What you usually see for 6×6×6 L2C is this:
There are six sets of cases for the last bar, where most sets have 15 cases. The oddball set with 19 cases is the one where the obliques for the last bar are already paired up—this you can solve like 5×5×5 L2C, so there isn't anything new to learn. These are the five remaining sets (feel free to suggest better names if you come up with any):
Note: these algs are written in SiGN (r = Rw, 3r = 3Rw, 3R = 3Rw Rw', 3-4r = 4Rw Rw') and the spoiler boxes contain more alternative algs than the tables.
If there's any interest in this, I might generate the rest of the sets.
(I guess some of you are going to be wisecrackers and point out that over half of the above cases have "insert cancelling into a commutator" as a solution, so this isn't much of an improvement over the intuitive method. That's true, and that's also the point! Just like intuitive F2L, sometimes looking at algorithmic methods can make you realise that there's a more efficient way to do certain cases, and the algorithm becomes intuition if you stare at it hard enough.)
Previously.
Changelog:
2018-02-18: Replaced the main algs for (opp FL BR), (opp BL FR), (far FL U), (far BR D), (far FL BL), (far FR BR), (far FR U), (far FR D).
2021-01-18: Fixed the VisualCube links.
- 2×4 block on left side of front face
- Extend to 3×4 block
- Use one of the obliques and the two outer x-centres to form a partial bar and insert
- Use a commutator if there's a stray oblique you need to insert
There are six sets of cases for the last bar, where most sets have 15 cases. The oddball set with 19 cases is the one where the obliques for the last bar are already paired up—this you can solve like 5×5×5 L2C, so there isn't anything new to learn. These are the five remaining sets (feel free to suggest better names if you come up with any):
- "separate low"
- "separate high"
- "opposite"
- "near diagonal"
- "far diagonal"
Note: these algs are written in SiGN (r = Rw, 3r = 3Rw, 3R = 3Rw Rw', 3-4r = 4Rw Rw') and the spoiler boxes contain more alternative algs than the tables.
FL FR (front 3bar):
mn: insert cancel into comm
(U) r U 3R U r' U' 3R'
BL BR (back 3bar):
mn: insert cancel into comm
(U') r U' 3R U' r' U 3R'
FL BR (pair + split):
mn: set up to far set
(U') r U' r' U' 3R U r U' r' U r U' 3r'
---
mn: break up the pair, pair obs, insert
r U r' U 3R U r U' 3r' U r U' r'
---
mn: set up to 5-mover
(U') l' r U' r' U l U' 3r U' r' U 3R'
---
(U2) 3R U r U' 3R' U' 3r r2' U r U' 3r'
(U2) r U r' U2 r U' r' U 3r U' r' U 3R'
(U2) r U2 r' U r U r' U 3r U' r' U 3R'
BL FR (pair + split):
mn: set up to far set
(U) r U r' U 3R U' r U r' U' r U 3r'
---
mn: break up the pair, pair obs, insert
r U' r' U' 3R U' r U 3r' U' r U r'
