R
Right face, clockwise (looking at it)
A guide for someone who already solves the cube but feels the ceiling of the layer-by-layer beginner method. We rebuild the mental model from first principles — permutation, orientation, conjugates, commutators — then ramp deliberately into CFOP, last-layer training, and the soft-skills that actually buy you seconds: lookahead, finger tricks, and color neutrality.
A 3×3 cube has 26 visible pieces, not 27. The exact center is a hollow internal mechanism that nothing on the surface ever touches. The 26 visible pieces fall into three classes that behave fundamentally differently.
Centers (6). One per face. They have a single sticker. They never move relative to each other — what looks like a center "moving" is the whole cube being reoriented in your hands. This is the most underused fact in the beginner's mental model: the centers define the cube. White is wherever the white center is. Period.
Edges (12). Two stickers each. They live between two adjacent faces. The white-blue edge is always the white-blue edge — it can be in any of 12 positions and either of 2 orientations, but it can never become the white-red edge.
Corners (8). Three stickers each. They live at the meeting point of three faces. Same conservation: a corner's three colors are intrinsic to the piece, only its position and rotation change.
Once this lands, two ideas follow naturally. First, a "move" doesn't shuffle 9 random stickers — it cycles 4 edges, 4 corners, and rotates them deterministically. Second, every solving method in existence is a sequence of edge-and-corner manipulations whose stickers happen to look like a solve at the end.
| Class | Count | Stickers | States |
|---|---|---|---|
| Centers | 6 | 1 | Fixed (1 each) |
| Edges | 12 | 2 | 12 pos × 2 orient |
| Corners | 8 | 3 | 8 pos × 3 orient |
Total reachable positions: 8! · 3⁷ · 12! · 2¹¹ / 2 ≈ 4.33 × 10¹⁹. The factor of 2 in the denominator excludes parity-impossible states; the exponents 3⁷ and 2¹¹ (not 3⁸, 2¹²) reflect that the last corner's twist and last edge's flip are determined by all the others.
Which slot a piece is in. There are 8! corner permutations and 12! edge permutations on the table; the cube reaches half of those.
How the piece is rotated within its slot. Corners have 3 orientations (twist), edges have 2 (flip).
Every face turn swaps an odd number of corner pairs and an odd number of edge pairs simultaneously. So edge and corner swap-parity are always linked. This is why some "swap two pieces" cases require parity-breaking algorithms.
Cube notation is the universal API. Every algorithm in every method is written in it. Six letters name the six faces; a prime mark inverts a turn; a 2 means a half-turn. Once it's reflexive, you read algorithms the way you read sheet music.
Every face turn is "clockwise looking at that face" — so D looks counter-clockwise when you hold the cube normally, because you're looking at it from the wrong side. This trips everyone up exactly once.
The "sexy move" — R U R' U' — is the most-used 4-move sequence in cubing. It's also a perfect commutator. Run it six times in a row: the cube returns to solved. That's a small clue about the structure underneath.
Beginners memorize algorithms as sacred strings of letters. That works to about 30 seconds and breaks down. To get faster you need to recognize the structure of each algorithm, because then you stop memorizing 21 PLLs and start memorizing perhaps 7 setups.
A conjugate is a setup move, a worker move, and the inverse of the setup. Written: A · B · A′. Read: "set up the cube into a position where B does the right thing, run B, undo the setup."
Most last-layer algorithms have at least one conjugate buried inside them. Once you can spot them, you stop being surprised by the alg.
A commutator is A · B · A′ · B′ — written [A, B]. The "sexy move" R U R' U' is exactly [R, U]. Commutators have a beautiful property: if A and B only overlap on a small region, the commutator changes only that region and leaves the rest of the cube untouched.
This is the secret of every "3-cycle" algorithm. They cycle 3 pieces and leave 23 pieces alone. Pure commutators are how blindfold solvers do everything.
R U R' U' R' F R2 U' R' U' R U R' F'
A T-perm is two recognizable pieces sewn together: a sexy at the start and an F R conjugate frame at the end. Once you see it that way, you can execute it without "remembering" any individual letter.
Run R U R' U' once: the cube looks scrambled in two pieces.
Run it twice: still messy.
Run it three times: it actually does something nameable — a 3-cycle.
Six times total: back to solved. The order of [R, U] in the cube group is exactly 6.
When you understand structure, three things change. You memorize new algs faster (you're seeing patterns, not letters). You execute more smoothly because your fingers chunk on natural breakpoints. And when you misexecute, you can recover rather than scramble — because you know what the algorithm was trying to do.
