These are sequences that move cubies around the top face (Up) without disturbing the rest of the cube.

All these operators were invented by me except the American operator.

Note that if all the rest of the cube is solved except the top face, there are built in restrictions on what way the cubies can be arranged on the top face:

• the number of flipped edges will be even
• if we count a corner twisted clockwise as +1 and a corner twisted anticlockwise as -1, the total twist will be a multiple of 3
• if all the corners are in the right position, there can be 0, 3 or 4 edges in the wrong place, but not 2.

Operators 1, 2 and 6 are included for completeness but I would not use them for any solutions.

Operator 10 could be used in a "solve edges first, then corners" approach, but you'd also need to find a corner mover operator.

Suggested solution of final top layer:

• use 4 and 5 to position corners

  • four corners wrong - turn until at least one is right
  • three corners wrong - use 5 to cycle them
  • two corners wrong - use 4 to swap them

• use 3 to twist corners
• use 7 or 8 to position edges - if number of flipped edges can be reduced by using 7, use it, otherwise use 8
• use 9 to flip any remaining edges

1.EOIN1

My first operator, discovered in 1981. This was designed to shuffle the edges and corners on the bottom face D. I hadn't yet thought of turning the cube upside down and solving the top face U.

R' D² R D² R F' R' F

Turning this over so that it is the top face that is modified, we get:

L' U² L U² L F' L' F

Effect: Shuffles 3 corners, 3 edges and flips and twists

2. EOIN2

My 2nd operator. This is a variation of EOIN1, turning the bottom face by one turn instead of two. Turned over, it is:

L' U' L U L F' L' F

Effect: Shuffles 3 corners, 3 edges and flips and twists

3. American Operator

Shown to me by an American in Rome Youth Hostel, Summer 1981. It turns only two faces. He described it as:

"Down Over Over Up Over Down Over Up"

In standard notation, this is:

R' U² R U R' U R

I've modified this by adding a U². This was implicit in the way the American used the operator:

R' U² R U R' U R U²

Effect: Twists 3 corners clockwise without moving them. Leaves UFR corner untouched. Shuffles edges without flipping them. This is very useful in a "solve corners first, then edges" solution.

4. FUFU

It is one of the shortest operators. It uses the FUF'U' sequence, turning two faces, but wraps this in an L L' to position things for max effect.

L F U F' U' L'

Effect: this shifts both corners and edges of the top face. Significantly, it swaps the corners in two pairs, which is equivalent to leaving two diagonally opposite corners fixed and swapping the other two diagonally opposite corners. This can be used in combination with a number of other operators to position the corners in the right place

5. LURU

A very neat and useful operator.

L' U R U' L U R' U'

Effect: Leaves edges untouched. Shuffles 3 corners and twists the same three.

6. Double FUFU

This consists of the FUFU operator 4 followed by the mirror image of it. This reverses some of the effects and not others.

[L F U F' U' L'] [R' F' U' F U R]

Effect: Flips two edges, twists four corners but doesn't move any edges or corners.

7. Edge Mover Flipper

This moves and flips edges without disturbing the corners.

[R'L F RL'] U² [R'L F RL']

8. Edge Mover

This moves edges without flipping them and doesn't disturb the corners.

[R²D'] [R'L F² L'R U²] [DR²]

9. Edge Flipper

This flips the UF edge and another edge of your choice on the top face. A choice of U, U² or U' can be used in the middle of this operator to move the other edge to be flipped into the UF position. The corresponding opposite move, U', U² or U, must be done at the end.

[R'L F RL' U R'L F² RL'] U [R'L F² RL' U' R'L F' RL'] U'

10. Corner Twister

This twists two corners in opposite directions and doesn't affect anything else.

[R' D R][F D F'] U [F D’ F'][R' D' R] U'

By changing the U and U' in this to U² or to U' and U, different pairs of corners on the top face can be twisted.