ELL

2011-09-18T10:41:47Z

@uguste: /* 4-flip Z-PLL */

{{Method Infobox
|name=ELL
|image=ELL.png
|proposers=[[Guus Razoux Schultz]]
|year=1981
|anames=
|variants=[[EOLL]], [[EPLL]], [[L5E]]
|steps=1
|algs=29
|moves=~11 [[STM]] (Speed-optimized) Optimal: 11.27 ([[HTM]]), 9.03 ([[STM]])
|purpose=<sup></sup>
* [[Speedsolving]], [[BLD]], [[FMC]]
}}

:''This page is about the ELL that solves edges preserving corners, for the method that does not, see [[LLEF|LL edges first]]''
'''Edges of Last Layer''', or normally '''[[ELL]]''', is a [[method]] that solves the last layer [[edge]]s of the [[3x3x3]] in one algorithm as the last step in the solution, normally after performing [[CLL]] to solve the last layer [[corner]]s. There are 29 cases in ELL, of these are three pure flips, four are [[EPLL]] and six cases are 3-cycles (besides the two in EPLL), all useful also for other methods, like [[BLD]].

ELL is also used for a method of solving the last layer edges on larger cubes. Since there are 8 of each type of [[wing]], though, ELL for larger cubes requires more than one look due to the large number of cases, see [[KBCM Step 6|KBCM]] for a compleate 3-look ELL for the [[4x4x4 cube]].

All ELL that are pure 3-cycles are used in the blindfold method [[TuRBo]].

== See Also ==
* [[CFCE]]
* [[CLL]]
* [[L5E]], [[L5EOP]]
* [[LLEF]]

== External Links ==
* [http://www.erikku.110mb.com/ELL.html Erik Akkersdijk's ELL algs]
* [http://www.speedsolving.com/forum/showthread.php?t=22737 Kirjava's ELL algs]
* [http://sa967st.webs.com/ellalgs.htm Sa967St's ELL algs]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=817 New ELL Algorithms!]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=3789 Why Not Teach CLL/ELL?]

{{ELL}}

== Intuitive:==
If you like to find algs for ELL in the MU-group, then knowing these short "proto algs" will help a lot:

* O = M' U M ... Orient
* O' = M' U' M ... Orient inverse
* P = M' U2 M ... Permute

If you combine these and also insert U-turns you can find optimal or near optimal algs for most ELLs

Example, 4-flip: '''P U2 O U2 P U'''' ... P U2 sets up for O that flips four edges (O' works the same in this case, choose the fastets), U2 P is restoration of the setup and last U is AUF.

==2-look ELL:==
Use any ELL that orients what you currently got (3 cases) from the listings below and finnish it using [[EPLL]] (4 cases). Most [[OLL]]s that preserves corner orientation will probably also do for the first look but don't count on it, some may change corner permutation while orienting the edges.

Another way to solve ELL in 2 looks is to use [[L5E]], but that is desigend for solving one more edge than this is so there will be nearly the same number of algs as full ELL (5+16).

=ELL Algorithms=
{{Algnote}}

The naming convention here is; wich edges are fliped if they where [[permute]]d and which [[EPLL]] would it be if all was correctly [[orient]]ed.
==Pure flips==

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

|-valign="top"
|
=== 2-flip (Adjacent) ===
{{case
|image=ELL 2-flip (a).jpg
|name=Pure adjacent 2-flip
|methods=[[ELL]], [[BLD]]
|optimal=13 [[HTM]], 12 [[STM]]
|text=
}}
{{Alg|r U R' U' r' U2 R U R U' R2 U2 R}}
{{Alg|R' U2 R2 U R' U' R' U2 r U R U' r'}}
{{Alg|M U M' U2 M U M U M U2 M' U M2}}
{{Alg|(y) M2 U M U2 M' U M' U M' U2 M U M'}}
{{Alg|(x') U2 M2 U R U' M2 U2 M' U' R' U M}}
{{Alg|(y) R U R' U M R U2 R' U' R' U' R U' M' R' U2 R U}}
{{Alg|(y') R2 d' M' U' M U2 F2 U M' U M U2}}

