Last Four Corners

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Last Four Corners
LLEF.png
Information
Proposer(s): unknown
Proposed: unknown
Alt Names: L4C
Variants: none
Subgroup:
No. Algs: 84
Avg Moves: 11.73 (Optimal HTM)
Purpose(s):
Previous state: LL:EO+EP cube state
Next state: Solved cube state

LL:EO+EP cube state -> Last Four Corners step -> Solved cube state


The Last Four Corners step is the step between the LL:EO+EP cube state and the Solved cube state.

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. L4C is and is not a method in the CxLL group, not because it has twice the number of cases as all the other methods of the group (42/84).

Usage:

  • For a 2-look last layer this is preceeded with LLEF (ELL-CLL).
  • FMC, aspecially linear FMC to solve the last layer corners but also normal FMC where a block + edge skeleton leaves 4 corners in diffrent layers, that are setup to one side and solved using L4C (not so effective but as a last resort).
  • BLD, the sub group L3C is used by many freestylers and is also a part of the Beyer-Hardwick Method. E and X cases are double 2-cyles, that can solve 4 corners in one go if the case is represented in the scramble or if it is easy to setup.

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 (see OCLL-EPP) and then end the solve using CPLL. This will use lesser algs but more turns than the first approach.

L4C with a beginner method

Another approach is a beginner's method of last layer, permutation first:
U R U' L' U R' U' L - permute corners except front-right-up corner
R' D' R D - repeat - rotates corners. Must rotate only up face to switch which corner is rotated.

See also:

External links


L4C

Pure CO | CPLL | L3C | L3C 1: 2-twist , 3-twist , 4-twist | E cases | X cases | edit

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.

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. (how to add algorithms)

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

The first algorithm given for each case is the optimal solution in half turn metric.

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.

L3C 1

One corner placed but twisted: 54 in the group, 18 are pure twists (see CO for the cases), 36 cases are having both orientation and permutation and of these 18 are 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

L4C 1CW Ua.jpg

Speedsolving Logo tiny.gif Alg R' F' L F R F' L F' R2 F L2 F' R2 F2


ULb

L4C 1CCW Ub.jpg

Speedsolving Logo tiny.gif Alg (y) L F R' F' L' F R' F L2 F' R2 F L2 F2


LUa

L4C 1CW Lb.jpg

Speedsolving Logo tiny.gif Alg (y) F2 L2 F' R2 F L2 F' R F' L F R F' L'


LUb

L4C 1CCW Lb.jpg

Speedsolving Logo tiny.gif 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

L4C 1CCW Ta.jpg

Speedsolving Logo tiny.gif Alg B' U B R2 B R2 U' R2 U B2 U' B R2


TLb

L4C 1CW Tb.jpg

Speedsolving Logo tiny.gif Alg (y) B U' B' L2 B' L2 U L2 U' B2 U B' L2


LTa

L4C 1CCW La.jpg

Speedsolving Logo tiny.gif Alg (y) L2 B U' B2 U L2 U' L2 B L2 B U B'


LTb

L4C 1CW La.jpg

Speedsolving Logo tiny.gif Alg R2 B' U B2 U' R2 U R2 B' R2 B' U' B


For the following cases mirror and inverse are the same.

Mirror/inverse to the side.

TTa

L4C 1CW Ta.jpg

Speedsolving Logo tiny.gif Alg (y) U F R B U2 B' U B U2 B2 R B R2 F'


TTb

L4C 1CCW Tb.jpg

Speedsolving Logo tiny.gif Alg U' F' L' B' U2 B U' B' U2 B2 L' B' L2 F


UUa

L4C 1CCW Ua.jpg

Speedsolving Logo tiny.gif Alg B' R B2 L' B D2 L' D2 L B' L B' R'


UUb

L4C 1CW Ub.jpg

Speedsolving Logo tiny.gif Alg R B L' B L' D2 L D2 B' L B2 R' B


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)

L4C 1CW S1a.jpg

Speedsolving Logo tiny.gif Alg U R2 D R' U2 R D' R' U L' U R' U' L


-Sb (RF)

L4C 1CCW S1b.jpg

Speedsolving Logo tiny.gif Alg (y) U' L2 D' L U2 L' D L U' R U' L U R'


Sa (BR)

