Difference between revisions of "L5E"

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'''E35''' is a method that solves the last eight edges of the U and D layers, first three D layer edges are done and then the last five ones. Always preserving all corners and E-slice edges. In most cases the first part also solves the centres.
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{{Substep Infobox
 +
|name=L5E
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|image=L5E.png
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|proposers=
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|year=
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|anames=Last five edges
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|variants=[[L5EOP]], [[L5EP]]
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|subgroup=
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|algs=245 for full L5E, 5 for L5EO and 16 for L5EP
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|moves=about 14
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|purpose=Speedsolving
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|previous=[[5 Edges Missing cube state]]
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|next=[[Solved cube state]]
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}}
  
E35 is not a compleate brute force method, it uses a combination of intuition and algorithms, an advanced user even include [[ELL]] in the method to save turns in some cases but most times you end in [[EPLL]] or 5 edge permutation. It is much as [[Roux]] last step but here orientation is done after all centres are solved to make recognition easier/faster so the M-permut used last in Roux is not really useful here (you solve centres and BD before orient instead of RU/LU after).
+
'''L5E, Last five edges''', is an experimental method that solves five [[edges]], the four in U and one in the D layer, preserving all other pieces.
  
'''Short description:'''
+
[[ELL]] is a sub group of L5E, all ELL's may be solved in two steps using this method.
* '''E3 part''' First pair up RD and LD edges, then place them together with R and L centres or simply do one at the time, the first one as a pair with the centre and the second using AUF M' U/U'/U2 M, last palce BD + B centre as a pair.
 
* '''E5 part''' this part has got two main sub-parts, first orient the edges using the Roux M' U M style (5 cases, newer the worst 6 edge case of Roux). If possible also place FD during orientation, else do it after using M' U2 M and end in [[EPLL]]. You can also first orient and then permute all five edges in one go (EP5).
 
  
E35 may be used in [[CF]] if the E-slice is solved after the corners or in any method that solves columns first, like doing all pairs first and then [[CxLL|CMLL]] (or CMSLL). The E5 part is a stand alone method that can be used for Roux if the BD edge and centres are solved before edge orientation.
+
== Description ==
 +
There are two main sub-parts. First the edges are oriented using M' U M like in Roux; there are 5 cases for this, and the worst case in Roux (6 edges) is impossible. Then the edges must be permuted; you can place FD during orientation or right after using [U] M' U2 M (named 'P') and end with [[EPLL]], or just permute all five edges in one step.
  
==Intermediate system for E5==
+
L5E can be useful for [[Corners First]] if the E-slice, centres and three FL edges are solved after the corners. It is also useful in any method that starts with [[columns]], such as one which does the F2L pairs first and then finishes with [[CxLL|CMLL]], it is an alternative to the last step of [[Roux]] if the centres are placed together with the BD edge at first, also for any LBL style, cross minus one edge at first and then the LL corners have been finished with [[CLL]] or [[CMLL]] or the same for Fridrich with 2-look [[OLL]], corners first, then L5E orientation, place FD using P if it was not solved and end it all in PLL as usally.
===Intuitive:===
+
 
This intuitive style is not all intuitive because you need to know EPLL. First orient all unorientd edges, then place the FD edge to it's correct position and end the solve in EPLL. For that you basicly need this:
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==Zipper L5E/L5E-FR==
 +
Zipper L5E or L5E-FR is used in the [[Zipper Method]], specifically in [[Zipper Method#Zipper-b|Zipper-b]]. The difference between this variant and standard L5E is that instead of the FD edge, the FR edge is permuted. This approach, however, cannot be solved [[2-Gen]] (with only M and U moves) like standard L5E.
 +
 
