Speedsolving.com Wiki - User contributions [en]

Forum cubers by location

2011-02-07T17:47:12Z

Riffz: /* Canada */

__NOTOC__
=Speedsolving.com Forum Cubers by Location=

This is a list of the members of the speedsolving.com forum by their location. This list is not complete, so if you notice someone who is not on this list feel free to add their name under the category for their country. If the country is not already listed, go ahead and create a new category for it.

Another list of cubers by location can be found on [http://www.frappr.com/speedcubers Frappr].

==Africa==

===South Africa===
:[http://www.speedsolving.com/forum/member.php?u=1176 DAE_JA_VOO]

==Asia==

===India===
:[http://www.speedsolving.com/forum/member.php?u=311 Karthik]

==Europe==

===Denmark===
:[http://www.speedsolving.com/forum/member.php?u=474 LarsN] -- ''Lars Vennike Nielsson'' -- [http://www.worldcubeassociation.org/results/p.php?i=2008NIEL01 WCA Profile]

===France===
:'''Paris'''
::[http://www.speedsolving.com/forum/member.php?u=1684 TMOY]

===Iceland===
:'''Reykjavík'''
::[http://www.speedsolving.com/forum/member.php?8608 Karth] Living in Finland until end of June 2011

===Sweden===
:'''Stockholm'''
::[http://www.speedsolving.com/forum/member.php?u=479 Kenneth] -- ''[[User:Kenneth|Kenneth Gustavsson]]'' -- [http://www.worldcubeassociation.org/results/p.php?i=2005GUST01 WCA Profile]
::[http://www.speedsolving.com/forum/member.php?u=1673 Coinman] -- ''Tommy Gustavsson'' -- [http://www.worldcubeassociation.org/results/p.php?i=2005GUST02 WCA Profile]

:'''Strängnäs'''
::[http://www.speedsolving.com/forum/member.php?u=9120 Oljibe] -- ''Rickard Jonsson'' -- [http://www.worldcubeassociation.org/results/p.php?i=2010JONS01 WCA Profile]

===United Kingdom===
:[http://www.speedsolving.com/forum/member.php?u=1742 msemtd] -- Michael Erskine, Sherwood, Nottingham. [http://www.worldcubeassociation.org/results/p.php?i=2008ERSK01 WCA profile] --[[User:Msemtd|Msemtd]]
:[[User:Cride5|Cride5]]

==North America==

===Canada===
:'''Saskatchewan'''
::[http://www.speedsolving.com/forum/member.php?u=1569 Connorcuber]
:'''Ontario'''
::[http://www.speedsolving.com/forum/member.php?u=1144 Sa967St]
::[http://www.speedsolving.com/forum/member.php?u=2487 Riffz]
:'''Manitoba'''
::[http://www.speedsolving.com/forum/member.php?u=4060 miniGOINGS]