L4C 1CW S3a.jpg

Speedsolving Logo tiny.gif Alg (y) R U' L' U R' U L' D' L U2 L' D L2 U


-Sb (FL)

L4C 1CCW S3b.jpg

Speedsolving Logo tiny.gif 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)

L4C 1CCW S3a.jpg

Speedsolving Logo tiny.gif Alg R L B R' F R B' R2 F' L' F R F'


Sb (FL)

L4C 1CW S3b.jpg

Speedsolving Logo tiny.gif Alg (y) L' R' B' L F' L' B L2 F R F' L' F


-Sa (RF)

L4C 1CCW S2a.jpg

Speedsolving Logo tiny.gif Alg (y) F' L F R' F' L2 B' L F L' B R L


Sb (RF)

L4C 1CW S2b.jpg

Speedsolving Logo tiny.gif 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)

L4C 1CW S2a.jpg

Speedsolving Logo tiny.gif Alg R U' L' U2 R2 U' R' U' L U F2 R2 F2


-Sb (BR)

L4C 1CCW S2b.jpg

Speedsolving Logo tiny.gif Alg (y) L' U R U2 L2 U L U R' U' F2 L2 F2


-Sa (FL)

L4C 1CCW S1a.jpg

Speedsolving Logo tiny.gif Alg U2 R U2 R' F U2 F L' F' U2 F L F2


Sb (BR)

L4C 1CW S1b.jpg

Speedsolving Logo tiny.gif 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 (+)

L4C 1CW Ha.jpg

Speedsolving Logo tiny.gif Alg U2 R' F R F' U2 R2 B L' B L B2 R2


Hb (-)

L4C 1CCW Hb.jpg

Speedsolving Logo tiny.gif Alg (y) U2 L F' L' F U2 L2 B' R B' R' B2 L2


pia (T+)

L4C 1CW pi2a.jpg

Speedsolving Logo tiny.gif Alg (y) L2 B2 R B R' B L2 U2 F' L F L' U2


pib (T-)

L4C 1CCW pi2b.jpg

Speedsolving Logo tiny.gif 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 (-)

L4C 1CCW Ha.jpg

Speedsolving Logo tiny.gif Alg (y) F2 L U L2 F2 D F2 D' L F2 L U' L'


Hb (+)

L4C 1CW Hb.jpg

Speedsolving Logo tiny.gif Alg F2 R' U' R2 F2 D' F2 D R' F2 R' U R


pia (U-)

L4C 1CCW pi1a.jpg

Speedsolving Logo tiny.gif Alg R' U' R F2 R D' F2 D F2 R2 U R F2


pib (U+)

L4C 1CW pi1b.jpg

Speedsolving Logo tiny.gif 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+)

L4C 1CW pi1a.jpg

Speedsolving Logo tiny.gif Alg U2 F U2 F' U2 F' L F' R' F' R F' L'


pib (U-)

L4C 1CCW pi1b.jpg

Speedsolving Logo tiny.gif Alg L F R' F R F L' F U2 F U2 F' U2


pia (T-)

L4C 1CCW pi2a.jpg

Speedsolving Logo tiny.gif Alg R2 U R2 B' D R2 D' R2 B D' F2 D F2 U'


pib (T+)

L4C 1CW pi2b.jpg

Speedsolving Logo tiny.gif 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.

Uea

L4C UE (a).jpg

Speedsolving Logo tiny.gif Alg F R2 B2 D2 R U2 L' F2 D2 L U2 R F'


Ueb

L4C UE (b).jpg

Speedsolving Logo tiny.gif Alg R' F' U' F R B L F U F' L' B'
Speedsolving Logo tiny.gif Alg (y2) r' U' M' F' M U M' F R


Order 2

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

Tea

L4C TE (a).jpg

Speedsolving Logo tiny.gif Alg U R U' R2 F' L' F R2 U R' U' F' L F


Teb

L4C TE (b).jpg

Speedsolving Logo tiny.gif Alg R U' F' D2 F2 D' F' U' F D F2 D2 F U2 R'


For the following 3 * 2 cases mirror and inverse are the same.

Mirror/inverse to the side.