|

=== 2-flip (Opposite) ===
{{case
|image=ELL 2-flip (b).jpg
|name=Pure opposite 2-flip
|methods=[[ELL]], [[BLD]]
|optimal=14 [[HTM]], 11 [[STM]]
|text=
}}
{{Alg|M' U' M' U' M' U2 M U' M U' M U2}}
{{Alg|U M' U M' U M' U M2 U M' U M' U M' U}}
{{Alg|M' d' M d' M' U2 M d M' d M U2}}
{{Alg|U2 M' U2 M d M U' R2 U M' U' R2}}
{{Alg|U2 M' U' M' U' F2 U M U' M F2}}
{{Alg|R F R U R' F' R' F U' (y') R2' U2 R U' R' U' R}}
{{Alg|F M' F M' F2 U2 M F M F' U2}}
{{Alg|B' R B R' U R' U' M' U R U' R B' R' B M}}
{{Alg|(y) R' U R2 U R' U' R' U2 r U R U' r' R' U R}}

|-valign="top"
|

=== 4-flip ===
{{case
|image=ELL 4-flip.jpg
|name=Pure 4-flip
|methods=[[ELL]], [[BLD]]
|optimal=14 [[HTM]], 10 [[STM]]
|text=
}}
{{Alg|M' U2 M U2 M' U' M U2 M' U2 M U}}
{{Alg|U B2 M' B2 M2 U' F2 M F2 M2}}
{{Alg|M' U M' U M' U M' U' M' U M' U M' U M' U'}}
{{Alg|U R2 U2' R' F2 U2' R2' F R l F2 D2 R F2 R2' (x)}}
{{Alg|F2 M F2 M2 U' M2 F2 M' F2 U}}

|
Smile =)
|}

==EPLLs==
Please do not add algs to the EPLL section, the ones here are just examples, all EPLLs are at the [[PLL|PLL-page]], put your contributions there too, else we will end up having two separate lists and we don't want that.
----
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U-PLL a ===
{{case
|image=ELL U-PLL (a).jpg
|name=U-PLL a
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|F2 U M' U2 M U F2}}
{{Alg|M2 U' M U2 M' U' M2}}
{{Alg|L' U L' U' L' U' L' U L U L2}}

|

=== U-PLL b ===
{{case
|image=ELL U-PLL (b).jpg
|name=U-PLL b
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|F2 U' M' U2 M U' F2}}
{{Alg|M2 U M U2 M' U M2}}
{{Alg|R U' R U R U R U' R' U' R2}}

|-valign="top"
|
=== Z-PLL ===
{{case
|image=ELL Z-PLL.jpg
|name=Z-PLL
|methods=[[EPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M2 U' M E2 M E2 U M2}}
{{Alg|U2 M2 U' M2 U' M2 (x') U2 M2 U2}}
{{Alg|L F U' R U R' F' L' F U R U' R' F'}}
{{Alg|(y') M2 u M2 D' M S2 M'}}

|

=== H-PLL ===
{{case
|image=ELL H-PLL.jpg
|name=H-PLL
|methods=[[EPLL]], [[CPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|R L U2 R' L' (y) R' L' U2 R L}}
{{Alg|M2 U' M2 U2 M2 U' M2}}
{{Alg|R2 U2 R U2 R2 U2 R2 U2 R U2 R2}}

|}

==B edge solved (3-cycles)==
The cases in this group, including [[U-PLL]] a and b, are used in the edge blindfold method [[TuRBo]].