 +
==L5EP==
 +
{| border="1" class="infobox-template" style="float: right; border-collapse:collapse; width: 22em; font-size: 90%; margin: 0 0 10px 10px;"
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|
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{| border="0" cellpadding="3" bgcolor="#F0F0F0" cellspacing="2" style="color:black; text-align:center; width: 100%"
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|-
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| bgcolor="#D0DFEE" colspan="2" style="font-size: 125%;" | '''{{{name|}}} L5EP'''
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|-
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| colspan="2" style="font-size:90%;"| {{#if:{{{image}}}|[[Image:{{{image|L5EP2.png}}}]]|}}
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|-
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| bgcolor="#E0E8EF" colspan="2" | '''Information'''
 +
|-
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| bgcolor="#F0F0F0"  align="right" | '''Proposers:'''
 +
| align="left" |
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* L5EP-U/E: [[Duncan Dicks]]
 +
* L5EP-U/D: [[Mike Bennett]]
 +
|-
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| bgcolor="#F0F0F0"  align="right" | '''Proposed:'''
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| align="left" |
 +
* L5EP-U/E: 2004
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* L5EP-U/D: 2005
 +
|-
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| bgcolor="#F0F0F0"  align="right" | '''No. Algs:'''
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| align="left" | 16
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|-
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| bgcolor="#F0F0F0"  align="right" | '''Avg Moves:'''
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| align="left" | ~7-9
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|-
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| bgcolor="#F0F0F0"  align="right" | '''Purpose:'''
 +
| align="left" | {{{purpose|[[Speedsolving]]}}}
 +
|-
 +
|}
 +
|}
 +
 
 +
'''Last 5 Edges Permute''', often abbreviated '''L5EP''', is a [[3x3x3|3x3]] subset that permutes the 4 edges on the last layer and an edge from another layer while simultaneously preserving all other pieces.
 +
 
 +
The five affected edges must be correctly oriented for L5EP to work. L5EP is often used in methods like [[Petrus-W]] and [[Portico]], when there are only five edges left to solve on the cube.
 +
 
 +
There are 16 algorithms for L5EP, 10 excluding mirrors and 7 excluding mirrors and [[EPLL]].
 +
 
 +
===Variants===
 +
Although it is generally agreed upon that L5EP permutes the four U layer edges, the location of the fifth edge is not always clear. Because of that, multiple variants exist:
 +
 
 +
'''Standard L5EP (L5EP-U/D):''' This is the original proposal by Mike Bennet where the UF, UR, UB, and UL edges and an edge on the D layer are permuted simultaneously. It originated as an alternate strategy for the Roux method's last six edges step.[https://sites.google.com/view/methodlibrary/steps/l5ep]. It was independently proposed again in 2006 by [[James Straughan]] as part of the [[MI1]] method and again in 2008 by [[Jason Baum]][https://www.speedsolving.com/threads/new-idea-the-partial-cross-method.4259/post-52705]. That same year, [[Kenneth Gustavsson]] developed a naming scheme and James Straughan developed a way to represent the cases in images[https://www.speedsolving.com/threads/last-edges-roux-amoung-other-methods.6754/post-91969]. Any case can be simplified to an [[EPLL]] by first permuting the D layer edge. Intuitive L5EP can also be used, but it is recommended to learn algorithmic L5EP due to the faster execution and low number of algorithms.
 +
 
 +
'''EHKPLL:''' EHKPLL is a subset of [[HKPLL]] which was invented for [[Hawaiian Kociemba]]. Here, the fifth permuted edge is the DR edge.
 +
 
 +
'''L2L4 / Zipper L5EP (L5EP-U/E):''' This variant was first used in Duncan Dicks' [[L2L4]] method.[https://sites.google.com/view/methodlibrary/3x3-methods/l2l] In Duncan Dicks' variant, the F layer is the last layer and the fifth edge is on the S layer at UR. This same variant is also used in the [[Zipper Method]] and permutes the U layer edges and either the FR or BR edge.
 +
 
