## Threefold moves for the Rubik’s Cube

 (1) B2 • R’ D R F D F’ • U F D’ F’ R’ D’ R • U’ • B2 This also rotates the back corner piece counterclockwise.
 (2) Do parts (a) and (b): Part a: R • U’ R’ F’ L’ B’ • U’ BLFR • U2 • R’ Part b: L’ • D LBRF • D F’ R’ B’ L’ • D2 • L Part (a) does the clockwise floret on the front three sides; part (b) does the counterclockwise floret on the back three sides.
 (3) F2 U2 F’ R2 F (do part 2a) F’ R2 F U2 F2 From the back three sides, this looks like a counterclockwise (5).
 (4) F L2 F’ L F R’ F’ L’ F R F’ F L2 F’ From the back three sides, this looks like a counterclockwise (6).
 (5) F2 R2 F U2 F’ (do part 2a) F U2 F’ R2 F2 From the back three sides, this looks like a counterclockwise (3).
 (6) R’ F L’ U R U’ L U R’ U’ F’ R From the back three sides, this looks like a counterclockwise (4).
 (7) V’ H V H’

Key

• F, R, B, L, U, D: quarter-turn clockwise (as viewed from outside of the cube) of front, right, back, left, up, and down faces, respectively.

• F2, etc.: half-turn of front face, etc.

• F’, etc.: counterclockwise quarter-turn of front face, etc. (This is shorthand for F-1.)

• Bullets (•) are used as delimiters, solely for mnemonic purposes.

• S and S’ are slice and antislice moves, respectively. While the other moves leave the centerposts in place, the slice and antislice move the centerposts, as shown:  S S’

• Related to these are the horizontal and vertical slice moves, and their corresponding antislice moves:  H H’ V V’