{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== RF-flip U-PLL a ===
{{case
|image=ELL 3LF (b).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M U M' U2 M U M'}}
{{Alg|(y2) M' U M U2 M' U M}}
{{Alg|(y') R U2 R' F' L' B' U2 B L F}}
{{Alg|(y'x') U2 M2 U R U' M2 U R' U}}
{{Alg|(y) R' F' R2 u2 R2 F' R2 u2 R'}}

|

=== LF-flip U-PLL b ===
{{case
|image=ELL 3RF (a).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=9 [[HTM]], 7 [[STM]]
|text=
}}
{{Alg|M U' M' U2 M U' M'}}
{{Alg|(y2) M' U' M U2 M' U' M}}
{{Alg|(y) L' U2 L F R B U2 B' R' F'}}
{{Alg|(y x') U2 M2 U' L' U M2 U' L U'}}

|-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"
|

=== RL-flip U-PLL a ===
{{case
|image=ELL 3RL (a).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y' x') U' R U M' U' R' U M}}
{{Alg|(y') r' U' R U M' U' R' U R}}

|
=== RL-flip U-PLL b ===
{{case
|image=ELL 3RL (b).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y x') U L' U' M' U L U' M}}
{{Alg|(y') r U R' U' M U R U' R'}}

|-valign="top"
|
=== LF-flip U-PLL a ===
{{case
|image=ELL 3LF (a).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y x') M' U L' U' M U L U'}}
{{Alg|(y') R U R' U' M' U R U' r'}}

|
=== RF-flip U-PLL b ===
{{case
|image=ELL 3RF (b).jpg
|name=Pure 3-cycle
|methods=[[ELL]], [[BLD]]
|optimal=10 [[HTM]], 8 [[STM]]
|text=
}}
{{Alg|(y' x') M' U' R U M U' R' U}}
{{Alg|(y') R' U' R U M U' R' U r}}

|}

==B edge in position but flipped==
The first six cases in this group are the worst of ELL, and that counts for both recognition and solving :-/
----
{|border="0" width="100%" valign="top" cellpadding="3"
|-valign="top"
|
=== 4-flip U-PLL a ===
{{case
|image=ELL U4 (a).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y') U' R2 U2 (y') M U' M' d' R2 d' M' U2 M}}
{{Alg|(y) M' U M U' M' U' M U' M' U' M U2 M' U M}}
{{Alg|M' U M U M' U2 M' U M' U M U M' U M'}}
{{Alg|F U R U' R' b' R2 (z') R' U' R' F R F' U R U2}}
{{Alg|(y) M U M2 d' R U R S' R' U' R'}}
{{Alg|(y2) (f R U R' U' f') (R' U' R' F R F' U R)}}
{{Alg|(y') M' U M U2 r U R' U M U' R U' R' U}}

|

=== 4-flip U-PLL b ===
{{case
|image=ELL U4 (b).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y) U L2 U2 (y) M U M' d L2 d M' U2 M}}
{{Alg|(y') M' U' M U M' U M U M' U M U2 M' U' M}}
{{Alg|M' U' M U' M' U2 (M' U')*2 M (U' M')*2}}
{{Alg|U R' U' R' F R F' (y') R' U2 R2 U2' R2' U' R2 U' R' U (y) R U}}
{{Alg|(y') M U' M2 d L' U' L' S L U L}}
{{Alg|(y2) (f' L' U' L U f) (L U L F' L' F U' L')}}
{{Alg|(y') M U' M' U2 r' U' R U' M' U R' U R U'}}

|-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"
|

=== BF-flip U-PLL a ===
{{case
|image=ELL U2AF (a).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M' U' M' U2 M' U M U' M' U2 M U M2}}
{{Alg|(y2) M U' M' U M' U M' U' M' U' M U M2}}
{{Alg|M' U' F2 M2 U' M U F2 U M2}}
{{Alg|(y') r2 U2 R2 U M' U' R2 U' M' U2 M2 U r2}}

|

=== BF-flip U-PLL b ===
{{case
|image=ELL U2AF (b).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M' U M' U2 M' U' M U M' U2 M U' M2}}
{{Alg|(y2) M U M' U' M' U' M' U M' U M U' M2}}
{{Alg|M' U F2 M2 U M U' F2 U' M2}}
{{Alg|(y') r' U' R U2 R2 U2 R r U R2 U R2 r' U r U2}}

