L4C method

Information about the method
Proposer(s):	unknown
Proposed:	unknown
Alt Names:	none
Variants:	none
No. Steps:	unknown
No. Algs:	84
Avg Moves:	11.73 (Optimal HTM))
Purpose(s):	Speedsolving, FMC

Last four corners, abbrevaited L4C (or 4LC), is a method that solves the last layer corners preserving all the rest, a sub group of ZBLL and ZZLL. For a 2-look last layer this is preceeded with LLEF (ELL first).

See also:

Last Three Corners

L4C Cases

Because edges are solved at this point you cannot AUF as in CxLL so the number of cases is quadrupled, but because you cannot have parity that is reduced again by factor 2. The orientations are the usual seven COs plus the solved case (CPLL). The permutations (with fix position orientations) that occure are permutation solved, A-PLL a and b from all four angles, the two possible ways of E-PLL and finally X-PLL (that is H-PLL + U2) giving a total of twelve possible permutations. This gives a total of 8 * 12 = 96 cases, but it is possible to reduce that a bit because of duplicates. The whole group is larger, corner orientations are for real 27 so you will have 27 * 12 = 324, so the chance of a skip is 1:324.

2-look L4C

It is possible to solve most L4C in two looks using 3-cycle commutators. The method is to use the first 3-cycle to solve one piece and at the same time move any placed but twisted corner out from position (to avoid the pure twists that uses long algs) and then follow it up with a second 3-cycle. This will solve all cases but the pure twists with 4 corners wrong, that you can solve in two looks using only the U-twist and puzzle orientations, the other pure cases, T and U use the U-twist, L and S; cycle the twisted corners using any 3-cycle and then the appropiate cycle to move them back.

Another way is to use COs that preserves edges but not corner permutation and then end the solve using CPLL. This will use lesser algs but more turns than the first approach.

Algorithms

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.

Click on an algorithm (not the camera icon) to watch an animation of it.

Pure COs

See Corner Orientation for the seven cases and algorithms to solve them.

All corners oriented

Use the CPLLs for this, cases are A-PLL a and b, E-PLL and H-PLL (X-PLL).

Mabye list the optimal algs for the cases here but with no images, for FMC usage (I'm trying to save a little on the size of the page ... and work creating images =)

L3C

Another sub group of L4C is L3C. Two of the cases are the A-PLLs listed in the previous group, leaving 16 that have both orientation and permutation and these you can find at the L3C page, the rest of the cases are the pure twists U, T, L, S and -S.