Lea

L4C LE (a).jpg

Speedsolving Logo tiny.gif Alg (y) F' U2 F2 R' F' R2 B L U2 L' B' R' U2


Leb

L4C LE (b).jpg

Speedsolving Logo tiny.gif Alg U2 R B L U2 L' B' R2 F R F2 U2 F


Sea

L4C SE (a).jpg

Speedsolving Logo tiny.gif Alg (y') L U2 B' R B R' U2 L' B' U2 B2 U2 B'


-Seb

L4C aSE (a).jpg

Speedsolving Logo tiny.gif Alg R' U2 B L' B' L U2 R B U2 B2 U2 B


-Sea

L4C aSE (b).jpg

Speedsolving Logo tiny.gif Alg R L B R' F R F' B' L' F R' F'


Seb

L4C SE (b).jpg

Speedsolving Logo tiny.gif Alg (y') F R F' L B F R' F' R B' L' R'
Speedsolving Logo tiny.gif Alg (y') R2 U' R2 U' R2 U2 L U L' U' R2 U2 L U2 L'


Order 2 (triple FRURUF)

Order 2

Hea

L4C HE (a).jpg

Speedsolving Logo tiny.gif Alg R U2 R2 F2 L D2 R' D2 R2 F2 L' U2
Speedsolving Logo tiny.gif Alg F (R U R' U')3 F'
Speedsolving Logo tiny.gif Alg L U2 R2 F2 R U2 R' F2 R2 U2 l' U2 M


Heb

L4C HE (b).jpg

Speedsolving Logo tiny.gif Alg U2 F2 R D2 R' F2 U2 F2 L B2 L' F2
Speedsolving Logo tiny.gif Alg R U2 L D2 L' U2 R' L U2 R D2 R' U2 L'


Order 2

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

piea

L4C piE (b).jpg

Speedsolving Logo tiny.gif Alg U F U F2 R2 F2 U' F' U' L2 B' D2 B L2


pieb

L4C piE (a).jpg

Speedsolving Logo tiny.gif Alg U' R U' R2 D' R U2 R' U' F2 U F2 D R
Speedsolving Logo tiny.gif Alg U L' U L2 D L' U2 L U F2 U' F2 D' L'


Four corners wrong (X)

8 to solve and one of these is X-PLL, leaving 7, all solveable using only RU (2-gen).


Tx is the inverse of Ux.

These can be solved with optimal movecount with 2 conjugates (first alg in the lists).

Ux

L4C UX.jpg

Speedsolving Logo tiny.gif Alg (y2) R2 B2 R F R' B2 R2 B' R' F' R B
Speedsolving Logo tiny.gif Alg U2 R2 U' R2 U2 R U R' U R' U R' U R2 U2 R


Tx

L4C TX.jpg

Speedsolving Logo tiny.gif Alg (y2) F R B' R' F' R2 F2 R' B R F2 R2
Speedsolving Logo tiny.gif Alg U2 R' U2 R2 U' R U' R U' R U' R' U2 R2 U R2


Lx is self inverting and self mirroring, only one case here.

Any variation of triple Sune/anti/fat/mirror to solve fast (but not optimally).

Lx

L4C LX.jpg

Speedsolving Logo tiny.gif Alg L' U L2 F' L D' B L B' L2 D L' F U'
Speedsolving Logo tiny.gif Alg (y') R U R' U R U' R' U R U' R' U R U2 R'


Sx and -Sx are mirror cases.

'Sune-Bruno' is the optimal alg.

Sx

L4C SX.jpg

Speedsolving Logo tiny.gif Alg U2 R' U' R U' R U R2 U R2 U2 R'


-Sx

L4C aSX.jpg

Speedsolving Logo tiny.gif Alg (y') R U R' U R' U' R2 U' R2 U2 R U2


Hx

L4C HX.jpg

Speedsolving Logo tiny.gif Alg (y) L2 R D' R' U B2 U B2 U' R D L2 R' U'
Speedsolving Logo tiny.gif Alg R U2 R2 U2 R' U R' U' R U2 R U R U' R' U


Pix

L4C piX.jpg

Speedsolving Logo tiny.gif Alg F' R D2 R' F U' F' R D2 R' F U
Speedsolving Logo tiny.gif Alg (y) R U2 R2 U' R' U R2 U' R' U' R' U2 R' U2 R
Speedsolving Logo tiny.gif Alg L U' R' U L' U' R2 U' L' U R' U' L U2




L4C

Pure CO | CPLL | L3C | L3C 1: 2-twist , 3-twist , 4-twist | E cases | X cases | edit