|-valign="top"
|

=== BL-flip U-PLL a ===
{{case
|image=ELL U2OL (a).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M2 U M' U2 M U' M' U M U2 M U' M}}
{{Alg|M2 D R2 D S' D' R2 S2 D' S' M2}}
{{Alg|(y) R' U' R (x) U (x) U R2 U' R' (x') U' (x') U R2 U2 R'}}
{{Alg|(y') U' M' U M2 U' M' U F2 U M U' M' F2}}
{{Alg|(y2) M2 U M U' M' U' M' U M' U M' U' M}}
{{Alg|U' F R2 U' R' F U R2 U' R' F' U R U F' U}}
{{Alg|M2 U F2 U M' U' M2 F2 U' M}}
{{Alg|(y') r2 U M2 U2 M' U' R2 U' M' U R2 U2 r2}}

|

=== BR-flip U-PLL b ===
{{case
|image=ELL U2OR (b).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M2 U' M' U2 M U M' U' M U2 M U M}}
{{Alg|M2 D' L2 D' S D L2 S2 D S M2}}
{{Alg|(y) R U R' (x') U' (x') U' R2 U R (x) U (x) U' R2 U2 R}}
{{Alg|(y) U M' U' M2 U M' U' F2 U' M U M' F2}}
{{Alg|(y2) M2 U' M U M' U M' U' M' U' M' U M}}
{{Alg|R' F2 U F R' U' F2 U F R U' F' U' R}}
{{Alg|M2 U' F2 U' M' U M2 F2 U M}}
{{Alg|(y) r U r' R2 U R2 U R2 U2 R2 U2 r U' r' U2}}

|-valign="top"
|

=== BR-flip U-PLL a ===
{{case
|image=ELL U2AR (a).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y) M' U' M' U2 M U' M2 U' M' U}}
{{Alg|(y2) M' U' M'2 U' M U2 M' U' M'}}

|
=== BL-flip U-PLL b ===
{{case
|image=ELL U2AL (b).jpg
|name=3-cycle 1-flip
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y') M' U M' U2 M U M2 U M' U'}}
{{Alg|(y2) M' U M2 U M U2 M' U M' U'}}
|}

==No edges in position==

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

|-valign="top"
|
=== LF-flip Z-PLL ===
{{case
|image=ELL Z2AFR.jpg
|name=Adjacent flip Z-PLL a
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M U' M' U2 M U' M U' M' U2 M U' M2}}
{{Alg|(y') F R U R' U' F2 L' U' L U F}}
{{Alg|(y') R2 U' R' U' R U R U R2 U' M' U R' U' R2 r'}}
{{Alg|(y2) f R U R' U' f2 z U' R' U R B}}
{{Alg|(y') R' F' U' F U R U F R U R' U' F' U'}}

|

=== LB-flip Z-PLL ===
{{case
|image=ELL Z2ABR.jpg
|name=Adjacent flip Z-PLL b
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y2) M' U M U M' U2 M U' M' U' M}}
{{Alg|(y2) F R U R' U' F' R' U' R' F R F' U R}}

|-valign="top"
|

=== FB-flip Z-PLL ===
{{case
|image=ELL Z2ORL.jpg
|name=Opposite flip Z-PLL a
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M' U M U' M' U M U M' U2 M}}
{{Alg|(y') R2' U' F U R' U' R2 F' R' U R U' R2}}

|

===LR-flip Z-PLL ===
{{case
|image=ELL Z2OFB.jpg
|name=Opposite flip Z-PLL b
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|(y) M' U' M U M' U' M U' M' U2 M}}
{{Alg|(y) R2' U R' U' R F R2 U R U' F' U R2}}

|}

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

|-valign="top"
|

=== 4-flip Z-PLL ===
{{case
|image=ELL Z4.jpg
|name=4-flip Z-PLL
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|F2 M F2 U' M2 U B2 M B2}}
{{Alg|(x) U2 M U2 (x') U' M2 U (x') U2 M U2 (x)}}
{{Alg|M U' M' U2 M U' M2 U M U2 M' U M}}
{{Alg|(y) M' U M U2 M' U M'2 U' M' U2 M U' M'}}
{{Alg|(y) R2' U2 l D (x) U2' R2' U2 F2 R2 U2' R2' F R' U2' R2}}
{{Alg|(y) F' R E2 R' F U2 F' R E2 R' F U2}}
{{Alg|r' u M2 u' r U2 r' u M2 u' r U2}}
{{Alg|r' U M2 U' r U2 r' U M2 U' r U2}}