 +
===See also===
 +
* [[EPLL]]
 +
* [[L2L4]]
 +
* [[MI1]]
 +
* [[PCMS]]
 +
* [[Hawaiian Kociemba]]
 +
* [[Portico]]
 +
* [[Zipper]]
 +
* [[Petrus-W]]
 +
* [[Mehta]]
 +
 
 +
==External links==
 +
* [https://docs.google.com/document/d/1kb4JFX2WY5mh0gchb9gkbI-RoINaFfX5w0i4VJ1z5ek/edit?usp=sharing Standard L5EP Algorithms]
 +
* [https://docs.google.com/spreadsheets/d/1rnTlbYK3nWsFi743198UZMltqU_WtcIIasC_8EGUjhA Zipper L5EP and EHKPLL]
 +
* [https://docs.google.com/document/d/1oZO7TXjWXZOiokOaENHd-7b5IjIvYQ_Vt5yFYNziI5A/edit?usp=sharing Standard L5EP Algorithms]
 +
 
 +
==Intermediate system==
 +
 
 +
===Intuitive===
 +
This style is not completely intuitive, because it is still necessary to know [[EPLL]]. First orient all unoriented edges, then place the FD edge to its correct position and finally end the solve in EPLL. The necessary intuitive steps are:
  
 
* P = M' U2 M
 
* P = M' U2 M
 
 
* O = M' U M
 
* O = M' U M
 
* O' = M' U' M
 
* O' = M' U' M
* O2 = P
 
  
From that plus some U turns you can solve any case, example: O U P = (M' U M) U (M' U2 M). O solves orientation U P places FD edge and then the EPLL solves permutation for the last four edges, all now in LL (if it did not skip, it is a 1:12 chance).
+
Using that plus some U turns you can solve any case, even all [[ELL]] case. For example, O U P = (M' U M) U (M' U2 M) is a sample algorithm which solves orientation, then places FD. There is a 1 in 12 chance that EPLL is skipped; otherwise there is one algorithm left.
 +
 
 +
There is another notation which can make it shorter to write algorithms:
 +
 
 +
* F(moves) = F2 (moves) F2
 +
 
 +
It is important here that the moves inside the parentheses keep the corners solved, so that they will still be correct after this algorithm. An example is the [[U-perm]], F(U P U) = F2 (U M' U2 M U) F2. F(O U') is a nice way to solve orientation and place FD all at once if the FD edge is in the middle of three unoriented edges in LL.
  
The algorithms for some cases can be shorter if you also add this to the system:
+
===Using algorithms===
 +
The intuitive style lets you find and understand the orientation algorithms yourself. Another approach is to learn the algorithms instead of finding them; the cases are:
  
* F() = F2 ( moves ) [u] F2
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{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
 +
| colspan="2" | <center>'''Basic orientations'''</center>
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:FUL Solved.jpg|80px]]
 +
|NAME=''Intuitive solution''
 +
|ALGO=''(Possibly optimised) alg''
 +
|INFO=''Comment''
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EO5 2 adjacent.jpg|80px]]
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|NAME=O U2 O
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|ALGO=(M' U M) U2 (M' U M)
 +
|INFO=Orients UL and UB.
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EO5 2 opposite.jpg|80px]]
 +
|NAME=O U' O
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|ALGO=(M' U M) U' (M' U M)
 +
|INFO=Orients UF and UB.
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EO5 4.jpg|80px]]
 +
|NAME=P U2 O'
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|ALGO=(M' U2 M) U2 (M' U' M)
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|INFO=Orients UR, UF, UL and UB
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EO5 1.jpg|80px]]
 +
|NAME=O U O'
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|ALGO=(M' U M) U (M' U' M)
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|INFO=Orients FD and UB
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EO5 3.jpg|80px]]
 +
|NAME=O'
 +
|ALGO=(M' U' M)
 +
|INFO=Orients FD, UR, UF and UL
 +
}}
 +
|---
 +
| colspan="2" | <center>''All images show white on top (U) and green in front (F).''</center>
 +
|}
 +
''More algs are at the [[L5EOP|L5EOP page]]''
  
