Last Three Corners

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Last Three Corners
L3C.png
Information
Proposer(s): Anthony Snyder, Ryan Heise
Proposed: unknown
Alt Names: L3C
Variants: L4C, CxLL
Subgroup:
No. Algs: 24
Avg Moves: ~10 HTM, 9.56 optimal HTM
Purpose(s):
Previous state: L3C cube state
Next state: Solved cube state

L3C cube state -> Last Three Corners step -> Solved cube state


The Last Three Corners step is the step between the L3C cube state and the Solved cube state.

Last three corners, abbrevaited L3C (or 3LC), is a method that solves three of the last layer corners preserving all the rest, a sub group of L4C, ZBLL and ZZLL.

Usage: besides L4C, CxLL, ZBLL and ZZLL it is useful for FMC and the 3-cycles are nice for Freestyle BLD. L3C is the final stage in the Snyder Method.

See also:

External links

  • [1] Ryan Heise explains an intuitive approach to solve the last three corners.

L3C Cases

The group have 27 cases including solved, 3*3 orientations and 3 permutations. Most of the cases (18) are pure 3-cycles, the rest are pure twists U, T, L, S and -S. Some of the twist occures 2 times (U, T and L) and the T-twist is the same as the U-twist if the puzzle is reoriented. Subtracting the duplicates and solved it will be 22 cases left. 16 of them are pure L3C cases and listed at this page, the rest are in one of two sub groups.

Sub groups

The naming system used here is adapted to BLD, the ULB corner is always the solved one and URF is the 'buffer' with U as the buffer sticker. The piece in the buffer will go to two places, either URB or UFL and the sticker in U will go to any of the three stickers on each goal position and that sticker is in uppercase, the other two letters will be in lowercase. The second half of the name is the same but from the goal position of the first. The last piece will always go to the first buffer position so that will not be in the name.

Example: CW A-PLL is Ufl-Urb and CCW A-PLL is Urb-Ufl.

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 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.

uFl-Urb

L3C case1(a).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

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


uRb-Ufl

L3C case1(b).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

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


Ufl-uRb

L3C case1(c).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

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


Urb-uFl

L3C case1(d).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

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


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.

ufL-uRb

L3C case2(a).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

Speedsolving Logo tiny.gif Alg (y x) R2 D2 R U2 R' D2 R U2 l


urB-uFl

L3C case2(b).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

Speedsolving Logo tiny.gif Alg (x) L2 D2 L' U2 L D2 L' U2 r'


uFl-urB

L3C case2(c).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

Speedsolving Logo tiny.gif Alg r U2 L D2 L' U2 L D2 L2 (x')


uRb-ufL

L3C case2(d).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM

Speedsolving Logo tiny.gif Alg (y) l' U2 R' D2 R U2 R' D2 R2 (x')


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.

ufL-Urb

L3C case3(a).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif Alg (y) r' U' R U L U' R' U (x)
Speedsolving Logo tiny.gif Alg (x') R U R' D R U' R' D' (x)

urB-Ufl

L3C case3(b).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif Alg (y2) l U L' U' R' U L U' (x)
Speedsolving Logo tiny.gif Alg r U R' U' r' F R F'

Ufl-urB

L3C case3(c).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif Alg (x') U L' U' R U L U' l'


Urb-ufL

L3C case3(d).jpg

Name: 3-cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif Alg (y x') U' R U L' U' R' U r
Speedsolving Logo tiny.gif Alg (x') D R U R' D' R U' R' (x)

ufL-urB

L3C case4(a).jpg

Name: Niklas
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

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


urB-ufL

L3C case4(b).jpg

Name: Niklas b
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM

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


uFl-uRb

L3C case5(a).jpg

Name: Anti Niklas a
Used in: L3C, L4C, BLD
Optimal moves: 10 HTM

Speedsolving Logo tiny.gif Alg B L' U2 L B' L' B U2 B' L
Speedsolving Logo tiny.gif Alg (y2 x') U2 R2 D R U2 R' D' R U2 R U2 (x y2)
Speedsolving Logo tiny.gif Alg (y' x) R2 U2 L U R2 U' L' U R2 U R2 (x' y)

uRb-uFl

L3C case5(b).jpg

Name: Anti Niklas b
Used in: L3C, L4C, BLD
Optimal moves: 10 HTM

Speedsolving Logo tiny.gif Alg L' B U2 B' L B L' U2 L B'
Speedsolving Logo tiny.gif Alg (y2 x') U2 R' U2 R' D R U2 R' D' R2 U2 (x y2)
Speedsolving Logo tiny.gif Alg (y' x) R2 U' R2 U' L U R2 U' L' U2 R2 (x' y)