutation + an odd corner permutation = an even overall permutation. So from solved, no matter what you do, the combined edge + corner permutation is always even. PLL corners are done (corners = even), so the edge permutation must also be even.
Even permutations have only two structures: a permutation's parity depends on swap count — 1 swap = odd, 2 swaps = even. A 3-cycle seems to move 3 edges, but cycling 3 pieces takes only 2 swaps (swap A↔B, then A↔C = one full rotation) → even. 8 total. A double-swap is two pairs swapping at once = 2 swaps → even. 3 total. A single swap (1 swap) and a 4-cycle (3 swaps) are both odd — physically impossible here.
Ua/Ub are 3-cycles → sufficient: a 3-cycle against a 3-cycle → 1 pass. A 3-cycle acting on a double-swap → the result is still a 3-cycle (an anchor appears) → one more pass → 2 total. Two structures, one tool (the 3-cycle), at most 2 passes.
| Permutation type | Anchors | U-perm count | States |
|---|---|---|---|
| 3-cycle | 1 | 1× | 8 |
| Double-swap | 0 | 2× | 3 |
| Total | ≤2× | 11 |
Advanced: H-perm & Z-perm
For no-anchor cases (double-swaps), instead of two U-perms you can use H-perm or Z-perm for a one-shot solve — M-slice formulas that only move the middle layer. Optional speed tools. To tell them apart: look at any edge's side sticker — wants to go opposite → H-perm, wants to go adjacent → Z-perm.
All 4 edges swap in opposite pairs — UF↔UB, UR↔UL (across) → H-perm solves in one step.
All 4 edges swap in adjacent pairs — UF↔UR, UB↔UL (next to each other) → Z-perm solves in one step.
Common Mistakes
This step only has two formulas (Ua/Ub) — problems usually come from direction recognition, anchor placement, and execution.
- Wrong direction: anchor is at UB, but UF wanted to go right and you did left (or vice versa) → not solved → do the other U-perm.
- Anchor not at UB: doing the formula with the anchor elsewhere → the 3-cycle fixes the wrong position → U-turn the anchor to UB first.
- 0-anchor confusion: just do any U-perm → an anchor appears → continue the 1-anchor flow. At most 2×.
- Layers scatter mid-formula: the first two layers break apart during the U-perm — don't panic, finishing the formula always restores them, only the top edges moved.
Done!
Congratulations! You can now solve a Rubik's Cube from scratch using LBL — Daisy → Cross → First Layer → Second Layer → Yellow Cross → Yellow Corners → Corner Permutation → Edge Permutation, 8 steps total. The cube is solved. Want to go faster? Next, learn the CFOP method — solve in four steps. Go practice these edge formulas until you don't need the tutorial.
Practice PLL Edges →