PLL Corners Tutorial — Rubik's Cube (LBL)
Recap
OLL is done — the entire top face is yellow (all orientations correct). But the four top corners may still be in the wrong positions: the colors face up correctly, but the pieces are shuffled. This step only fixes positions — orientations are already set.
Formulas used here: Aa-perm (corner permutation, 3-cycle) and E-perm (double-swap, advanced/optional). Both only move top corners — the bottom two layers stay intact. Notation: see Fundamentals.
Goal
Done = all four top corners in their correct positions, each corner's three colors matching the adjacent centers. Note: top edges are not yet placed (greyed out) — that's the next step (PLL Edges). This step only does corners.
Tool: Aa-perm
The Aa-perm is a 3-cycle: it holds one corner (ULF) fixed and rotates the other three. It is the only formula this step needs — the bar decision tells you when and where to use it.
Click the cube below to play Aa: you'll see the outlined ULF corner stay put while the three hatched corners cycle home. That's the entire mechanism — one formula for all corner-permutation cases.
- Bar at back: the outlined ULF is the anchor; the three hatched corners are about to be cycled home by Aa.R'FR'B2RF'R'B2R2（Execute Aa）
- Aa complete: 3-cycle solved
Aa-perm — R' F R' B2 R F' R' B2 R2
Method
Bar decision: check the four side faces (F/R/B/L) — is there a face where the two top-corner stickers match? That's a bar.
The two cases:
One side face has two matching top-corner stickers → U the bar to B + apply Aa → usually done.
No matching face → just apply Aa → a bar appears → follow the bar flow.
Why does Aa alone suffice?
bar at back → Aa → solved: Aa holds the ULF anchor fixed and 3-cycles the other three. Bar at back means those three cycling corners are arranged so Aa puts each one home in one step.
No bar → Aa → bar always appears: no-bar states are double-transpositions (two diagonal pairs swapped). Aa is a 3-cycle — applying a 3-cycle to a double-transposition always produces a bar state. This is a mathematical property of permutations, not luck.
At most two: worst case (no bar) = Aa creates a bar → AUF to B → another Aa finishes = two Aa's. No Ab needed, no direction recognition needed.
| Type | States | Share | Solution |
|---|---|---|---|
| Done (AUF-solvable) | 4 | 16.7% | Final AUF |
| Has bar | 16 | 66.7% | AUF to B + 1× Aa |
| No bar | 4 | 16.7% | 2× Aa or 1× E-perm |
| Total | 24 | 100% |
Advanced: E-perm
For the no-bar case (all four faces mismatch), instead of two Aa's you can use a single E-perm. Click the cube below to play E-perm: you'll see all four hatched corners move (no anchor) — two diagonal pairs swap at once, one formula solves the double-swap.
- No-bar state: no two matching top corners on any facex'RU'R'DRUR'D'RUR'DRU'R'D'x（Execute E-perm）
- E-perm complete: double-swap solved
E-perm — x' R U' R' D R U R' D' R U R' D R U' R' D' x
Common Mistakes
This step is simple — one formula (Aa) handles every case. Problems usually arise in recognition and the final alignment.
- Doing Aa before the bar reaches B — the anchor isn't aligned. Get the bar to B first.
- Forgetting the final U — corners are right but the whole layer is rotated one notch, looking unsolved.
- The first two layers scatter mid-Aa — don't panic, the full formula always restores them; only top corners change position.
- E-perm has x/x' rotations and scatters more — still restores at the end.
Practice, then the last step
Drill the flow: scramble → cross → first layer → second layer → top face (OLL) → corner permutation, until the bar decision is automatic; add E-perm later for speed. Then move to the final step — top edge permutation (PLL Edges) to solve the cube.
Practice corner permutation