Move notation

How to read R, U', M2, r, x and the pyraminx's tips: the letters every algorithm is written in.
An algorithm is a list of turns. Each letter names a layer, seen from the face it is on; a plain letter is a clockwise quarter turn as if you were looking straight at that face. A prime (') makes it counter-clockwise, a 2 makes it a half turn (direction does not matter). This site uses the standard WCA/SiGN notation, as used by competitions and most algorithm sheets.

Face turns

R (right), L (left), U (up), D (down), F (front), B (back). Hold the cube with the front facing you and the top up; each diagram shows the cube after the turn, with an arrow for the direction the front stickers moved.
R: the right layer turns away from you (front goes up).
Checked by the engine: U2=F U5=F U8=F
R
R': the right layer turns towards you.
Checked by the engine: D2=F D5=F D8=F
R'
U: the top layer turns clockwise seen from above (front goes left).
Checked by the engine: L0=F L1=F L2=F
U
U': the top layer turns the other way (front goes right).
Checked by the engine: R0=F R1=F R2=F
U'
F: the front face turns clockwise.
Checked by the engine: R0=U R3=U R6=U
F
L: the left layer turns towards you (front goes down).
Checked by the engine: D0=F D3=F D6=F
L
D: the bottom layer turns clockwise seen from below (front goes right).
Checked by the engine: R6=F R7=F R8=F
D
B: the back face turns clockwise seen from behind (the top row goes left, out of view).
Checked by the engine: L0=U L3=U L6=U
B
R2: a half turn of the right layer; R2 and R2' are the same.
Checked by the engine: D2=U D5=U D8=U
R2

Slices, wide turns and rotations

  • •
    M, E, S: the middle slices. M turns like L (between L and R), E like D (between U and D), S like F (between F and B).
  • •
    Wide turns: Rw (or r) turns the right two layers together; on bigger cubes 3Rw is three layers. A lowercase letter on a 3x3 means the same as w.
  • •
    Inner slices on big cubes: 2R is the second layer from the right alone.
  • •
    Rotations x, y, z turn the whole cube: x like R, y like U, z like F. They do not change the state, only how you hold it.
M: the middle slice turns like L (front goes down).
Checked by the engine: D1=F D4=F D7=F
M
E: the equator turns like D (front goes right).
Checked by the engine: R3=F R4=F R5=F
E
r (Rw): the right two layers together.
Checked by the engine: U1=F U4=F U7=F U2=F U5=F U8=F
r
2R on a 4x4: only the second layer from the right.
Checked by the engine: U2=F U6=F U10=F U14=F F3=F F7=F F11=F F15=F
2R
y: the whole cube turns like U; the front face is now the old right face.
Checked by the engine: F0=R F4=R F8=R
y

Brackets

  • •
    (R U R' U') groups moves for readability or finger tricks; (R U R' U')2 repeats the group twice.
  • •
    [A, B] is a commutator: A B A' B'. [A: B] is a conjugate: A B A'. Both are expanded before checking or counting moves.

Pyraminx

Hold the pyraminx with one face towards you and a vertex on top. U, L, R and B turn the big layers around the top, left, right and back vertices (a third of a turn, clockwise seen from that vertex). Lowercase u, l, r, b turn only the tip. Uv, Lv, Rv, Bv turn the whole puzzle.
U: the top layer, a third of a turn clockwise from above.
Checked by the engine: 1 center moved, 3 edges moved, 1 tip moved
U
R: the layer around the right vertex.
Checked by the engine: 1 center moved, 3 edges moved, 1 tip moved
R
L: the layer around the left vertex.
Checked by the engine: 1 center moved, 3 edges moved, 1 tip moved
L
u: the top tip alone.
Checked by the engine: 0 centers moved, 0 edges moved, 1 tip moved
u

Counting moves

Move counts are given in three metrics. HTM (half-turn metric) counts every face or wide turn as 1 and a slice turn as 2. STM (slice-turn metric) counts slices as 1, which is closer to how M-heavy algorithms feel. QTM counts half turns as 2. Rotations count in none of them. Shorter is not always faster: an algorithm made of R and U turns can beat a shorter algorithm with awkward regrips.