The U turn can be any U, U' U2 or no U turn depending on how U moves inside the parentesis of the "function". F(U P) makes the usual 7 turn U-PLL = F2 (U M' U2 M) U F2. F(O) is a nice way to solve orientation and place FD in one go if it is in the middle of three unoriented edges in LL, just AUF as you where about to do only O.
+
Sometimes this will also solve the FD edge; the images show where the FD edge must be for the algorithm to solve it, but otherwise you should simply treat the yellow sticker as white. If you learn these positions, it can also be useful to learn the mirror algorithm for the case where FD is on the opposite side from the image. The easiest example is to use O' instead of O for the case with three flipped edges on U. Just like the intuitive step, if FD is not solved use P, and either way finish with [[EPLL]].
  
===Using algorithms:===
+
==Semi-advanced system==
The intuitive style lets you find and understand the algorithms you need to orient the 5 cases that are possible for the orientation part but another approach is to learn the algorithms instead of finding them.
 
  
'''Basic orientations:'''
+
[[L5EOP]] is an alternative to L5E, that always solves the FD edge while orienting ('P'lace). Then the last step will always be EPLL.
  
'''FD oriented:'''
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===FD placement + EPLL (L5EP)===
* O U2 O ... (M' U M) U2 (M' U M) ... orients UL and UB
+
Another possibility for improving the intermediate style is to permutate the last five edges in one step. This only requires 16 algorithms in total, so counting the 5 orientations creates a system that solves L5E in two short steps. Even if you know this, it is still useful to place FD without extra moves if possible, since EPLL recognition is very fast.
* O U' O ... (M' U M) U' (M' U M) ... orients UF and UB
 
* P U2 O ... (M' U2 M) U2 (M' U M) ... orients UR, UF, UL and UB
 
  
'''FD unoriented:'''
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We will introduce the following function:
* O U O ... (M' U M) U (M' U M) ... orients FD and UB
+
* f(moves) = f2 (moves) [U] f2 ... This is the same as the F() function above, but with double layer f turns. Note that sometimes the adjusting U turns are not mentioned.
* O ... (M' U M) ... orients FD, UR, UF and UL
 
  
Sometimes you will solve FD permutation while doing this. If you learn the position of the edge before the orientation that leads to a solve you can for some situations also learn to use the mirror algorithm instead when the FD edge is on the opposite side from where you normally solve it, the easiest example is to use O' (M' U' M) instead of O (M' U M). In the cases where you cannot solve FD permutation while orienting you use AUF + P to solve it, it is at the most 4 turns, then EPLL.
+
Here are the algorithms for permutation of all 5 edges; make sure to use AUF to place the FD edge at the position it has in the image.
  