---
mn: set up to 5-mover
(U) l' r U r' U' l U 3r U r' U' 3R'
---
(U2) 3R U' r U 3R' U 3r r2' U' r U 3r'
(U2) r U2 r' U' r U' r' U' 3r U r' U' 3R'
(U2) r U' r' U2 r U r' U' 3r U r' U' 3R'
FL BL (two splits):
mn: insert split pair cancel into split pair comm
(U) r U (l' 3R) U r' U' (l 3R')
---
(U2) r U r' U' r U2 r' U2 3r U' r' U 3R'
(U2) r U r' U' 3r U2 r' U2 r U' r' U 3R'
(U2) r U' r' U r U2 r' U2 3r U r' U' 3R'
(U2) r U' r' U 3r U2 r' U2 r U r' U' 3R'
(U) 3R U 3R' U2 3r U' 3R' U' 3r r2' U 3R'
(U') 3R U' 3R' U2 3r U 3R' U 3r r2' U' 3R'
(U) 3R U r U' 3r' U 3R U r U2 r' U 3R'
(U') 3R U' r U 3r' U' 3R U' r U2 r' U' 3R'
(U) r U 3R U r' U' 3r' r2 U2 r' U' r U' r'
(U') r U' 3R U' r' U 3r' r2 U2 r' U r U r'
FR BR (two pairs):
mn: insert pair cancel into pair comm
(U') r U 3l' U r' U' 3l
---
3r U 3r' U 3r U2 r' U 3R' U 3r U 3r'
3r U' 3r' U' 3r U2 r' U' 3R' U' 3r U' 3r'
r U r' U r U2 r' U2 3r U r' U' 3R'
r U r' U 3r U2 r' U2 r U r' U' 3R'
r U' r' U' r U2 r' U2 3r U' r' U 3R'
r U' r' U' 3r U2 r' U2 r U' r' U 3R'
(U) 3r U 3r' U 3r U' r' U' 3R' U' 3r U' 3r'
(U') 3r U' 3r' U' 3r U r' U 3R' U 3r U 3r'
(U) r U 3R U r' U r U2 3r' U r U r'
(U) r U2 r' U r U r' U' 3r U' r' U 3R'
(U) r U2 r' U 3R U' r U 3r' U r U' r'
(U2) r U r' U' r U r' U' 3r U' r' U 3R'
(U2) r U r' U' 3R U' r U 3r' U r U' r'
(U2) r U' r' U r U' r' U 3r U r' U' 3R'
(U2) r U' r' U 3R U r U' 3r' U' r U r'
(U') r U2 r' U' r U' r' U 3r U r' U' 3R'
(U') r U2 r' U' 3R U r U' 3r' U' r U r'
(U') r U' 3R U' r' U' r U2 3r' U' r U' r'
(U2) 3r U 3r' U' 3r U' 3R' U r' U 3r U 3r'
(U2) 3r U' 3r' U 3r U 3R' U' r' U' 3r U' 3r'
U D:
mn: insert pair + pair comm
r U r' U2 r U' 3l' U r' U' 3l
---
r U r' U r U' r' U 3r U r' U' 3R'
r U r' U 3R U r U' 3r' U' r U r'
r U' r' U' r U r' U' 3r U' r' U 3R'
r U' r' U' 3R U' r U 3r' U r U' r'
r U r' U r U2 r' U' 3r U' r' U 3R'
r U' r' U' r U2 r' U 3r U r' U' 3R'
(U) r U' 3R U2 3R' U' r' U 3R U2 3R'
(U') r U 3R U2 3R' U r' U' 3R U2 3R'
BL U (split, nice 3bar):
mn: 3bar + comm
r U r' U2 r U 3R U' r' U 3R'
FL D (split, nice 3bar):
mn: 3bar + comm
r U' r' U2 r U' 3R U r' U' 3R'
FR U (pair, nice 3bar):
mn: 3bar + comm
(U2) r U r' U2 r U' 3R U r' U' 3R'
(U2) r U r' U2 r U 3L' U' r' U 3L
---
r U2 r' U r U' 3R U' r' U 3R'
BR D (pair, nice 3bar):
mn: 3bar + comm
(U2) r U' r' U2 r U 3R U' r' U 3R'
(U2) r U' r' U2 r U' 3L' U r' U' 3L
---
r U2 r' U' r U 3R U r' U' 3R'
FL U (split, bad 3bar):
mn: corners to r, sune cancel into comm
(U') r U r' U r 3L' U' r' U 3L
(U') r U r' U r U2 3R U r' U' 3R'
---
(U') r U r' U' 3R U2 r U' r' U' 3R'
r U2 r' U' r U r' U 3r U' r' U 3R'
BL D (split, bad 3bar):
mn: corners to r, mirror sune cancel into comm
(U) r U' r' U' r 3L' U r' U' 3L
(U) r U' r' U' r U2 3R U' r' U 3R'
