Speedsolving.com Wiki - User contributions [en]

Feliks Zemdegs

2014-09-13T01:56:58Z

Grady964: Added methods

{{Infobox
|NAME=Feliks Zemdegs
|IMAGE=FeliksZemdegs.jpg
|IMAGEYEAR=
|ALIASES=faz
|COUNTRY=Australia
|BIRTHDATE=20 December 1995
|AGE=17
|JOBS=Student
|YEARSACTIVE=2009-present
|ID=2009ZEMD01
|FAMOUSFOR=2x2, 3x3, 4x4, 5x5, 6x6, 3x3OH and 4x4BLD WRs
}}

'''Feliks Zemdegs''' is an [[Australia]]n speedcuber from Melbourne, Australia. He is the current world record holder for 3x3 average and 5x5 single and average. He is widely considered to be the most successful competitive cuber in history. Even though he is fast, Feliks is starting to lose world records, because he got very quick before anyone else, now other people are catching up to him, like [[Mats Valk]], that broke his 3x3 single(5.55), Sebastian Weyer, that broke his 4x4 average(29.17), and Christopher Olson, that broke his 2x2 average(2.02).
== Style ==
Feliks is a color-neutral CFOP user. His meteoric rise in 2009, together with [[Rowe Hessler]]'s earlier success, were the catalysts for the current popularity of [[Color neutrality]] in 3x3 speedsolving. (Also, str8baq) For the 2x2 cube, he uses CLL.
=== Methods ===
* 3x3x3: [[CFOP]]
* 2x2x2: [[CLL]]
* 4x4x4: [[Yau method]]

== Achievements ==
=== Milestones ===
Feliks was the first cuber to achieve the following milestones:

=== Official ===
* 3x3 speedsolve average: sub-10, sub-9, sub-8, sub-7
* 3x3 speedsolve single: sub-7, sub-6
* 4x4 speedsolve average: sub-40, sub-35
* 4x4 speedsolve single: sub-35 (in fact almost sub-30)
* 5x5 speedsolve sub-1min average of 5
* 5x5 speedsolve single: sub-1:00
* 3x3 one-handed average: sub-15, sub-15

=== World Records ===
Feliks currently holds 5 world records; 2 single records and 3 average records.

'''Single'''
*3x3x3 One-Handed: 9.03
*5x5x5 cube: 50.50

'''Average'''
*3x3x3 Cube: 6.54
*5x5x5 Cube: 57.64
*7x7x7 Cube: 2:52.09

=== Titles ===
{{S-start}}

{{S-ach| ach=World Titles}}

{{S-title-bef| before=[[Michał Pleskowicz]] | year=2011 }}
{{S-title| title=3x3 Speedsolve World Champion | year=2013 }}
{{S-inc}}

{{S-title-bef| before=[[Rowe Hessler]] | year=2009 }}
{{S-title| title=2x2 Speedsolve World Champion | year=2011 }}
{{S-title-aft | after=[[Cameron Stollery]] | year=2013}}

{{S-title-bef| before=[[Syuhei Omura]] | year=2009 }}
{{S-title| title=4x4 Speedsolve World Champion | year=2011,2013 }}
{{S-inc}}

{{S-title-bef| before=[[Dan Cohen]] | year=2009 }}
{{S-title| title=5x5 Speedsolve World Champion | year=2011 }}
{{S-title-aft | after=[[Kevin Hays]] | year=2013}}

{{S-title-bef| before=[[Arifumi Fushimi]] | year=2011 }}
{{S-title| title=3x3 OH World Champion | year=2013 }}
{{S-inc}}

{{S-title-bef| before=[[Dan Cohen]] | year=2009 }}
{{S-title| title=6x6 Speedsolve World Champion | year=2011 }}
{{S-title-aft | after=[[Kevin Hays]] | year=2013}}

{{S-end}}

== See also ==
* [[Color neutrality]]

== External links ==
* [http://en.wikipedia.org/wiki/Feliks_Zemdegs Wikipedia entry for Feliks Zemdegs]
* [http://www.youtube.com/user/fazrulz1 Feliks Zemdegs's YouTube channel]
* [http://www.cubecastpodcast.com/episodes/ CubeCast Podcast: Episode 02 - Feliks Zemdegs]
* [http://www.speedsolving.com/forum/showthread.php?34267-7.34-avg-12 7.34 avg 12]
=== Interviews ===
* [http://www.speedsolving.com/forum/entry.php?23-The-Faztest The Faztest]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?24929 Interview with Feliks Zemdegs]
* [http://www.speedsolving.com/forum/entry.php?21-Interview-with-Jessica-Fridrich-and-Zbigniew-Zborowski-about-Feliks-Zemdegs Interview with Jessica Fridrich and Zbigniew Zborowski about Feliks Zemdegs]
* [http://www.youtube.com/watch?v=mgbNYznXxEE Feliks Zemdegs Exclusive Interview - Rubik's Cube record holder]

=== Tribute Videos ===
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?35848-video-My-name-is-Feliks-Zemdegs (video) My name is Feliks Zemdegs]
* Youtube.com: [http://www.youtube.com/watch?v=aWRVUWEaOQo My name is Feliks Zemdegs]

[[Category:World record holders|Zemdegs, Feliks]]
[[Category:World champions|Zemdegs, Feliks]]
[[Category:Big Cube solvers|Zemdegs, Feliks]]
[[Category:OH cubers|Zemdegs, Feliks]]
[[Category:3x3x3 solvers|Zemdegs, Feliks]]
[[Category:4x4x4 solvers|Zemdegs, Feliks]]
[[Category:Speedcubers|Zemdegs, Feliks]]
[[Category:Cubers|Zemdegs, Feliks]]

Sebastian Weyer

2014-09-07T04:19:18Z

Grady964: Another fix

{{Infobox
|NAME=Sebastian Weyer
|IMAGE=Sebastian Weyer.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Germany
|BIRTHDATE=
|AGE=
|JOBS=
|YEARSACTIVE=2010-present
|ID=
|FAMOUSFOR=[[4x4]] WRs
}}

'''Sebastian Weyer''' is a [[Germany|German]] speedcuber. He set world records for 4x4 single of 26.44, and average of 30.81, and then improved it to 29.17 in 2012. He is also the first speedcuber ever to have a sub-30 4x4 average in an official tournament.