==Semi advanced system for E5==
+
{| style="border: 1px solid #808080; color: black; background-color: #FAFAFA;" cellspacing="0" cellpadding="2"
'''Orientations with FD permutation:'''<br>
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| colspan="2" | <center>'''Double two cycle permutations'''</center>
In many cases you can solve FD permutation wile orienting in the same number of turns as you do only orientation. For the rest of the cases it is a bad idéa to learn algorithms because they would most times end in the same turns as do anyway to solve FD after orientation or if not the length of the algorithm is of the same length as the 2-step or at least almost. But there are a number of good cases, here is the list:
+
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:FUL Solved.jpg|80px]]
 +
|NAME=''Intuitive solution''
 +
|ALGO=''(Possibly optimised) alg''
 +
|INFO=''Comment''
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 22 A.jpg|80px]]
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|NAME=F(H-PLL)
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|ALGO=M U M2 U2 M2 U M'
 +
|INFO=Swaps UF<->DF and UR<->UL
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 22 B1.jpg|80px]]
 +
|NAME=F(Z-PLL)
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|ALGO=(y') r2 U' 2x(M E2) U r2
 +
|INFO=Swaps UR<->DF and UL<->UB
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 22 B2.jpg|80px]]
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|NAME=F(Z-PLL')
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|ALGO=(y') r2 U 2x(M E2) U' r2
 +
|INFO=Swaps UL<->DF and UR<->UB
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 22 H.jpg|80px]]
 +
|NAME=[[PLL#H Permutation|H-PLL]]
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|ALGO=Ra U2 Ra' (y) Ra' U2 Ra
 +
|INFO=Swaps UR<->UL and UF<->UB
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 22 Z.jpg|80px]]
 +
|NAME=[[PLL#Z Permutation|Z-PLL]]
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|ALGO=M2 U' 2x(M E2) U M2
 +
|INFO=Swaps UR<->UB and UL<->UF
 +
}}
 +
|---
 +
| colspan="2" | <center>'''3-cycle permutations'''</center>
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 3 A.jpg|80px]]
 +
|NAME=P
 +
|ALGO= (M' U2 M)
 +
|INFO=Cycles UF->DF->UB
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 3 B1.jpg|80px]]
 +
|NAME=f(d' P)
 +
|ALGO=(y') r2 U' (M' U2 M) U' r2
 +
|INFO=Cycles UL->UB->DF
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 3 B2.jpg|80px]]
 +
|NAME=f(d P)
 +
|ALGO=(y') r2 U (M U2 M') U r2
 +
|INFO=Cycles UR->UB->DF
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 3 U1.jpg|80px]]
 +
|NAME=[[PLL#U Permutation : b|U-PLL]]
 +
|ALGO=F2 U (M' U2 M) U F2
 +
|INFO=Cycles UF->UL->UR
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 3 U2.jpg|80px]]
 +
|NAME=[[PLL#U Permutation : a|U-PLL']]
 +
|ALGO=F2 U' (M' U2 M) U' F2
 +
|INFO=Cycles UF->UR->UL
 +
}}
 +
|<center> </center>
 +
|---
 +
| colspan="2" | <center>'''5-cycle permutations'''</center>
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 H1.jpg|80px]]
 +
|NAME=P U P
 +
|ALGO=(M' U2 M) U (M' U2 M)
 +
|INFO=Cycles UF->UL->UR->DF->UB
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 H2.jpg|80px]]
 +
|NAME=P U' P
 +
|ALGO=(M' U2 M) U' (M' U2 M)
 +
|INFO=Cycles UF->UR->UL->DF->UB
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 Z1.jpg|80px]]
 +
|NAME=P Z-PLL
 +
|ALGO=2x(M2 U) (M U2 M')
 +
|INFO=Cycles UF->UR->UB->UL->FD
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 Z2.jpg|80px]]
 +
|NAME=P Z-PLL'
 +
|ALGO=2x(M2 U') (M U2 M')
 +
|INFO=Cycles UF->UL->UB->UR->DF
 +
}}
 +
|---
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 U1.jpg|80px]]
 +
|NAME=P U-PLL
 +
|ALGO=(M' U2 M') U' (M' U2 M) U' M2
 +
|INFO=Cycles UF->DF->UB->UL->UR
 +
}}
 +
|
 +
{{Casebox
 +
|IMAGE=[[Image:EP5 5 U2.jpg|80px]]
 +
|NAME=P U-PLL'
 +
|ALGO=(M' U2 M') U (M' U2 M) U M2
 +
|INFO=Cycles UF->DF->UB->UR->UL
 +
}}
 +
|
 +
|---
 +
| colspan="2" | <center>''These images have white on top (U) and green in front (F). Darker pieces change positions.''</center>
 +
|}
  
''Later...''
+
==Advanced system==
 +
The most advanced system is to solve all edges in one step. Solving the last five edges in a single step contains 245 algorithms and reduces the number of looks and the movecount. There are a few variants of L5E. One solves four edges of the U layer and one on the D layer. The first known developed and published method to use this single step L5E is the [[Nautilus]] method. Another L5E variant is one where the four U layer edges and an edge in the E layer are solved. This was first proposed for the [[Zipper]] method. A final L5E variant that has been proposed occasionally is one which solves three edges of the U layer and two edges on the D layer. This can be used in corners first and related methods such as [[Waterman]], [[Roux]], and [[LMCF]].
  