|

=== 4-flip H-PLL ===
{{case
|image=ELL H4.jpg
|name=4-flip H-PLL
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M' U2 M' U2 M' U' M U2 M U2 M U}}
{{Alg|r U R' U' M2 U R U' R' U' M'}}
{{Alg|M U R U R' U' M2 U R U' r'}}
{{Alg|(x) U R' U' M2 U R U' M' (x') U' M' U}}
{{Alg|R2' U2 l D2 (x) U2' R2 F R2 U2' (x') D2 (x) R' U2 R2 U}}
{{Alg|F2 M' F2 M2 U' M2 F2 M F2 U}}

|-valign="top"
|

=== FR-flip H-PLL ===
{{case
|image=ELL H2A.jpg
|name=Adjacent flip H-PLL
|methods=[[ELL]]
|optimal=
|text=
}}
{{Alg|M' U' M U' M' U' M U' M' U' M U}}
{{Alg|(y) M' U M U M' U M U M' U M U'}}
{{Alg|(y) R' U2 R U B L U2 L' U' B'}}
{{Alg|(y') L' U2 L U F R U2 R' U' F'}}
|

=== FB-flip H-PLL ===
{{case
|image=ELL H2O.jpg
|name=Opposite flip H-PLL
|methods=[[ELL]]
|optimal=11 [[STM]] 15 [[HTM]]
|text=
}}
{{Alg|M' U M U2 M' U (x') U' R U M U' R' U (x)}}
{{Alg|M' U M2 U2 M' U M' U2 M' U' M U' M}}
{{Alg|R' U2 R U' R' U' R' F R2 U R' U' R' F' R2}}
{{Alg|(yz) U' r2 U2 r' R' U M' U2 M' U' r R U'}}
{{Alg|F M' F U M2 U2 M2 U F' M F'}}
{{Alg|R U R' U' M' U2 R' U' R2 U' r' U R' U R U2}}

|}

{{ELL}}

[[Category:Cubing Terminology]]
[[Category:Abbreviations and Acronyms]]
[[Category:Methods]]
[[Category:3x3x3 Methods]]
[[Category:Last Layer Methods]]
[[Category:Algorithms]]
[[Category:Sub Steps]]

__NOTOC__

CxLL T F

2011-02-14T19:21:48Z

@uguste: /* COLL */

== T F ==
This case and the case [[CxLL U F|U F]] are inverses of each other so the same algorithm (9 move commutator or mirror) can be used to solve both.
<br><hr>
{|
|| [[image:CxLL T F.jpg|128px|]]
| valign="top"| As for all T cases you look at two "bars" of stickers, one at Fur-Ful and one at Urb-Ulb. In this case the bar at Ub has got one colour and the bar at the F-side has got two opposite colours.
|}

===COLL===
* (y2 x') U' R2 U' L2 U R2 U' L2 U2 (x)
* (y') l' U2 R' D2 R U2 R' D2 R2 (x')
* F U' r' F R2 F' r U R2 F'
* (U) F' R' F U2 F' R F R' U2 R
* (U2) F R U R' U' R U' R' U' R U R' F'

===CLL===
* L' U2 R d' R' U' R d R' U2 L ... X Y -X (Conjugate)

===CMLL===
* ...

===CLLEF===
* y2 R B' R' B y U2 R U2 B2 L' B' L B' R

===CF / 2x2x2 (Waterman)===
* ...

===EG===
'''EG 2''' --> 2x2x2

'''EG 1'''
* ...

'''EG 0'''
* ...

==Navigator==
{{CxLLnav}}

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ELL

CxLL T F