== See also ==
* [[List of World Records/4x4x4]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?29072-Sebastian-Weyer-4x4-single-31.66-WR Sebastian Weyer 4x4 single 31.66 WR]
* Speedsolvng.com: [http://www.speedsolving.com/forum/showthread.php?29094-4x4-official-World-record-single-31.66 4x4 official World record single 31.66]

[[Category:Former world record holders|Weyer, Sebastian]]
[[Category:4x4x4 solvers|Weyer, Sebastian]]
[[Category:Speedcubers|Weyer, Sebastian]]
[[Category:Cubers|Weyer, Sebastian]]

{{Stub}}

Sebastian Weyer

2014-09-07T04:19:03Z

Grady964: Grammar fix

{{Infobox
|NAME=Sebastian Weyer
|IMAGE=Sebastian Weyer.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Germany
|BIRTHDATE=
|AGE=
|JOBS=
|YEARSACTIVE=2010-present
|ID=
|FAMOUSFOR=[[4x4]] WRs
}}

'''Sebastian Weyer''' is a [[Germany|German]] speedcuber. He set world records for 4x4 single of 26.44, and average of 30.81, and then improved it to 29.17 in 2012. He is also the first speed cuber ever to have a sub-30 4x4 average in an official tournament.

== See also ==
* [[List of World Records/4x4x4]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?29072-Sebastian-Weyer-4x4-single-31.66-WR Sebastian Weyer 4x4 single 31.66 WR]
* Speedsolvng.com: [http://www.speedsolving.com/forum/showthread.php?29094-4x4-official-World-record-single-31.66 4x4 official World record single 31.66]

[[Category:Former world record holders|Weyer, Sebastian]]
[[Category:4x4x4 solvers|Weyer, Sebastian]]
[[Category:Speedcubers|Weyer, Sebastian]]
[[Category:Cubers|Weyer, Sebastian]]

{{Stub}}

Sebastian Weyer

2014-09-07T04:18:49Z

Grady964: Typo fixes

{{Infobox
|NAME=Sebastian Weyer
|IMAGE=Sebastian Weyer.jpg
|IMAGEYEAR=
|ALIASES=
|COUNTRY=Germany
|BIRTHDATE=
|AGE=
|JOBS=
|YEARSACTIVE=2010-present
|ID=
|FAMOUSFOR=[[4x4]] WRs
}}

'''Sebastian Weyer''' is a [[Germany|German]] speedcuber. He set world records for 4x4 single of 26.44, and average of 30.81, and then improved it to 29.17 in 2012. He is also the first speed cuber ever, to have a sub-30 4x4 average in an official tournament.

== See also ==
* [[List of World Records/4x4x4]]

== External links ==
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?29072-Sebastian-Weyer-4x4-single-31.66-WR Sebastian Weyer 4x4 single 31.66 WR]
* Speedsolvng.com: [http://www.speedsolving.com/forum/showthread.php?29094-4x4-official-World-record-single-31.66 4x4 official World record single 31.66]

[[Category:Former world record holders|Weyer, Sebastian]]
[[Category:4x4x4 solvers|Weyer, Sebastian]]
[[Category:Speedcubers|Weyer, Sebastian]]
[[Category:Cubers|Weyer, Sebastian]]

{{Stub}}

Master Pyramorphix

2014-08-13T17:47:25Z

Grady964:

The '''Master Pyramorphix''', also known as the '''Mastermorphix''', is a puzzle similar to the [[Pyramorphix]] but with one more layer.

== Solution ==

{{Method Infobox
|image=itsacube.jpg
|name=Petrus Master Pyramorphix Method
|proposers=[[Lars Petrus]] (Altered)
|year=1981, 2010
|steps=3
|purpose=
* [[Speedsolving]]
}}

The Mastermorphix (Master Pyramorphix) has two seperate versions. There is the one color version, and the four color version. This guide is written for the four color version.

I can't really ever find guides for the mastermorphix, I have seen a few forum posts talking about ideas. This is from the ideas, and the method that works for me.

The method used to solve this 4 sided puzzle is loosely based on the [[Petrus]] method. This puzzle doesn't have many people doing it, or solvers with any posted times. I see some people say this is one of the most difficult [[3x3x3]] shape mods. I am not doubtful about that, but I believe this puzzle can be achieved to sub-30, and maybe people have already done this. I have not seen any times below that though.

The best times I see for this puzzle are between 1:10.00 and 3:00.00

This puzzle is simply a shape mod of the [[3x3x3]] similar to Mirror Blocks, and many other puzzles. You can see in the diagram to the right where the corners and centers for this puzzle are located in the solved state.

This puzzle has 2 big differences to most [[3x3x3]] shape mods.

It's centers can become rotated; although this occurs on a normal [[3x3x3]] this doesn't affect you because these are solid colors. Unless of course you are solving a picture cube.

One corner can be rotated, unlike any [[3x3x3]], just one corner can be rotated while the rest of the cube is currently in the solved position. (This is only required for the actual corners of this puzzle.

This actually occurs because unseen by you another "corner" is actually rotated. the small triangular wedges can be rotated, and this is not visible. This means when 2 or more corners are rotated, it is very likely this will fall on one of the corners that has three colors. This means you will need to fix one or two of these at the end of every solve.

The following guide was written from scratch.

What you need to know before you start:

* How to solve a [[rubik's cube]] (beneficial)
* [[PLL]] (Very beneficial!)
* Intuitive [[F2L]]
* [[Notation]]
* Mapping from [[3x3x3]]
o Corners: The small single color triangular pieces (looks like the center of this puzzle)
o Corners: The three colored actual corners of this puzzle are also corners.
o Centers: The two colored diamond pieces on the edge of this puzzle.
o Edges: The solid colored "wedge" pieces.
o See image.

Step 1:

Build a 2x2x2 block (This can be broken into 3 sub steps)

You need to first orient 3 center pieces in the correct orientation (looking at this from the top going clockwise your centers may be :yellow-blue—blue-red—red-yellow: remember, the centers of this puzzle have 2 colors on them.

Now you have to begin to build your 2x2x2 block, you have to insert 2 edges so that they match. These edges (obviously) will be between the two centers on the puzzle. so for example between the yellow-blue and blue-red centers we would place a blue edge. Make sure you keep the proper orientation of the centers.

Now that you have 2 edges correctly placed you do one f2l placement. Find the corner for the [[slot]], match it with the missing edge and place it into the [[slot]].