Another reason for not learning all algorithms for placing FD while orienting is that you can do the permutation for all last five edges in one go using only 9 extra algorithms above the usual 4 EPLL's, a total of 13 algs, add to that the needed 5 orientations and you got a system of 18 algorithms to solve E5 in two short steps. But it is still recomended to use as many of the short algorithms for O + FD P because recognition is faster for EPLL than it is for most the of rest of the cases.
+
==See also==
 +
* [[ELL]]
 +
* [[PCMS]]
 +
* [[L5EOP]]
 +
* [[L5EP]]
  
''Permutation algorithms will also be added later...''
+
==External Links==
 +
* [https://docs.google.com/spreadsheets/d/161l8hKPIyuVa_5qW105r6VqcY_lzqCbesDgUS-nUSpQ/edit?usp=sharing L5E and L5EP Algorithms]
 +
* [https://docs.google.com/document/d/1oZO7TXjWXZOiokOaENHd-7b5IjIvYQ_Vt5yFYNziI5A/edit L5EP Algorithms]
 +
* [https://docs.google.com/spreadsheets/d/1feWj3FOAc6cH4Zpt_zGxuwJt8w_4aSkkmxoxpYzWdBA/edit?usp=sharing L5EP Algorithm Spreadsheet]
 +
* [https://docs.google.com/spreadsheets/d/1VPtGoN_yDoWbBnPVgPWkqlNfj9YjN4LykrpKvUjrw-g Zipper L5E Algorithms]
  
==Advanced system for E5==
+
[[Category:Experimental methods]]
The advanced style is to create algorithms for all extra ELL cases that solves E5 in one go. This has not ben done by anybody yet, it's your chance to get famous, create the system and post the algorithms with descriptions here =)
+
[[Category:3x3x3 other substeps]]
 +
[[Category:Acronyms]]

Latest revision as of 13:20, 1 July 2023

L5E
L5E.png
Information
Proposer(s):
Proposed:
Alt Names: Last five edges
Variants: L5EOP, L5EP
Subgroup:
No. Algs: 245 for full L5E, 5 for L5EO and 16 for L5EP
Avg Moves: about 14
Purpose(s): Speedsolving


L5E, Last five edges, is an experimental method that solves five edges, the four in U and one in the D layer, preserving all other pieces.

ELL is a sub group of L5E, all ELL's may be solved in two steps using this method.

Description

There are two main sub-parts. First the edges are oriented using M' U M like in Roux; there are 5 cases for this, and the worst case in Roux (6 edges) is impossible. Then the edges must be permuted; you can place FD during orientation or right after using [U] M' U2 M (named 'P') and end with EPLL, or just permute all five edges in one step.

L5E can be useful for Corners First if the E-slice, centres and three FL edges are solved after the corners. It is also useful in any method that starts with columns, such as one which does the F2L pairs first and then finishes with CMLL, it is an alternative to the last step of Roux if the centres are placed together with the BD edge at first, also for any LBL style, cross minus one edge at first and then the LL corners have been finished with CLL or CMLL or the same for Fridrich with 2-look OLL, corners first, then L5E orientation, place FD using P if it was not solved and end it all in PLL as usally.

Zipper L5E/L5E-FR

Zipper L5E or L5E-FR is used in the Zipper Method, specifically in Zipper-b. The difference between this variant and standard L5E is that instead of the FD edge, the FR edge is permuted. This approach, however, cannot be solved 2-Gen (with only M and U moves) like standard L5E.