---
(U) r U' r' U 3R U2 r U r' U 3R'
r U2 r' U r U' r' U' 3r U r' U' 3R'
BR U (pair, bad 3bar):
mn: TODO
(U) r U r' U 3r U' r' U 3R'
FR D (pair, bad 3bar):
mn: TODO
(U') r U' r' U' 3r U r' U' 3R'
mn: insert cancel into comm
(U) r U 3R U r' U' 3R'
BL BR (back 3bar):
mn: insert cancel into comm
(U') r U' 3R U' r' U 3R'
FL BR (pair + split):
mn: set up to far set
(U') r U' r' U' 3R U r U' r' U r U' 3r'
---
mn: break up the pair, pair obs, insert
r U r' U 3R U r U' 3r' U r U' r'
---
mn: set up to 5-mover
(U') l' r U' r' U l U' 3r U' r' U 3R'
---
(U2) 3R U r U' 3R' U' 3r r2' U r U' 3r'
(U2) r U r' U2 r U' r' U 3r U' r' U 3R'
(U2) r U2 r' U r U r' U 3r U' r' U 3R'
BL FR (pair + split):
mn: set up to far set
(U) r U r' U 3R U' r U r' U' r U 3r'
---
mn: break up the pair, pair obs, insert
r U' r' U' 3R U' r U 3r' U' r U r'
---
mn: set up to 5-mover
(U) l' r U r' U' l U 3r U r' U' 3R'
---
(U2) 3R U' r U 3R' U 3r r2' U' r U 3r'
(U2) r U2 r' U' r U' r' U' 3r U r' U' 3R'
(U2) r U' r' U2 r U r' U' 3r U r' U' 3R'
FL BL (two splits):
mn: insert split pair cancel into split pair comm
(U) r U (l' 3R) U r' U' (l 3R')
---
(U2) r U r' U' r U2 r' U2 3r U' r' U 3R'
(U2) r U r' U' 3r U2 r' U2 r U' r' U 3R'
(U2) r U' r' U r U2 r' U2 3r U r' U' 3R'
(U2) r U' r' U 3r U2 r' U2 r U r' U' 3R'
(U) 3R U 3R' U2 3r U' 3R' U' 3r r2' U 3R'
(U') 3R U' 3R' U2 3r U 3R' U 3r r2' U' 3R'
(U) 3R U r U' 3r' U 3R U r U2 r' U 3R'
(U') 3R U' r U 3r' U' 3R U' r U2 r' U' 3R'
(U) r U 3R U r' U' 3r' r2 U2 r' U' r U' r'
(U') r U' 3R U' r' U 3r' r2 U2 r' U r U r'
FR BR (two pairs):
mn: insert pair cancel into pair comm
(U') r U 3l' U r' U' 3l
---
3r U 3r' U 3r U2 r' U 3R' U 3r U 3r'
3r U' 3r' U' 3r U2 r' U' 3R' U' 3r U' 3r'
r U r' U r U2 r' U2 3r U r' U' 3R'
r U r' U 3r U2 r' U2 r U r' U' 3R'
r U' r' U' r U2 r' U2 3r U' r' U 3R'
r U' r' U' 3r U2 r' U2 r U' r' U 3R'
(U) 3r U 3r' U 3r U' r' U' 3R' U' 3r U' 3r'
(U') 3r U' 3r' U' 3r U r' U 3R' U 3r U 3r'
(U) r U 3R U r' U r U2 3r' U r U r'
(U) r U2 r' U r U r' U' 3r U' r' U 3R'
(U) r U2 r' U 3R U' r U 3r' U r U' r'
(U2) r U r' U' r U r' U' 3r U' r' U 3R'
(U2) r U r' U' 3R U' r U 3r' U r U' r'
(U2) r U' r' U r U' r' U 3r U r' U' 3R'
(U2) r U' r' U 3R U r U' 3r' U' r U r'
(U') r U2 r' U' r U' r' U 3r U r' U' 3R'
(U') r U2 r' U' 3R U r U' 3r' U' r U r'
(U') r U' 3R U' r' U' r U2 3r' U' r U' r'
(U2) 3r U 3r' U' 3r U' 3R' U r' U 3r U 3r'
(U2) 3r U' 3r' U 3r U 3R' U' r' U' 3r U' 3r'
U D:
mn: insert pair + pair comm
r U r' U2 r U' 3l' U r' U' 3l
---
r U r' U r U' r' U 3r U r' U' 3R'
r U r' U 3R U r U' 3r' U' r U r'
r U' r' U' r U r' U' 3r U' r' U 3R'
r U' r' U' 3R U' r U 3r' U r U' r'
r U r' U r U2 r' U' 3r U' r' U 3R'
r U' r' U' r U2 r' U 3r U r' U' 3R'
(U) r U' 3R U2 3R' U' r' U 3R U2 3R'
