CLL Transformation Table

Athefre · Feb 8, 2012

For CLL cases with at least one oriented corner it's possible to move one of those oriented corners to its correct position and transform to another case. This reveals why two seemingly completely different cases have a similar sequence of moves. Because there must be a correctly oriented corner, G and H cases can't be a starting point and can't be led to unless more moves are allowed. A2 and most of the D, E, and F cases have more than one set of possibilities and I've distinguished them by noting the location of certain colors on the unsolved corner within the layer to be adjusted. The moves in parentheses are optional and are only here to end the corners in the same position for each of the six orientations. My list follows Robert Yau's CLL document.

Cases:

A2: x' R2 U2 R' U' R U2 x R' U R'

Pair at Unsolved Corner:
- L(U2) > E3
- R > E3
- R'(U2) > E5
- L' > E5
Opposite Pair at Unsolved Corner:
- R(U') > D6
- R' > D6
- L(U) > D6
- L'(U2) > D6
- x(U2) > F2
- x' > F2
No Pair at Unsolved Corner:
- R(U') > D3
- R' > D2
- L(U) > D3
- L'(U2) > D2

A6: R' U L' U2 L F' U L' U2 L F' R

R > E2
R'(U2) > E2
L(U2) > E2
L' > E2

B1: R' U' R U' R' U2 R

R(U) > B1
R' > B1
L > B1
L'(U) > B1

B2: L' U L' U L U' L U x U' L U

R(U2) > F4
R'(U) > E4
L > F4
L'(U') > E4

B3: B' L U L' U2 R' U2 R

R(U2) > F6
R'(U') > B4
L > F6
L'(U) > B4

B4: L U2 L' U2 L' B L B'

R(U2) > B3
R'(U') > F6
L > B3
L'(U) > F6

B5: R' U L U' R U L'

R(U) > D4
R'(U') > F3
L(U') > D4
L'(U) > F3

B6: (U') R' U' R U' R' U R' F R F' U R

R(U) > D3
R'(U) > E5
L(U') > D3
L'(U') > E5

C1: L U L' U L U2 L'

R(U') > C1
R' > C1
L(U) > C1
L'(U2) > C1

C2: R' U2 R U2 R B' R' B

R(U') > F6
R' > C3
L(U) > F6
L'(U2) > C3

C3: B R' U' R U2 L U2 L'

R(U') > C2
R' > F6
L(U) > C2
L'(U2) > F6

C4: R U' R U' R' U R' U' x U R' U'

R(U) > E4
R' > F4
L(U') > E4
L'(U2) > F4

C5: L U' R' U L' U' R

R(U') > F5
R'(U2) > D5
L(U) > F5
L' > D5

C6: (U) R' F R2 F' R U2 R' U' R2

R(U) > E3
R'(U2) > D2
L(U') > E3
L' > D2

D1: R' U R' U2 R U' R' U R U' R2'

U Sticker on L or R:
- R > E1
- R'(U2) > E1
- L(U2) > E1
- L' > E1
U Sticker not on L or R:
- R(U2) > F1
- R' > F1
- L > F1
- L'(U2) > F1

D2: x' R' U2 R' U' R U2 R' F R2

U Sticker on L or R:
- R(U') > C6
- R'(U2) > E3
- L(U) > C6
- L' > E3
U Sticker not on L or R:
- R > A2
- R'(U) > E3
- L(U2) > A2
- L'(U') > E3

D3: R' U2 R U' R' U2 R U' y R U R'

U Sticker on L or R:
- R > E5
- R'(U') > B6
- L(U2) > E5
- L'(U) > B6
U Sticker not on L or R:
- R(U) > E5
- R' > A2
- L(U') > E5
- L'(U2) > A2

D4: R U' R' U' y R' F R

U Sticker on L or R:
- R(U2) > F3
- R'(U') > B5
- L > F3
- L'(U) > B5
U Sticker not on L or R:
- R(U) > E6
- R' > F3
- L(U') > E6
- L'(U2) > F3