L5EP

L5EP
L5EP2.png
Information
Proposers:
Proposed:
  • L5EP-U/E: 2004
  • L5EP-U/D: 2005
No. Algs: 16
Avg Moves: ~7-9
Purpose: Speedsolving

Last 5 Edges Permute, often abbreviated L5EP, is a 3x3 subset that permutes the 4 edges on the last layer and an edge from another layer while simultaneously preserving all other pieces.

The five affected edges must be correctly oriented for L5EP to work. L5EP is often used in methods like Petrus-W and Portico, when there are only five edges left to solve on the cube.

There are 16 algorithms for L5EP, 10 excluding mirrors and 7 excluding mirrors and EPLL.

Variants

Although it is generally agreed upon that L5EP permutes the four U layer edges, the location of the fifth edge is not always clear. Because of that, multiple variants exist:

Standard L5EP (L5EP-U/D): This is the original proposal by Mike Bennet where the UF, UR, UB, and UL edges and an edge on the D layer are permuted simultaneously. It originated as an alternate strategy for the Roux method's last six edges step.[1]. It was independently proposed again in 2006 by James Straughan as part of the MI1 method and again in 2008 by Jason Baum[2]. That same year, Kenneth Gustavsson developed a naming scheme and James Straughan developed a way to represent the cases in images[3]. Any case can be simplified to an EPLL by first permuting the D layer edge. Intuitive L5EP can also be used, but it is recommended to learn algorithmic L5EP due to the faster execution and low number of algorithms.

EHKPLL: EHKPLL is a subset of HKPLL which was invented for Hawaiian Kociemba. Here, the fifth permuted edge is the DR edge.

L2L4 / Zipper L5EP (L5EP-U/E): This variant was first used in Duncan Dicks' L2L4 method.[4] In Duncan Dicks' variant, the F layer is the last layer and the fifth edge is on the S layer at UR. This same variant is also used in the Zipper Method and permutes the U layer edges and either the FR or BR edge.

See also

External links

Intermediate system

Intuitive

This style is not completely intuitive, because it is still necessary to know EPLL. First orient all unoriented edges, then place the FD edge to its correct position and finally end the solve in EPLL. The necessary intuitive steps are:

  • P = M' U2 M
  • O = M' U M
  • O' = M' U' M

Using that plus some U turns you can solve any case, even all ELL case. For example, O U P = (M' U M) U (M' U2 M) is a sample algorithm which solves orientation, then places FD. There is a 1 in 12 chance that EPLL is skipped; otherwise there is one algorithm left.

There is another notation which can make it shorter to write algorithms:

  • F(moves) = F2 (moves) F2

It is important here that the moves inside the parentheses keep the corners solved, so that they will still be correct after this algorithm. An example is the U-perm, F(U P U) = F2 (U M' U2 M U) F2. F(O U') is a nice way to solve orientation and place FD all at once if the FD edge is in the middle of three unoriented edges in LL.

Using algorithms

The intuitive style lets you find and understand the orientation algorithms yourself. Another approach is to learn the algorithms instead of finding them; the cases are:

Basic orientations
FUL Solved.jpg
Intuitive solution

(Possibly optimised) alg

Comment
EO5 2 adjacent.jpg
O U2 O

(M' U M) U2 (M' U M)

Orients UL and UB.
EO5 2 opposite.jpg
O U' O

(M' U M) U' (M' U M)

Orients UF and UB.
EO5 4.jpg
P U2 O'

(M' U2 M) U2 (M' U' M)

Orients UR, UF, UL and UB
EO5 1.jpg
O U O'

(M' U M) U (M' U' M)

Orients FD and UB
EO5 3.jpg
O'

(M' U' M)

Orients FD, UR, UF and UL
All images show white on top (U) and green in front (F).

More algs are at the L5EOP page

Sometimes this will also solve the FD edge; the images show where the FD edge must be for the algorithm to solve it, but otherwise you should simply treat the yellow sticker as white. If you learn these positions, it can also be useful to learn the mirror algorithm for the case where FD is on the opposite side from the image. The easiest example is to use O' instead of O for the case with three flipped edges on U. Just like the intuitive step, if FD is not solved use P, and either way finish with EPLL.