You should now have completed a 2x2x2 block, you will hold the point of this to the bottom of the puzzle pointing towards the floor or table.

Notes about Step 1:

* You can insert the other 2 edges by repeatedly inserting f2l pairs with the missing corner.
* There three edges of the same color, and any of these can be used in the pairs.

Step 2:

Now this is kind of where the [[petrus]] method dies off. What you will do now is extend 2 sides of the puzzle (touching the 2x2x2 block) towards the top [[layer]]. (This will be a matching of 1 corner and 2 edges and will look something like angel wings being placed)

If you are building on yellow you could find and connect one corner with it's edge easily. You can also easily place this into the correct area (this should be very easy to figure out)

I am not going to go into detail for this, once you get the 2nd edge added you can place this into the appropriate position. This should be done intuitively to learn your own tricks for this part.

After you place 2 of these along the 2x2x2 block you will probably have to insert another f2l pair. Once again this should be obvious of where it is, and should be a very simple fix.

Once this has been finished one "edge" of the puzzle will be unsolved, the rest of the cube will be in the correct position. See center rotation if required.

The above will take practice.

Notes about step 2:

* Did you wind up with an inversed triangle around your face, you just can't figure out how to get it in position?
o Note: this is not [[parity]], you just have to reverse an edge. R U2 R' U2 L U' L'
* Yes this step requires a lot of practice, but once you get the hang of it it's easy.

Step 3:

Last Layer

For this step think about the cube as a 3x3x3, you can see this by rotating the puzzle slightly so you have a 3x3 on the top of the puzzle! This is determined by correct orientation of edges as well, the corners are easy to orient!

if the edges are oriented they will be in the apropriate position.

There are some great youtube videos for this, I'm sure you can find them.

Use the above to determine if you have the bar case; or the crooked bar case.

Remember! there are 2 sets of 2 identically colored edges! (use this to your advantage - U-perms)

The last layer of this puzzle is pretty much a permutation problem, more so than an orientation problem!

Notes for step 3:

* Rotate one center 180degrees ( [R U R' U]x6 ) - this will keep all other pieces oriented.
* Rotate one corner 120degrees ( [L' U' L U] [L' U2' L] [R U R' U R U2' R'] )
* Notable algorithms from 3x3x3
o J-Perms
o T-Perm
o U-Perms
o A-perms
o [[2-look OLL]] cases ([[Sune]]/Bar/L-shape)

Enjoy this puzzle, and good luck.

== External links ==
* [http://en.wikipedia.org/wiki/Pyramorphix#Master_Pyramorphix Wikipedia entry on Master Pyramorphix]

[[Category:Twisty puzzles]]

Rubik's cube (puzzle type)

2014-08-12T21:47:24Z

Grady964:

{{Puzzle Infobox|
|NAME=Rubik's Cube
|IMAGE=Roux solved.jpg
|ALTERNATIVENAMES=Regular cube, 3x3x3, 3x3
|SHAPE=Cube
|MECHANISM=3x3x3
|INVENTOR=Erno Rubik
|YEAR=1974
|COMPANIES=
|TIME=From a few seconds to many years}}

The '''Rubik's cube''' (also known as the '''3x3x3 cube''', and normally referred to in the cubing community as the '''3x3x3''' or '''3x3''') is a twistable [[puzzle]] in the shape of a cube that is cut two times along each of three axes. It is said to be the best-selling toy in history, with well over 300 million cubes sold, and because of this popularity it is the most commonly practiced cube in [[speedsolving]]. The most popular brand is [[Rubik's]], which was first patented by [[Erno Rubik]] in 1975, and which began being produced on a wide scale in the early 1980s. Recently the cubing community has seen the development of [[DIY]] cubes made in China, which many say are better for speedcubing than the official cubes.

This puzzle has 6 fixed [[center]]s, 12 [[edge]]s, and 8 [[corner]]s, and a total of 43,252,003,274,489,856,000 (or 4.3 x 10^19) positions. It has been proven that every position can be solved in 20 or fewer moves.

The current official [[world record]] single 3x3 speed solve is 5.55 seconds held by [[Mats Valk]].

== See Also ==
* [[3x3x3 Cubes]] (brands)
* [[3x3x3 Methods]]
* [[Rubik's Brand Cube]]
* [[3x3x3 notation]]
* [[World Record | World Records]]

== External Links ==
* [http://en.wikipedia.org/wiki/Rubik's_Cube The Wikipedia article]

{{Cubics}}

[[Category:Twisty puzzles]]
[[Category:Twisty puzzles used in WCA-official events]]

Rubik's cube (puzzle type)

2014-08-12T21:43:23Z

Grady964:

{{Puzzle Infobox|
|NAME=Rubik's Cube
|IMAGE=Roux solved.jpg
|ALTERNATIVENAMES=3x3x3, 3x3, The normal one
|SHAPE=Cube
|MECHANISM=3x3x3
|INVENTOR=Erno Rubik
|YEAR=1974
|COMPANIES=
|TIME=From a few seconds to many years}}

The '''Rubik's cube''' (also known as the '''3x3x3 cube''', and normally referred to in the cubing community as the '''3x3x3''' or '''3x3''') is a twistable [[puzzle]] in the shape of a cube that is cut two times along each of three axes. It is said to be the best-selling toy in history, with well over 300 million cubes sold, and because of this popularity it is the most commonly practiced cube in [[speedsolving]]. The most popular brand is [[Rubik's]], which was first patented by [[Erno Rubik]] in 1975, and which began being produced on a wide scale in the early 1980s. Recently the cubing community has seen the development of [[DIY]] cubes made in China, which many say are better for speedcubing than the official cubes.

This puzzle has 6 fixed [[center]]s, 12 [[edge]]s, and 8 [[corner]]s, and a total of 43,252,003,274,489,856,000 (or 4.3 x 10^19) positions. It has been proven that every position can be solved in 20 or fewer moves.

The current official [[world record]] single 3x3 speed solve is 5.55 seconds held by [[Mats Valk]].