The beginner method ("LBL") solves the cube top to bottom: white cross, white corners, middle layer edges, yellow cross, yellow corners (orient + permute). It is correct, complete, and structurally bad for speed.
It is bad for two reasons. First, you do work and then partially undo it: the white corner step and the middle-layer edge step both temporarily disturb the cross. Second, each phase is small — small phases mean lots of pauses between phases, and pauses are where time vanishes.
CFOP — Cross, F2L, OLL, PLL — fixes both. You build a cross on the bottom (8 moves max, ideally planned during the 15-second inspection). Then you insert four corner-edge pairs at once — that's F2L, "First Two Layers." When that finishes, the entire bottom two layers are solved and only the last layer remains. OLL orients the last layer (every yellow sticker on top), PLL permutes it (every piece in its right place). Done.
Find all four cross edges before you touch the cube. With 15 seconds of inspection, an experienced cuber plans the cross + first F2L pair. World-class plan all four pairs.
For each F2L slot: find the corner and its edge in the top layer, "pair" them so the corner and edge are joined correctly, then insert into the slot. 41 cases formally, but most are derivable.
Make the entire top face yellow. Full OLL is 57 cases. 2-look OLL is 10 cases (3 edge + 7 corner) — your bridge.
Move every top-layer piece into its solved slot. Full PLL is 21 cases. 2-look PLL is 6 cases — finish the cube without learning all 21 first.
A scrambled cube can always have its cross solved in 8 moves or fewer. Average optimum is around 5.8. Most beginners use 12–18. That gap — 6 to 12 wasted moves on every solve — is the single biggest unforced loss in the beginner-to-intermediate transition.
Solve the cross on the bottom, not the top. Beginners build the cross on top and rotate the cube before continuing. That rotation costs time and breaks lookahead. With cross-on-bottom, the moment your cross finishes you can already see the F2L pieces in the U layer.
Plan in inspection. Competition gives you 15 seconds to inspect the cube before the timer starts. Use them. Find your cross color, then trace each of the four cross edges: where it is, where it needs to go, and how to get it there. With practice, 15 seconds is enough to plan the cross and one F2L pair.
Color neutrality. The hardest cross out of a given scramble might be on white; the easiest might be on green. If you only solve white, you take whatever cross you get. Color neutral cubers (CN) inspect all six possible crosses and pick the cheapest — typically saving 1–2 seconds per solve, with much better F2L lookahead. Worth the months of retraining if you're committed to sub-15.
| Level | Cross moves | Cross time |
|---|---|---|
| Beginner LBL | 14–20 | 5–9s |
| CFOP, sub-30 | 9–12 | 3–5s |
| CFOP, sub-20 | 7–9 | 2–3s |
| CFOP, sub-15 | 6–8 | 1.5–2.5s |
| World class | 5–7 | under 1.5s |
Generate a scramble. Inspect without time pressure until you can verbally narrate the entire cross solution before touching the cube. Execute. Repeat for an hour. Do this three sessions across a week. Your average cross drops by a third.
F2L solves the four corner-edge "slots" of the bottom two layers. Each slot needs its corner piece and its matching edge piece. Beginner method puts them in separately. F2L joins them in the top layer first — into a "pair" — and then drops the joined pair into the slot in one move sequence.
There are 41 formal F2L cases. You do not need to memorize 41 cases. You need to internalize three things:
The first half of intuitive F2L is recognizing the case. The second half is executing 4–8 moves with no thought. With a few weeks of practice you'll see any F2L case as one of a handful of subgoals.
Empty-slot rule. Always insert a pair into an empty slot. If a slot has a wrong piece in it, your first F2L move pulls that piece out. Never solve into an occupied slot — you'll trap yourself.
Lookahead. While your hands execute the current pair, your eyes find the next pair. This is the hardest single skill in CFOP and the largest single source of speed beyond sub-20. Drill it by deliberately slowing your hands while keeping your eyes ahead.
Almost every F2L solution boils down to one of these four insertions of an already-paired corner+edge:
U R U' R' — pair on right, insert right
U' L' U L — pair on left, insert left
U' F' U F — pair on front, insert front
U R U R' — pair "split", rejoin then insert
All four are conjugates of R U R' with a setup. Same shape, different angle.
OLL turns the entire top face one solid color (yellow, by convention). Full OLL is 57 algorithms. You don't learn them first. You learn 2-look OLL: ten algorithms split into two phases. First, orient the four edges. Then, orient the four corners. Two algorithm executions instead of one — costs you maybe 1.5 seconds, saves you months of memorization.