D5: F' R U R' U' R' F R

U Sticker on L or R:
- R(U') > C5
- R' > F5
- L(U) > C5
- L'(U2) > F5
U Sticker not on L or R:
- R(U2) > F5
- R'(U') > F5
- L > F5
- L'(U') > E6

D6: L' U2 L2 F' L' F L' U2 L

U Sticker on L or R:
- R(U2) > F2
- R' > F2
- L > F2
- L'(U2) > F2
U Sticker not on L or R:
- R(U) > A2
- R'(U') > A2
- L(U') > A2
- L'(U) > A2

E1: (U) R U' R U' R U' R' U R' U R'

R(U) > D1
R'(U2) > D1
L(U') > D1
L' > D1
x' > F1

E2: (U') z' U2 R' U' R2 U' R' U' R U' R'

R > A6
R' > A6
L > A6
L' > A6
x'(U2) > E2

E3: R2 U L' U2 L F' L' U2 L'

U Sticker on U:
- R(U) > A2
- R'(U) > C6
- L(U') > A2
- L'(U2) > C6
U Sticker not on U:
- R' > A2
- R(U) > D2
- L(U') > D2
- L'(U') > A2

E4: x R U' R U' R' U L' U' L

U Sticker on U:
- R(U2) > B2
- R' > C4
- L > B2
- L'(U2) > C4
U Sticker not on U:
- R(U') > F4
- R'(U') > F4
- L(U) > F4
- L' > F4

E5: L2 U' R U2 R' F R U2 R

U Sticker on U:
- R(U2) > B6
- R' > D3
- L > B6
- L'(U2) > D3
U Sticker not on U:
- R(U') > A2
- R'(U2) > D3
- L(U) > A2
- L' > D3

E6: (U) F' L' U' L U F

U Sticker on U:
- R(U') > D5
- R' > D4
- L(U) > D5
- L'(U2) > D4
U Sticker not on U:
- R(U') > F3
- R'(U') > F5
- L(U) > F3
- L'(U) > F5

F1: R' U R' U R' U' R U' R U' R

R(U') > D1
R' > D1
L(U) > D1
L'(U2) > D1
x > E1

F2: L F' L' U2 L2 F' L' U L'

R(U) > D6
R'(U2) > D6
L(U') > D6
L' > D6
x(U) > A2

F3: (U') L' U' L U L F' L' F

U Sticker on U:
- R(U2) > B5
- R'(U2) > E6
- L > B5
- L' > E6
U Sticker not on U:
- R(U') > D4
- R'(U2) > D4
- L(U) > D4
- L' > D4

F4: (U') x L' U R U' L U L' U R'

U Sticker on U:
- R > E4
- R'(U2) > E4
- L(U2) > E4
- L' > E4
U Sticker not on U:
- R(U') > C4
- R'(U') > B2
- L(U) > C4
- L'(U) > B2

F5: (U) R U R' U' R' F R F'

U Sticker on U:
- R > E6
- R' > C5
- L(U2) > E6
- L'(U2) > C5
U Sticker not on U:
- R(U) > D5
- R' > D5
- L(U') > D5
- L'(U2) > D5

F6: (U') R U L F' R U' R' U L' U L2

U Sticker on U:
- R(U2) > B4
- R' > C2
- L > B4
- L'(U2) > C2
U Sticker not on U:
- R(U') > C3
- R'(U') > B3
- L(U) > C3
- L'(U) > B3

Edit: Fixed old images.

riffz · Feb 10, 2012

I don't really have much to say about this other than that it's interesting and that this deserves a bump.

Escher · Feb 10, 2012

I wonder if this can be applied to EG cases also, in order to find better algs?

Athefre · Feb 10, 2012

Escher said:
I wonder if this can be applied to EG cases also, in order to find better algs?

For speed, maybe. For move count, those solutions are already found by computers.

CLL Transformation Table

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Escher

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