== See Also ==
* [[3x3x3 Cubes]] (brands)
* [[3x3x3 Methods]]
* [[Rubik's Brand Cube]]
* [[3x3x3 notation]]
* [[World Record | World Records]]

== External Links ==
* [http://en.wikipedia.org/wiki/Rubik's_Cube The Wikipedia article]

{{Cubics}}

[[Category:Twisty puzzles]]
[[Category:Twisty puzzles used in WCA-official events]]

Rubik's cube (puzzle type)

2014-08-12T21:42:39Z

Grady964:

{{Puzzle Infobox|
|NAME=Rubik's Cube
|IMAGE=Roux solved.jpg
|ALTERNATIVENAMES=3x3x3, 3x3, The normal one
|SHAPE=Cube
|MECHANISM=3x3x3
|INVENTOR=Erno Rubik
|YEAR=1974
|COMPANIES=
|TIME=From a few seconds to many years}}

The '''Rubik's cube''' (also known as the '''3x3x3 cube''', and normally referred to in the cubing community as the '''3x3x3''' or '''3x3''') is a twistable [[puzzle]] in the shape of a cube that is cut two times along each of three axes. It is said to be the best-selling toy in history, with well over 300 million cubes sold, and because of this popularity it is the most commonly practiced cube in [[speedsolving]]. The most popular brand is [[Rubik's]], which was first patented by [[Erno Rubik]] in 1975, and which began being produced on a wide scale in the early 1980s. Recently the cubing community has seen the development of [[DIY]] cubes made in China, which many say are better for speedcubing than the official cubes.

This puzzle has 6 fixed [[center]]s, 12 [[edge]]s, and 8 [[corner]]s, and a total of 43,252,003,274,489,856,000 (or 4.3 x 10^19) positions. It has been proven that every position can be solved in 20 or fewer moves.

The current official [[record]] speed solve is 5.55 seconds held by [[Mats Valk]].

== See Also ==
* [[3x3x3 Cubes]] (brands)
* [[3x3x3 Methods]]
* [[Rubik's Brand Cube]]
* [[3x3x3 notation]]
* [[World Record | World Records]]

== External Links ==
* [http://en.wikipedia.org/wiki/Rubik's_Cube The Wikipedia article]

{{Cubics}}

[[Category:Twisty puzzles]]
[[Category:Twisty puzzles used in WCA-official events]]

Speedsolving.com Wiki:Requested articles

2014-08-07T07:01:25Z

Grady964:

* Add pages to [[:Category:Official events|Official events]] (should distinguish event from puzzle, e.g. the Magic event should be a separate page from the Magic puzzle)
* There certainly needs to be a history section with several paragraphs for [[Speedsolving Forums]]. A link to an eventual "See main article: History of English-speaking cube forum" too.

== Manufacturers ==

* Lubix
* Moyu

== Puzzles ==

* Pyramorphix

[[Category:Speedsolving.com Wiki maintenance]]

Teraminx

2014-08-07T06:53:24Z

Grady964: Cleaned up

The '''Teraminx''', like the [[Megaminx]], is a dodecahedral puzzle. It has 7 layers and is available commercially at [http://cubeforyou.com/product-631.html Cube4You] and [http://www.shop.mf8.com.cn mf8].

== See also ==
* [[Megaminx]]
* [[Gigaminx]]
* [[Petaminx]]
* [[Pyraminx]]

[[Category:Twisty puzzles]]

{{Stub}}

Petaminx

2014-08-07T06:51:20Z

Grady964: Cleaned it up :)

[[File:Petaminx.jpg|200px|thumb|right|Petaminx]]
The '''Petaminx''' is the largest mass-produced puzzle in the [[Megaminx]] family. The puzzle is two layers larger than the [[Teraminx]] and has 950 moving pieces.

== See also ==
* [[Megaminx]]
* [[Gigaminx]]
* [[Teraminx]]
* [[Pyraminx]]

[[Category:Twisty puzzles]]

{{Stub}}

Speedsolving.com Wiki:Requested articles

2014-08-07T06:38:41Z

Grady964: Organized & added a page

Template:H-PLL

2014-08-07T06:32:26Z

Grady964: /* H Permutation */ Added two algs

===H Permutation===
{{case
|image=H.gif
|name=H-PLL, X-PLL
|methods=[[EPLL]], [[CPLL]], [[PLL]], [[ELL]], [[ZBLL]], [[ZZLL]]
|optimal=10 [[HTM]], 7 [[STM]]
|text=X-PLL is H-PLL + U2.
}}
{{Alg|M2' U M2' U2 M2' U M2'|PLL|vidurl=http://www.youtube.com/watch?v=RkznplJdcAI}}
{{Alg|M2' U' M2' U2' M2' U' M2'|PLL|vidurl=http://www.youtube.com/watch?v=4YqOYb6pHSs}}
{{Alg|M2' U2 M2' U' M2' U2 M2'|PLL}}
{{Alg|(y') M2' U2 M2' U M2' U2 M2'|PLL}}
{{Alg|R2 U2 R U2 R2 U2 R2 U2 R U2 R2|PLL}}
{{Alg|R2' U2 R' U2 R2' U2' R2' U2 R' U2 R2'|PLL|vidur2=http://www.youtube.com/watch?v=HI9ff1ACklU}}
{{Alg|R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2|PLL}}
{{Alg|R U2' R' U' R' U' R2 U' R2' U2' R2 U2' R' (U)|PLL}}
{{Alg|L2 U2 L' U2 L2 U2 L2 U2 L' U2 L2|PLL}}
{{Alg|L R U2 L' R' F' B' U2 F B|PLL}}
{{Alg|L R U2 L' R' (y) L' R' U2 L R|PLL}}
{{Alg|(M2' U)6|PLL}}
{{Alg|(M2' U')6|PLL}}
{{Alg|(R' S R u) 6|PLL}}
{{Alg|S R U2 R2 U2 R2 U2 R S'|PLL}}
{{Alg|F2 M2' F2 U' F2 M2' F2|PLL}}
{{Alg|(x) U2 M2' U2 B' U2 M2' U2 (x')|PLL}}
{{Alg|L R U2 L' l' U' u' L2 U (z) L|PLL}}
{{Alg|M2' u M2' u2 M2' u M2'|PLL}}
{{Alg|M2' u' M2' u2' M2' u' M2'|PLL}}

L2L4

2014-08-07T06:29:27Z

Grady964: /* The Steps */ Fixed the alignment

{{Method Infobox
|name=L2Ln
|image=
|proposers=[[Duncan Dicks]] (L2L4) [[Stachu Korick]] (L2Lk)
|year=late 1990s (L2L4) 2010-2011 (L2Lk)
|anames=
|variants=L2L4 L2Lk
|steps=5, typically
|moves=~55
|algs=L2L4: 220 L2Lk: 213
|purpose=|purpose=
* [[Speedsolving]]
* [[One-Handed Solving]]
}}

'''L2L4''' ('''L'''ast '''2''' '''L'''ayers, the '''4'''th proposal) is a [[3x3]] speedsolving [[method]] invented by [[Duncan Dicks]] in the 1990s.
'''L2Lk''' ('''L'''ast '''2''' '''L'''ayers, as proposed by [[Stachu Korick|Stachu '''K'''orick]]) is an alternate 3x3 speedsolving method developed in late 2010 through 2011.

== History ==
L2L4 was conceived by Duncan Dicks, who first posted about a series of L2L strategies (L2L1 through L2L4) on the [[Yahoo! speedsolving group]] in 2004.[http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/11055] Duncan found many algorithms, while [[Richard Carr]] also provided several.[http://games.groups.yahoo.com/group/speedsolvingrubikscube/message/12099] Duncan set up a website with algorithms. After these initial thoughts, however, there was little to no development.

Recent developments came in 2010 after the method was "rediscovered" on Speedsolving.com. [[Stachu Korick]] led the development of L2Lk, publishing documentations for both L2L4 and L2Lk in 2010-2011.

==The Steps==
'''-''' First, a 1x3x3 block is completed, typically on the D face, and called the "First Layer."

'''-''' From this point, each of the LL-specific configurations of CO, CP, EO, and EP are completed, not necessarily separately or in that order.

==Variants==

====L2L4====
CO, CP, EO, EP

====L2Lk====
CO, CP, L2E, ELL

== Pros ==
* Once the first layer is done, little thought is needed. Processing and turning speed are both raised at this point.

== Cons ==
* High alg-count
* First layer is difficult to optimize.

== External links ==
* [http://stachu.cubing.net/l2l4/ L2L4 Documentation by Stachu Korick]

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

Corner Orientation

2014-08-07T06:25:53Z

Grady964: God rid of orient from see also

{{Method Infobox
|name=Corner Orientation
|image=COinfo.png
|anames=CO
|variants=[[OCLL]]
|purpose=
* [[Speedsolving]], [[BLD]], [[FMC]]
}}
'''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[substep]] in many [[method]]s.

For the [[last layer]] of the [[3x3x3 cube]] there are three main variations used for the seven cases of CO, one that is named [[Corner Orientation#Pure CO|pure CO]] wich orients the corners without affecting anything else, not even corner permutation, one preserves edge orientation wich is [[OCLL]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).

The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation".

'''Algorithms'''; at this page you can find algortihms for two diffrent variations of CO;
* [[Corner Orientation#Pure CO|Pure CO]]: orients corners preserving edge orientation and both corner and edge permutation.
* [[Corner Orientation#OCLL-EPP|OCLL-EPP]]: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Orientation]]
* [[Corner Permutation]]
* [[OCLL]]
* [[Winter Variation]]
* [[CLS]]
* [[Partial Corner Control]]
= Pure CO =
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];

[[3OP]] is a [[blindfold method]] that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix [[orientation parity]] and then 2-4 corners in the top layer and then the same for the bottom layer. ''Algs for pure orientation of the edges can be found at the [[ELL|ELL page]]''.

Any other BLD method, to fix orientation for corners that are in position but unoriented from the scramble (a few setup moves to get the pieces into the same layer may be needed then).

For [[FMC]] to solve the last pieces (but that won't give any WR, better to try some diffrent start of the last layer that gives a easier case in the end).

===Algorithms===
All cases here have long [[algorithm]]s, the H case is actually the worst LL case of them all and the pi case is second worst. The good thing is that all cases are solveable using only two sides (RU [[2-gen]]). There are diffrent sections for diffrent types of algorithms, first is optimal 2-gen followed by 2-gens of any length. All cases can be solved using two or more [[Sune]], the third section is for these combinations (double, anti and mirrors included). Next comes algs optimal in [[Half Turn Metric]], using as many sides that is needed for that (2-6) and the last section is for any other alg that solves the case.

{{Algnote}}

==Two corners unoriented==
Note that the T-twist is the same case as the U-twist if you reorient the cube (for these images that will be z' y2).
{|border="0" width="100%" valign="top" cellpadding="3"

|-valign="top"
|
=== U ===
{{case |image=Pure twist U.jpg
|name=U, [[Headlights]], Superman
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}

'''Any other 2-gen:'''
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}

'''Sune combos:'''
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}

'''HTM optimal:'''
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}

'''Any other:'''
{{Alg|(x) U2 R' U' R U' R' L' U2 L U L' U L R (x')}}
{{Alg|(z') (U R U' R')2 L' (R U R' U')2 L (z)}}
{{Alg|(y2) (R U R' U')2 L' (U R U' R')2 L}}

|

=== T ===
{{case |image=Pure twist T.jpg
|name=T
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}

'''Any other 2-gen:'''
{{Alg|(U2) R U R' U' R' U R U2 R U2 R' U R' U2 R}}
{{Alg|(U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'}}

'''Sune combos:'''
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}

'''HTM optimal:'''
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}

'''Any other:'''
{{Alg|(z') (R U R' U')2 L' (U R U' R')2 L (z)}}
{{Alg|(y2) (U R U' R')2 L' (R U R' U')2 L}}

|-valign="top"
|

=== L ===
{{case |image=Pure twist L.jpg
|name=L, Bowtie
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}

'''Any other 2-gen:'''
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}

'''Sune combos:'''
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}

'''HTM optimal:''' (12 move commutator)
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}

'''Any other:'''
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}}
{{Alg|y' R' U L U' R U2 y' R' U' R F' R' U R U2}}

|
|}

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

|-valign="top"
|
=== S ===
{{case |image=Pure twist S.jpg
|name=S, Sune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}

'''Any other 2-gen:'''
{{Alg|R U R2 U' R2 U R U R' U' R U R U R U' R' (U)}}
{{Alg|(R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')}}

'''Sune combos:'''
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}

'''HTM optimal:'''
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}

'''Any other:'''
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}

|

=== -S ===
{{case |image=Pure twist aS.jpg
|name=-S, Antisune
|methods=[[L3C]], [[L4C]], [[BLD]]
|optimal=13 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}

'''Any other 2-gen:'''
{{Alg|R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R}}
{{Alg|(U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)}}

'''Sune combos:'''
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}

'''HTM optimal:'''
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}

'''Any other:'''
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}

|}

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

|-valign="top"
|
=== H ===
{{case |image=Pure twist H.jpg
|name=H
|methods=[[L4C]], [[BLD]]
|optimal=16 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)}}
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2') (R U' R' U') (R U R U) (R U' R)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}

'''Any other:'''
{{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}}
{{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}}
{{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}}
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}}

|

=== pi ===
{{case |image=Pure twist pi.jpg
|name=pi, Bruno
|methods=[[L4C]], [[BLD]]
|optimal=15 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)}}
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}

'''Any other 2-gen:'''
{{Alg|(y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')}}
{{Alg|(y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)}}

'''Sune combos:'''
{{Alg|!}}

'''HTM optimal:'''
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}

'''Any other:'''
{{Alg|(y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R}}
{{Alg|B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)}}
{{Alg|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}}
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}

|}

= OCLL-EPP =
'''Orientation of the corners of the last layer - edges permutation preserved'''; orients the [[last layer]] corners preserving edge permutation but ignoring corner permutation.

'''Usage'''; to solve the [[last four corners]] in two looks if the edges are solved (3-look [[LLEF]], OCLL-EPP and [[CPLL]], total 26 algs. 4-look [[EO]], [[EP]], OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

===Algorithms===
{{Algnote}}

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

|-valign="top"
|
=== U (EPP) ===
{{case |image=OCLL-EPP U.jpg
|name=U, Headlights, Superman
|methods=2-look [[L4C]]
|optimal=9 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R}}

'''HTM optimal:'''
{{Alg|R2 D' R U2 R' D R U2 R}}
{{Alg|R2 F2 R' B2 R F2 R' B2 R'}}
{{Alg|(z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)}}

'''Any other:'''
{{Alg|R U2 R2 U L U' R2 U L' U R'}}
{{Alg|R' U2 R F' R' F U2 F' R F}}

|

=== T (EPP) ===
{{case |image=OCLL-EPP T.jpg
|name=T
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R' U R U2 R U2 R' U R' U2 R U2 R U}}

'''HTM optimal:'''
{{Alg|R' F' R B' R' F R B}}
{{Alg|(x) R' U' R D' R' U R D (x')}}
{{Alg|(x') R' D' R U' R' D R U (x)}}
{{Alg|(y') r U R' U' r' F R F'}}
{{Alg|(y) l U L' U' R' U L U' (x)}}

'''Any other:'''
{{Alg|F U F' R' F U' F' U R U'}}
{{Alg|(y') R U R' U' L' U R U' M' (x')}}

|-valign="top"
|

=== L (EPP) ===
{{case |image=OCLL-EPP L.jpg
|name=L, Bowtie
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U}}

'''HTM optimal:'''
{{Alg|R B' R' F R B R' F'}}
{{Alg|(y) F R' F' r U R U' r'}}
{{Alg|(x') U' R U L' U' R' U r}}

'''Any other:'''
{{Alg|U' F U R' U' R F' R' U R}}
{{Alg|R U R U' L' U R' U' M' (x')}}

|
|}

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

|-valign="top"
|
=== S (EPP) ===
{{case |image=OCLL-EPP S.jpg
|name=S, Sune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}}

'''HTM optimal:'''
{{Alg|R U' L' U R' U' L U}}

'''Any other:'''
{{Alg|!}}

|

=== -S (EPP) ===
{{case |image=OCLL-EPP aS.jpg
|name=-S, Antisune
|methods=2-look [[L4C]]
|optimal=8 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}}

'''HTM optimal:'''
{{Alg|U' L' U R U' L U R'}}

'''Any other:'''
{{Alg|!}}

|}

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

|-valign="top"
|
=== H (EPP) ===
{{case |image=OCLL-EPP H.jpg
|name=H
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}}

'''HTM optimal:'''
{{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}}

'''Any other:'''
{{Alg|F (R U R' U')3 F'}}

|

=== pi (EPP) ===
{{case |image=OCLL-EPP pi.jpg
|name=pi, Bruno
|methods=2-look [[L4C]]
|optimal=12 [[HTM]]
|text=
}}
'''Optimal 2-gen:'''
{{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}}

'''HTM optimal:'''
{{Alg|R F' D2 F R' U' R F' D2 F R' U}}

'''Any other:'''
{{Alg|R' U L U' R U L2 U R U' L U R' U2}}
{{Alg|L U' R' U L' U' R2 U' L' U R' U' L U2}}

|}

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

__NOTOC__

== OLC Algorithms ==

'''O'''rient '''L'''ast '''C'''orners (OLC), also known as '''O'''rient '''L'''ast '''4''' '''C'''orners (OL4C), is a subset of OLL used in [[ZZ-reduction]] following [[Phasing]] that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited [[PLL]] set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

{{Algnote}}

=== OLC 1 ===
Probability 4/27
{{case
|image=o27.gif
|name=S, Sune, Swimming Left
|methods=[[ZZ-reduction]]
|text=
}}
{{Alg|R U' L' U R' U' L|OLL}}
{{Alg|y2 R' U L U' R U L'|OLL}}
{{Alg|U R U' L' U R' U' L|OLL}}

=== OLC 2 ===
Probability 4/27
{{case
|image=o26.gif
|name=-S, Antisune, Swimming Right
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|L' U R U' L U R'|OLL}}

=== OLC 3 ===
Probability 2/27
{{case
|image=o21.gif
|name=H, Double Sune, Flip, Cross
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]], ? [[STM]]
|text=
}}
{{Alg|y F (R U R' U')3 F'|OLL}}
{{Alg|R U2 R' F R' F' R F2 L F L' F|OLL}}

=== OLC 4 ===
Probability 4/27
{{case
|image=o22.gif
|name=pi, Bruno, wheel, T-shirt
|methods=[[ZZ-reduction]]
|optimal=? [[HTM]]
|text=
}}
{{Alg|f (R U R' U') F f' (R U R' U') F'|OLL}}
{{Alg|y U L' U2 L2 U L2 U L2 U2 L' U2|OLL}}

=== OLL 23 ===
Probability 4/27
{{case
|image=o23.gif
|name=U, [[Headlights]], Superman
|methods=[[OCLL]], [[OLL]]
|optimal=9 [[HTM]]
|text=
}}
{{Alg|R2' D' R U2 R' D R U2 R|OLL}}
{{Alg|y' F L' D2 L U2 L' D2 L U2 F'|OLL}}
{{Alg|y' B L2 B R2 B F2 R2 B L2 F2|OLL}}
{{Alg|y' B' F2 R2 B L2 B' R2 B L2 F2|OLL}}
{{Alg|L2 D L' U2 L D' L' U2 L'|OLL}}
{{Alg|(y2) R' F2 R U2 R U2 R' F2 R U2 R'|OLL}}
{{Alg|(y2) R2 D R' U2 R D' R' U2 R'|OLL}}
{{Alg|R2 D R' U2' R D' R' U2 R'|OLL}}
{{Alg|F R U' R' U R U R' U R U' R' F'|OLL}}
{{Alg|(R' U' R U') R' U2 R2 U (R' U R U2 R')|OLL}}
{{Alg|l2 U' R D2 R' U R D2 R|OLL}}
{{Alg|l2' U' z' U R2 U' L U R2 U z'|OLL}}
{{Alg|y2 R2' B2 R F2' R' B2 R F2' R|OLL}}
{{Alg|(x) R' B2' (R U' R' U) B2' (U' R U)|OLL}}
{{Alg|y' F' L2 F' R2 B2 F' R2 F' L2 B2|OLL}}

=== OLL 24 ===
Probability 4/27
{{case
|image=o24.gif
|name=T, chameleon, shark, Hammerhead, Little Horse, stingray
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|r U R' U' L' U R U' x'|OLL}}
{{Alg|r U R' U' r' F R F'|OLL}}
{{Alg|(y' x') R U R' D R U' R' D'|OLL}}
{{Alg|(y') F R U R' U' R U' R' U' R U R' F'|OLL}}
{{Alg|(y x) D' R' U R D R' U' R x'|OLL}}
{{Alg|(y x) D L U' L' D' L U L' x' |OLL}}
{{Alg|(y x') U' R' D R U R' D' R x|OLL}}
{{Alg|(y2) R' F' L F R F' L' F|OLL}}
{{Alg|(y2) R' F' r U R U' r' F|OLL}}
{{Alg|(y2) l' U' L U R U' r' F|OLL}}
{{Alg|(y') l U l' F R B' R' F'|OLL}}

=== OLL 25 ===
Probability 4/27
{{case
|image=o25.gif
|name=L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
|methods=[[OCLL]], [[OLL]]
|optimal=8 [[HTM]]
|text=
}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|R U2 R' U' (R U R' U') (R U R' U') R U' R'|OLL}}
{{Alg|R U R' U (R U' R' U) (R U' R' U) R U2 R'|OLL}}
{{Alg|y2 R' F R B' R' F' R B|OLL}}
{{Alg|y2 F R' F' L F R F' L'|OLL}}
{{Alg|y F' L F R' F' L' F R|OLL}}
{{Alg|y' F' r U R' U' r' F R|OLL}}
{{Alg|y' x U R' U' L U R U' r'|OLL}}
{{Alg|R' F' L' F R F' L F|OLL}}
{{Alg|y2 R U2' R D R' U2 R D' R2'|OLL}}
{{Alg|y2 F R' F' r U R U' r'|OLL}}
{{Alg|y2 l' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x' L' U' R' U L U' R U|OLL}}
{{Alg|x' D R U R' D' R U' l'|OLL}}
{{Alg|x' U L' U' R U L U' l'|OLL}}
{{Alg|x' R' D R U' R' D' R U x|OLL}}
{{Alg|x R' U R D' R' U' R D x'|OLL}}
{{Alg|y2 x L U' L' D L U L' D' x'|OLL}}
{{Alg|l' U' L' U R U' L U x'|OLL}}
{{Alg|U r U R U' L' U R' U' x'|OLL}}
{{Alg|R U2 R' U' (R U R' U')2 R U' R'|OLL}}
{{Alg|y2 L' R U R' U' L U R U' R'|OLL}}
{{Alg|F R B R' F' l U' l'|OLL}}
{{Alg|U R U2 R' L' U' L U' R U' R' L' U2 L|OLL}}
{{Alg|y R U R' U' R' F R U R U' R' F'|OLL}}

Permutation

2014-08-07T06:25:14Z

Grady964: Got rid of permute from the see also

'''Permutation''' is a mathematical term that refers refers broadly to rearranging or the rearrangement of objects. In puzzle theory, the term is applied to puzzle pieces. The permutation of pieces refers to their location on the puzzle or, equivalently, to the relocation required to place them in their correct location. One also speaks of a single piece's permutation to mean its location or where it needs to be moved, which contrasts with its [[orientation]], its state (flip/orientation) in place.

== Relation to orientation ==
Although (changes in) permutation and orientation suffice to characterize any legal move on many puzzles, they are in general not independent. In mathematical terms, the group of the puzzle cannot in general be decomposed as a ''direct'' product of the permutation group and the orientation group. For example, on the [[3x3]], the decomposition is instead a ''semi-direct'' product; a general permutation affects orientation.

Orientation and permutation may be viewed independently by restricting to ''pure orientation'' or ''pure permutation'', affecting one but not the other. For example, in [[3OP]] blindfold solving method, pieces are first oriented in place (trivial permutation), then permuted while preserving the orientation. Here, the precise definition of orientation affects which permutations preserve orientation, hence affect the notion of pure permutation.

== Permutation parity ==
On a puzzle with different types of pieces, the permutation naturally breaks down into permutations of the different piece types. For example, the full permutation of a [[3x3]] can be specified by the permutation of its 12 edges and the permutation of its 8 corners. On many puzzles, however, group theoretic considerations show that there are constraints on the possible permutations of different piece types. For example, every legal move on a 3x3 has an even full permutation; corner and edge permutations must be either even and even or odd and odd. This means in particular that a single pair of edges cannot be switched without also switching a single pair of corners.

A '''permutation parity''' refers to a situation where the full permutation cannot be corrected using only permutations of a single piece type. On a 3x3, this means odd corner permutation and odd even permutation, so that pair of corners and a pair of edges must be switched to ''fix the parity.'' This makes it impossible to treat the corners and edges completely independently, which has unpleasant consequences in 3x3 blindfold cubing. In cubes bigger than 3x3, the center pieces of the same type and of the same color are not distinguishable, which makes it impossible to determine the parity of their permutation from centers alone. In 4x4 (or any even number) [[reduction method]]s, which solve the center first, this can lead a full odd permutation in the 3x3 phase that cannot be resolved without permuting the already "solved" centers, another example of a permutation parity.

== See also ==
* [[Orientation]]
* [[Edge Permutation]]
* [[Corner Permutation]]

[[Category:Puzzle theory]]

Permute

2014-08-07T06:24:37Z

Grady964: Changed it to a redirect page

#REDIRECT [[Permutation]]

Permute

2014-08-07T06:23:48Z

Grady964: Got rid of the orient in see also

'''Permute''' simply means to move a piece. See [[PLL]] for permutations and cycles of the last layer of the [[Fridrich]] method.

== See also ==
* [[Orientation]]
* [[Permutation]]

[[Category:Puzzle theory]]

Orientation

2014-08-07T06:23:00Z

Grady964: Cleaned up the page a bit

'''Orientation''' refers to the way a piece is flipped or rotated. On the 3x3x3 Rubik's cube, corners and edges each have their own orientation; corners can be oriented 3 different ways, and edges can be oriented in 2 different ways. On a '''Super Cube''' or '''Picture Cube''', the centers can also be oriented (resulting in extra work to solve), but this is not the case on standard cubes. Because of how the cube behaves, only ''pairs'' of like pieces can be oriented; it is impossible to orient just one piece. If you rotate one corner clockwise, another must be rotated counterclockwise.

== See also ==
* [[Permute]]
* [[Orientation]]
* [[Permutation]]

[[Category:Puzzle theory]]

Orient

2014-08-07T06:19:14Z

Grady964: Grady964 moved page Orient to Orientation: "Orient" and "orientation" pages are basically the same topic

#REDIRECT [[Orientation]]

Orientation

2014-08-07T06:19:14Z

Grady964: Grady964 moved page Orient to Orientation: "Orient" and "orientation" pages are basically the same topic

'''Orient''' means to flip/rotate a piece. On the 3x3x3 Rubik's cube, corners and edges each have their own orientation; corners can be flipped 3 ways, and edges can be flipped in 2 ways. If the cube has a picture on it, the centres can also be oriented (resulting in extra work to solve), but this is not the case on standard cubes. Because of how the cube behaves, only ''pairs'' of like pieces can be oriented; it is impossible to orient just one piece. If you rotate one corner clockwise, another one must be rotated counterclockwise.

== See also ==
* [[Permute]]
* [[Orientation]]
* [[Permutation]]

[[Category:Puzzle theory]]

Edge Orientation

2014-08-07T06:15:40Z

Grady964: Typo/grammar fixes

The '''orientation of edges of the cube''', often only '''EO''' (edge orientation). Methods such as [[Roux]] (6 edges), [[ZZ]] (all edges), and [[Petrus]] (7 edges) include this as a [[substep]]. Also other [[puzzle]]s such as the [[Square-1]] have EO as a common sub step (EO on a Square-1 is more precisely a separation of edges to the correct layers but it is always referred to as edge orientation.)

== See also ==
* [[Orientation]]
* [[Permutation]]
* [[Edge Permutation]]
* [[Corner Orientation]]
* [[EOLine]]
* [[ZBLL]]
* [[VH Method]]
* [[Partial Edge Control]]

[[Category:Puzzle theory]]
[[Category:3x3x3 other substeps]]

3CFCE

2014-07-30T03:35:19Z

Grady964:

'''3CFCE''' is a more advanced version of [[3CFCEP]]. It stands for ''3 cross'' pieces, ''[[F2L]]'', ''[[CLL]]'' and ''[[ELL]]''

The steps in this method are as follows:
# Complete a mock cross of three edges and one (possibly unoriented) edge of opposite color.
# Complete all F2L corner-edge pairs.
# Solve the corners using ''[[COLL]]''
# Solve all edges using an expanded version of ''[[ELL]]'' such as ''[[L5E]]'' or ''[[L5EOP]]''

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

[[Category:Acronyms]]

3CFCE

2014-07-30T03:34:50Z

Grady964:

'''3CFCE''' is a more advanced version of [[3CFCEP]]. It stands for ''3 cross'' pieces, ''[[F2L]]'', ''[[CLL]]'' and ''[[ELL]]''

The steps in this method are as follows:
# Complete a mock cross of three edges and one (possibly unoriented) edge of opposite color.
# Complete all F2L corner-edge pairs.
# Solve the corners using ''[[COLL]]''
# Solve all edges using an expanded version of ''[[ELL]]'' such as [[L5E]] or [[L5EOP]]

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

[[Category:Acronyms]]

3CFCE

2014-07-30T02:49:25Z

Grady964:

'''3CFCE''' is a more advanced version of [[3CFCEP]]. It stands for ''3 cross'' pieces, ''[[F2L]]'', ''[[CLL]]'' and ''[[ELL]]''

The steps in this method are as follows:
# Complete a mock cross of three edges and one (possibly unoriented) edge of opposite color.
# Complete all F2L corner-edge pairs.
# Solve the corners using ''[[COLL]]''
# Solve all edges using ''[[L5E]]'', an expanded version of ''[[ELL]]''

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

[[Category:Acronyms]]

3CFCE

2014-07-30T02:49:02Z

Grady964: Fixed the quotes :/

'''3CFCE''' is a more advanced version of [[3CFCEP]]. It stands for ''3 cross'' pieces, ''[[F2L]]'', ''[[CLL]]'' and ''[[ELL]]''

The steps in this method are as follows:
# Complete a mock cross of three edges and one (possibly unoriented) edge of opposite color.
# Complete all F2L corner-edge pairs.
# Solve the corners using ''[[COLL]]''
# Solve all edges using [[L5E]], an expanded version of ''[[ELL]]''

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

[[Category:Acronyms]]

3CFCE

2014-07-30T02:48:36Z

Grady964: Added L5E link

'''3CFCE''' is a more advanced version of [[3CFCEP]]. It stands for ''3 cross'' pieces, ''[[F2L]]'', ''[[CLL]]'' and ''[[ELL]]''

The steps in this method are as follows:
# Complete a mock cross of three edges and one (possibly unoriented) edge of opposite color.
# Complete all F2L corner-edge pairs.
# Solve the corners using ''[[COLL]]''
# Solve all edges using "[[L5E]]", an expanded version of ''[[ELL]]''

[[Category:3x3x3 methods]]
[[Category:Experimental methods]]

[[Category:Acronyms]]