Below: all 10 algorithms for 2-look OLL, with diagrams. Yellow squares mean the sticker is already pointing up; gray squares mean the sticker is pointing sideways and needs to be rotated up.
Three cases. Look at only the four edge-stickers on the top face. Solved is when all four point up.
Seven cases. After step 1, the four edge-stickers are yellow. Now look at the corners.
Beyond 2-look: full OLL learns all 57 cases as a single algorithm. The recognition is harder, but you save the U-layer rotation between steps and the look. Average savings of 1.0–1.5 seconds per solve. Most cubers learn full OLL in pieces over months — the cross + dot + bar shapes first, then the P / W / Z shapes, etc. Use a tool like algdb.net to pick algorithms whose fingertricks you actually like; speed-friendly > theoretical-shortest.
After OLL, every yellow sticker is on top, but the side stickers can still be wrong. PLL fixes that. Full PLL is 21 algorithms. 2-look PLL splits it: first permute the corners (2 cases), then permute the edges (4 cases). Six total — entirely learnable in a weekend.
Two cases. Look at the corners only. Either two adjacent corners need swapping, or two diagonal corners do. Identical alg, used at different angles.
Four cases. Corners are now correct. The four edges either form a 3-cycle (U-perm, two flavors), an opposite-edge swap (Z-perm), or a double-opposite swap (H-perm).
All 21 cases. Group A = "corners only" (E only — the other corner-only perms are handled inside the EPLL+CPLL set above). The rest mix corner and edge permutation in one alg. Recognition is by the side-sticker pattern — match colored bars on the front-side stickers, then identify the case.
Recognition tip for full PLL: at the end of OLL, before any U-rotation, look at the front face's three stickers. The pattern (e.g., blue blue blue = solid bar; blue red blue = "headlights"; red blue red = "headlights" too, on a different perm) often pins down the case from one face. Then peek at the right face for confirmation. Two-face recognition is what world-class cubers do; it's faster than rotating the cube to see all four sides.
By the time you've drilled CFOP, your average is somewhere around 18–22 seconds. The rest of the path to sub-15 isn't more algorithms — it's execution, perception, and hardware. These are the levers, ranked by cost-effectiveness.
The single biggest factor between sub-20 and sub-15. Goal: zero pauses between F2L pairs. Your eyes are reading the next pair while your fingers finish the current one. Drill: solve at half-speed with your eyes locked on the U layer except during inspection. It feels slower; your average drops.
Fast cubers turn faces with single fingers, not whole hands. R U R' U' is one wrist motion plus four index/thumb flicks, not four discrete grabs. Standard fingertricks: R with right index push, R' with right index pull, U with left index push from underneath, U' with right thumb push, F with right hand grip-and-flick. Watch slow-motion solves on YouTube — the hand barely moves.
Sub-15 means roughly 4 TPS sustained, with bursts of 6+. Chase this through algorithm-only drills: pick one PLL, run it on a solved cube 50 times back-to-back, time only the execution. Then optimize finger choreography on the moves that feel slow.
A good speedcube genuinely makes you faster — magnets snap each turn into alignment, eliminating "lockups," and modern cubes are factory-tuned. Names worth searching: GAN, MoYu, QiYi. Budget under $20, mid $30–60, flagship $80+. The flagship-vs-mid difference is real but small. Lubricants like Traxxas 50k for the core and Lubicle Silk for pieces are the standard.
Use the full 15 seconds. Goal: cross + first F2L pair planned before the timer starts. Then no thinking through the first ~12 moves. Drill: take a scramble, plan, then close your eyes and solve the cross from memory. Sounds absurd; it works.
Solving on white only means you accept whatever cross the scramble gives you. Going color-neutral (CN) lets you pick the easiest cross out of six. CN takes 2–3 months of plateau to retrain, and many strong cubers stay non-CN. Worth it past sub-15 if you're committed to long-term speed.
Speed is bought in plateaus. You will not get linearly faster. You will sit at one time for two weeks, then drop two seconds in a single session. Track your ao12 — average of 12 solves with the best and worst dropped — not your single solves; singles are noise.
An hour a day, six days a week, gets a sub-30 cuber to sub-15 in roughly four to six months. Less time means a longer ramp, not no ramp.
Until you're solidly sub-15, ignore: ZBLL, OLLCP, COLL, advanced cross techniques (XX-cross, partial-pair cross), Roux, ZZ. They're all real things real cubers use, but they're refinements on a foundation you don't yet have. The compounding return on full OLL + better F2L lookahead beats any fringe technique until you're past the 15-second wall.