Semi-advanced system

L5EOP is an alternative to L5E, that always solves the FD edge while orienting ('P'lace). Then the last step will always be EPLL.

FD placement + EPLL (L5EP)

Another possibility for improving the intermediate style is to permutate the last five edges in one step. This only requires 16 algorithms in total, so counting the 5 orientations creates a system that solves L5E in two short steps. Even if you know this, it is still useful to place FD without extra moves if possible, since EPLL recognition is very fast.

We will introduce the following function:

  • f(moves) = f2 (moves) [U] f2 ... This is the same as the F() function above, but with double layer f turns. Note that sometimes the adjusting U turns are not mentioned.

Here are the algorithms for permutation of all 5 edges; make sure to use AUF to place the FD edge at the position it has in the image.

Double two cycle permutations
FUL Solved.jpg
Intuitive solution

(Possibly optimised) alg

Comment
EP5 22 A.jpg
F(H-PLL)

M U M2 U2 M2 U M'

Swaps UF<->DF and UR<->UL
EP5 22 B1.jpg
F(Z-PLL)

(y') r2 U' 2x(M E2) U r2

Swaps UR<->DF and UL<->UB
EP5 22 B2.jpg
F(Z-PLL')

(y') r2 U 2x(M E2) U' r2

Swaps UL<->DF and UR<->UB
EP5 22 H.jpg
H-PLL

Ra U2 Ra' (y) Ra' U2 Ra

Swaps UR<->UL and UF<->UB
EP5 22 Z.jpg
Z-PLL

M2 U' 2x(M E2) U M2

Swaps UR<->UB and UL<->UF
3-cycle permutations
EP5 3 A.jpg
P

(M' U2 M)

Cycles UF->DF->UB
EP5 3 B1.jpg
f(d' P)

(y') r2 U' (M' U2 M) U' r2

Cycles UL->UB->DF
EP5 3 B2.jpg
f(d P)

(y') r2 U (M U2 M') U r2

Cycles UR->UB->DF
EP5 3 U1.jpg
U-PLL

F2 U (M' U2 M) U F2

Cycles UF->UL->UR
EP5 3 U2.jpg
U-PLL'

F2 U' (M' U2 M) U' F2

Cycles UF->UR->UL
5-cycle permutations
EP5 5 H1.jpg
P U P

(M' U2 M) U (M' U2 M)

Cycles UF->UL->UR->DF->UB
EP5 5 H2.jpg
P U' P

(M' U2 M) U' (M' U2 M)

Cycles UF->UR->UL->DF->UB
EP5 5 Z1.jpg
P Z-PLL

2x(M2 U) (M U2 M')

Cycles UF->UR->UB->UL->FD
EP5 5 Z2.jpg
P Z-PLL'

2x(M2 U') (M U2 M')

Cycles UF->UL->UB->UR->DF
EP5 5 U1.jpg
P U-PLL

(M' U2 M') U' (M' U2 M) U' M2

Cycles UF->DF->UB->UL->UR
EP5 5 U2.jpg
P U-PLL'

(M' U2 M') U (M' U2 M) U M2

Cycles UF->DF->UB->UR->UL
These images have white on top (U) and green in front (F). Darker pieces change positions.

Advanced system

The most advanced system is to solve all edges in one step. Solving the last five edges in a single step contains 245 algorithms and reduces the number of looks and the movecount. There are a few variants of L5E. One solves four edges of the U layer and one on the D layer. The first known developed and published method to use this single step L5E is the Nautilus method. Another L5E variant is one where the four U layer edges and an edge in the E layer are solved. This was first proposed for the Zipper method. A final L5E variant that has been proposed occasionally is one which solves three edges of the U layer and two edges on the D layer. This can be used in corners first and related methods such as Waterman, Roux, and LMCF.

See also

External Links