(U') r U 3R U2 3R' U r' U' 3R U2 3R'
BL U (split, nice 3bar):
mn: 3bar + comm
r U r' U2 r U 3R U' r' U 3R'
FL D (split, nice 3bar):
mn: 3bar + comm
r U' r' U2 r U' 3R U r' U' 3R'
FR U (pair, nice 3bar):
mn: 3bar + comm
(U2) r U r' U2 r U' 3R U r' U' 3R'
(U2) r U r' U2 r U 3L' U' r' U 3L
---
r U2 r' U r U' 3R U' r' U 3R'
BR D (pair, nice 3bar):
mn: 3bar + comm
(U2) r U' r' U2 r U 3R U' r' U 3R'
(U2) r U' r' U2 r U' 3L' U r' U' 3L
---
r U2 r' U' r U 3R U r' U' 3R'
FL U (split, bad 3bar):
mn: corners to r, sune cancel into comm
(U') r U r' U r 3L' U' r' U 3L
(U') r U r' U r U2 3R U r' U' 3R'
---
(U') r U r' U' 3R U2 r U' r' U' 3R'
r U2 r' U' r U r' U 3r U' r' U 3R'
BL D (split, bad 3bar):
mn: corners to r, mirror sune cancel into comm
(U) r U' r' U' r 3L' U r' U' 3L
(U) r U' r' U' r U2 3R U' r' U 3R'
---
(U) r U' r' U 3R U2 r U r' U 3R'
r U2 r' U r U' r' U' 3r U r' U' 3R'
BR U (pair, bad 3bar):
mn: TODO
(U) r U r' U 3r U' r' U 3R'
FR D (pair, bad 3bar):
mn: TODO
(U') r U' r' U' 3r U r' U' 3R'
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(FL FR) (U) r U 3R U r' U' 3R' | (BL BR) (U') r U' 3R U' r' U 3R' | (FR BR) (U') r U 3l' U r' U' 3l | (FL BL) (U) r U (l' 3R) U r' U' (l 3R') |
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(FL BR) (U') r U' r' U' 3R U r U' r' U r U' 3r' r U r' U 3R U r U' 3r' U r U' r' | (BL FR) (U) r U r' U 3R U' r U r' U' r U 3r' r U' r' U' 3R U' r U 3r' U' r U r' | (U D) r U r' U2 r U' 3l' U r' U' 3l | |
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(FR U) (U2) r U r' U2 r U 3L' U' r' U 3L r U2 r' U r U' 3R U' r' U 3R' | (BR D) (U2) r U' r' U2 r U' 3L' U r' U' 3L r U2 r' U' r U 3R U r' U' 3R' | (FL D) r U' r' U2 r U' 3R U r' U' 3R' | (BL U) r U r' U2 r U 3R U' r' U 3R' |
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(FR D) (U') r U' r' U' 3r U r' U' 3R' | (BR U) (U) r U r' U 3r U' r' U 3R' | (FL U) (U') r U r' U r 3L' U' r' U 3L | (BL D) (U) r U' r' U' r 3L' U r' U' 3L |
If there's any interest in this, I might generate the rest of the sets.
(I guess some of you are going to be wisecrackers and point out that over half of the above cases have "insert cancelling into a commutator" as a solution, so this isn't much of an improvement over the intuitive method. That's true, and that's also the point! Just like intuitive F2L, sometimes looking at algorithmic methods can make you realise that there's a more efficient way to do certain cases, and the algorithm becomes intuition if you stare at it hard enough.)
Previously.
Changelog:
2018-02-18: Replaced the main algs for (opp FL BR), (opp BL FR), (far FL U), (far BR D), (far FL BL), (far FR BR), (far FR U), (far FR D).
2021-01-18: Fixed the VisualCube links.
Last edited: