Rubik's Cube Notation
Algorithms are written as a sequence of moves. Each letter turns one face of the cube; the cube rotations turn the whole thing. Here's the full set.
Moves
- Each letter is a 90° clockwise turn
- Add ' for anti-clockwise
- Add 2 for a double turn
The ' notation is called prime. U' is spoken as U-prime.
Face turns
Wide turns
A lowercase letter turns the outer face together with the middle layer beside it, two layers at once. You'll also see these written with a w (Rw, Lw, Uw, Dw, Fw, Bw).
Slice moves
A slice turns just the middle layer between two opposite faces, leaving both outer faces still. Each one follows the direction of one of the faces it sits between.
Cube rotations
Rotate the entire cube without turning any face.
Algorithms
What's an algorithm?
- A sequence of these moves done in order, like RUR'U' .
- Memorise a handful of them to solve the cube.
Triggers: the building blocks of algorithms
A few short sequences come back again and again across every alg set, and your hands learn each one as a single motion: those are triggers. Most algs are three or four in a row, boxed and tinted by family so you read the shape before the letters. Anything that belongs to no trigger stays unboxed.
The sune: a whole alg that is one trigger. It shows up inside longer algs too.
A Rightie straight into a sledgehammer. Two triggers, eight moves, nothing loose.
That same sledgehammer, dropped into the middle of a sune. Boxes nest when one trigger sits inside another.
The Y perm, three boxes long. The last eight moves are the Rightie and the sledgehammer from above, so most of it is already in your hands.
Variations
A trigger comes mirrored, reversed, or wide. Same motion, same family, same colour. Some of those variants picked up a name of their own: a mirrored Rightie is the Leftie, a reversed sledgehammer is the hedgeslammer, a reversed sune is the antisune.
Conjugates and commutators
The two shapes almost every algorithm is built from, and the reason the boxes on this site nest the way they do.
A conjugate sets up, does the work, then undoes the setup
The setup does no work of its own: it brings the pieces into reach and puts them back. That frame is what the boxes draw, with the work nested in a deeper box inside it.
A commutator alternates two parts so they cancel out
Do the first part, do the second, undo the first, undo the second, where either part can be longer than a single move. Everything ends up back where it started except the pieces the two parts share.
Alg lists also write these as [F: R U R' U'] and [R, U].
The same algorithm, written differently
Different moves can leave the cube in the same state, so one algorithm shows up written several ways.
Other ways you'll see it written
- “i” for inverse: R' written as Ri, so R U R' U' becomes R U Ri Ui.
- “w” for wide turns: the two-layer turns written as Rw, Lw, Uw, Dw, Fw, Bw. We use the shorter lowercase form (r, l, u, d, f, b); the two mean exactly the same move.
- Brackets: [R, U] = RUR'U' , [R: U] = RUR' - see conjugates and commutators above.
- The standard letters are Singmaster notation, from around 1980.
Frequently asked questions
- What does the apostrophe (') mean in cube notation?
- A prime (') after a letter means turn that face a quarter turn anti-clockwise. R turns the right face clockwise, R' turns it anti-clockwise. Clockwise is always judged as if you were looking straight at that face.
- What's the difference between a conjugate and a commutator?
- The punctuation tells you. A conjugate [A: B] means A B A': set up, do the move you wanted, undo the setup, so one thing follows the colon. A commutator [A, B] means A B A' B': two things take turns, one on each side of the comma. Short version: a comma has two things around it, a colon has one thing after it.
- What is a trigger?
- A short burst of moves your hands run as a single motion, like R U R' U'. Algorithms are learned as a few triggers in a row rather than as a list of letters, which is why every algorithm here is drawn as coloured boxes around its moves.