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L4C

Last Four Corners method

Information about the method
Proposer(s):	unknown
Proposed:	unknown
Alt Names:	L4C
Variants:	none
No. Steps:	1
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). L4C is and is not a method in the CxLL group, not becuse it has twice the number of cases as all the other methods of the group (42/84).

See also:

Last Three Corners

2-look L4C

It is possible to solve most L4C in two looks using 3-cycle commutators (see L3C). 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.

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.

Sub groups:

Pure CO; see Corner Orientation for the seven cases of pure orientation 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).
One corner solved; Last Three Corners, 16 cases that have both orientation and permutation, these you can find at the L3C page.

Recognition:

For recognition the same systems that are used for CxLL works fine. You can find the CxLLs separated into the diffrent groups of the listing of the cases at this page, the CxLLs that have corners correctly permuted you can find in the group with pure CO and also in the X-PLL group, the CxLLs with diagonal permutation are in the E-PLL group and the CxLLs with adjacent permutation are in the A-PLL group (L3C/L3C 1-twist).

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.

L3C 1-twist

54 in the group, 18 are pure twists, 36 cases are having both orientation and permutation and of these are 18 mirror cases.

Two corners twisted

The names for the cases are first the actual orientation (U, T or L) followed by the orientation of the inverse case (the case you get if you apply the alg on a solved cube) and last is the direction for the permutation cycle (a or b).

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

ULa

Alg

R' F' L F R F' L F' R2 F L2 F' R2 F2

ULb

Alg

(y) L F R' F' L' F R' F L2 F' R2 F L2 F2

LUa

Alg

(y) F2 L2 F' R2 F L2 F' R F' L F R F' L'

LUb

Alg

F2 R2 F L2 F' R2 F L' F R' F' L' F R

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

TLa

Alg

!

TLb

Alg

!

LTa

Alg

!

LTb

Alg

!

For the following cases mirror and inverse are the same.

Mirror/inverse to the side.

UUa

Alg

!

UUb

Alg

!

TTa

Alg

!

TTb

Alg

!

Three corners twisted

The names here are following the images, the first letter is the orientation, either Sune (S) or Antisune (-S), the second is the direction for the permutation cycle that is either a or b and in the parentesis is the location of the oriented corner that is one of three positions (BR, RF or FL).

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

Sa (RF)

Alg

U R2 D R' U2 R D' R' U L' U R' U' L

-Sb (RF)

Alg

(y) U' L2 D' L U2 L' D L U' R U' L U R'

Sa (BR)

Alg

(y) R U' L' U R' U L' D' L U2 L' D L2 U

-Sb (FL)

Alg

L' U R U' L U' R D R' U2 R D' R2 U'

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

-Sa (BR)

Alg

R L B R' F R B' R2 F' L' F R F'

Sb (FL)

Alg

(y) L' R' B' L F' L' B L2 F R F' L' F

-Sa (RF)

Alg

(y) F' L F R' F' L2 B' L F L' B R L

Sb (RF)

Alg

F R' F' L F R2 B R' F' R B' L' R'

For the following cases mirror and inverse are the same.

Mirror/inverse to the side.

Sa (FL)

Alg

R U' L' U2 R2 U' R' U' L U F2 R2 F2

-Sb (BR)

Alg

(y) L' U R U2 L2 U L U R' U' F2 L2 F2

-Sa (FL)

Alg

U2 R U2 R' F U2 F L' F' U2 F L F2

Sb (BR)

Alg

(y) U2 L' U2 L F' U2 F' R F U2 F' R' F2

Four corners twisted

The names for the cases are first orientation (H or pi) followed by the direction for the permutation cycle (a or b). In the parentesis is the orientation for the placed corner (+ or -) and for the pi cases also if this corner is on the U or the T side of the pi (For H it is only one situation).

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

Ha (+)

Alg

U2 R' F R F' U2 R2 B L' B L B2 R2

Hb (-)

Alg

(y) U2 L F' L' F U2 L2 B' R B' R' B2 L2

pia (T+)

Alg

(y) L2 B2 R B R' B L2 U2 F' L F L' U2

pib (T-)

Alg

R2 B2 L' B' L B' R2 U2 F R' F' R U2

The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

Ha (-)

Alg

(y) F2 L U L2 F2 D F2 D' L F2 L U' L'

Hb (+)

Alg

F2 R' U' R2 F2 D' F2 D R' F2 R' U R

pia (U-)

Alg

R' U' R F2 R D' F2 D F2 R2 U R F2

pib (U+)

Alg

(y) L U L' F2 L' D F2 D' F2 L2 U' L' F2

For the following cases mirror and inverse are the same.

Mirror/inverse to the side.

pia (U+)

Alg

U2 F U2 F' U2 F' L F' R' F' R F' L'

pib (U-)

Alg

L F R' F R F L' F U2 F U2 F' U2

pia (T-)

Alg

R2 U R2 B' D R2 D' R2 B D' F2 D F2 U'

pib (T+)

Alg

U F2 D' F2 D B' R2 D R2 D' B R2 U' R2

Four corners wrong (E)

16 cases, two are E-PLL, leaving 14.

Some cases are order 2 and some are order 6 but in practice most works as 2-cycles if you add a y2. The rest of the order 6 cases may have a mirror or a inverse.

Order 2

Order 6, but adding y2 makes the inverse case the same as this, in practice a 2-cycle.