View source for Last Three Corners

{{Substep Infobox
|name=Last Three Corners
|image=L3C.png
|proposers=[[Anthony Snyder]], [[Ryan Heise]]
|anames=L3C
|variants=[[L4C]], [[CxLL]]
|subgroup=
|algs=24
|moves=~10 [[HTM]], 9.56 optimal [[HTM]]
|purpose=<sup></sup>
* [[Speedsolving]], [[FMC]], [[BLD]]
|previous=[[L3C cube state]]
|next=[[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:'''
* [[Last Four Corners]]
* [[Beyer-Hardwick Method]]

== External links ==
* [http://www.ryanheise.com/cube/corner_3_cycles.html] 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-cycle]]s, 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===
*'''Pure twists''' you can find at the [[Corner orientation|Corner orientation page]].
*'''Only permutation''', see [[CPLL]], corner permutation of the last layer.''

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==
{{Algnote}}
----

{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== uFl-Urb ===
{{case |image=L3C case1(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}} 
{{Alg|R2 D R' U2 R D' R' U2 R'}}

|
=== uRb-Ufl ===
{{case
|image=L3C case1(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) L2 D' L U2 L' D L U2 L}}

|-valign="top"
|
=== Ufl-uRb ===
{{case |image=L3C case1(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) L' U2 L' D' L U2 L' D L2}}

|
=== Urb-uFl ===
{{case |image=L3C case1(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R U2 R D R' U2 R D' R2}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== ufL-uRb ===
{{case |image=L3C case2(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y x) R2 D2 R U2 R' D2 R U2 l}}

|

=== urB-uFl ===
{{case |image=L3C case2(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(x) L2 D2 L' U2 L D2 L' U2 r'}}

|-valign="top"
|

=== uFl-urB ===
{{case |image=L3C case2(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|r U2 L D2 L' U2 L D2 L2 (x')}}

|
=== uRb-ufL ===
{{case |image=L3C case2(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|(y) l' U2 R' D2 R U2 R' D2 R2 (x')}}

|-valign="top"
| bgcolor="f0f4f8" |
The following four cases are mirror + inverses of the first so you only need '1 alg' for all.
| bgcolor="f0f4f8" |
Mirror to the side and inverse in diagonal.

|-valign="top"
|
=== ufL-Urb ===
{{case |image=L3C case3(a).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y) r' U' R U L U' R' U (x)}}
{{Alg|(x') R U R' D R U' R' D' (x)}}
|
=== urB-Ufl ===
{{case |image=L3C case3(b).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y2) l U L' U' R' U L U' (x)}}
{{Alg| r U R' U' r' F R F'}}
|-valign="top"
|
=== Ufl-urB ===
{{case |image=L3C case3(c).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(x') U L' U' R U L U' l'}}

|
=== Urb-ufL ===
{{case |image=L3C case3(d).jpg
|name=3-cycle commutator
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|(y x') U' R U L' U' R' U r}}
{{Alg|(x') D R U R' D' R U' R' (x)}}
|-valign="top"
|
=== ufL-urB ===
{{case |image=L3C case4(a).jpg
|name=Niklas
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|R' U L U' R U L' U'}}

|
=== urB-ufL ===
{{case |image=L3C case4(b).jpg
|name=Niklas b
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|U L U' R' U L' U' R}}

|-valign="top"
|
=== uFl-uRb ===
{{case |image=L3C case5(a).jpg
|name=Anti Niklas a
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|B L' U2 L B' L' B U2 B' L}}
{{Alg|(y2 x') U2 R2 D R U2 R' D' R U2 R U2 (x y2)}}
{{Alg|(y' x) R2 U2 L U R2 U' L' U R2 U R2 (x' y)}}
|
=== uRb-uFl ===
{{case |image=L3C case5(b).jpg
|name=Anti Niklas b
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=10 [[HTM]]
|text=
}}
{{Alg|L' B U2 B' L B L' U2 L B'}}
{{Alg|(y2 x') U2 R' U2 R' D R U2 R' D' R2 U2 (x y2)}}
{{Alg|(y' x) R2 U' R2 U' L U R2 U' L' U2 R2 (x' y)}}
|}

[[Category:3x3x3 last layer substeps]]

__NOTOC__