===United States===
:'''AL (Alabama)'''
::[http://www.speedsolving.com/forum/member.php?u=1119 Adam Morgan (ajmorgan25)]
:'''CA (California)'''
::[http://www.speedsolving.com/forum/member.php?u=1707 Unknown.soul]
::'''San Francisco Bay Area'''
:::[http://www.speedsolving.com/forum/member.php?u=182 deathbypapercutz]
:::[http://www.speedsolving.com/forum/member.php?u=2 Lucas Garron]
:::[http://www.speedsolving.com/forum/member.php?u=657 whatsinacube]
::'''Los Angeles Area'''
:::[http://www.speedsolving.com/forum/member.php?u=765 Dene] (first half of 2009)
:::[http://www.speedsolving.com/forum/member.php?u=808 qqwref] - [[User:Qqwref|qqwref]] (when at college)
:'''CO (Colorado)'''
::[http://www.speedsolving.com/forum/member.php?u=1 PJK]
::[http://www.speedsolving.com/forum/member.php?u=2923 JTW2007]
:'''FL (Florida)'''
::[http://www.speedsolving.com/forum/member.php?u=348 Dudemanpp]
:'''GA (Georgia)'''
::[http://www.speedsolving.com/forum/member.php?u=1042 Hadley4000]
:'''IN (Indiana)'''
::[http://www.speedsolving.com/forum/member.php?u=402 Mike Hughey] - Indianapolis
:'''KY (Kentucky)'''
::[http://www.speedsolving.com/forum/member.php?u=872 Shaden Smith] - Lexington
:'''MA (Massachusetts)'''
::[http://www.speedsolving.com/forum/member.php?u=131 Tim Reynolds] - Cambridge
:'''MD (Maryland)'''
::[http://www.speedsolving.com/forum/member.php?u=1614 Brett]
::[http://www.speedsolving.com/forum/member.php?u=768 fanwuq]
:'''MN (Minnesota)'''
::[http://www.speedsolving.com/forum/member.php?u=640 Bryan Logan] - Rochester
::[http://www.speedsolving.com/forum/member.php?u=4831 Logan (Kelly)] - Hastings
::[http://www.speedsolving.com/forum/member.php?u=7507 Tyjet66] - Waterville
:'''MO (Missouri)'''
::[http://www.speedsolving.com/forum/member.php?u=1403 Vault312] (during summer)
:'''NC (North Carolina)'''
::[http://www.speedsolving.com/forum/member.php?u=63 cmhardw] - Morrisville
::[http://www.speedsolving.com/forum/member.php?u=147 Athefre]
:'''NJ (New Jersey)'''
::[http://www.speedsolving.com/forum/member.php?u=1309 PatrickJameson]
::[http://www.speedsolving.com/forum/member.php?u=61 macky] - Princeton
::[http://www.speedsolving.com/forum/member.php?u=902 Auburn Manlangit] - Northern NJ
::[http://www.speedsolving.com/forum/member.php?u=76 Bob] - Kearny
:'''NM (New Mexico)'''
::[http://www.speedsolving.com/forum/member.php?u=1518 Kiel0]
:'''NY (New York)'''
::[http://www.speedsolving.com/forum/member.php?u=131 Tim Reynolds] Pleasantville (when not at school)
::[http://www.speedsolving.com/forum/member.php?u=808 qqwref] - [[User:Qqwref|qqwref]] (when at home)
:'''OH (Ohio)'''
::[http://www.speedsolving.com/forum/member.php?u=1358 JBCM627]
::[http://www.speedsolving.com/forum/member.php?u=1493 CAT13]
::[http://www.speedsolving.com/forum/member.php?u=912 Pcharles93]
:'''PA (Pennsylvania)'''
::[http://www.speedsolving.com/forum/member.php?u=2250 That70sShowDude]
::[http://www.speedsolving.com/forum/member.php?10830 Your Mother]
::[http://www.speedsolving.com/forum/member.php?u=1403 Vault312] (during school year)
::[http://www.speedsolving.com/forum/member.php?u=1891 StachuK1992]
:'''TX (Texas)'''
::[http://www.speedsolving.com/forum/member.php?u=2160 Fobo911]
:'''UT (Utah)'''
::[http://www.speedsolving.com/forum/member.php?u=1889 not_kevin]
:'''VA (Virginia)'''
::[http://www.speedsolving.com/forum/member.php?u=792 Siraj A.]
:'''WV (West Virginia)'''
::[http://www.speedsolving.com/forum/member.php?u=7077 nlcuber22]
::[http://www.speedsolving.com/forum/member.php?u=7568 skatemaster78]
::[http://www.speedsolving.com/forum/member.php?u=7184 CitricAcid]

==Oceania==

===Australia===
:'''Sydney'''
::[http://www.speedsolving.com/forum/member.php?u=1765 Rawn]
::[http://www.speedsolving.com/forum/member.php?u=5581 AndyRoo789]
::[http://www.speedsolving.com/forum/member.php?u=8574 TacoCube]
:'''Victoria'''
::[http://www.speedsolving.com/forum/member.php?u=9059 hic0057]

===New Zealand===
:[http://www.speedsolving.com/forum/member.php?u=1293 *LukeMayn*]
:'''Hamilton'''
::[http://www.speedsolving.com/forum/member.php?u=1345 auhsoj]
:'''Christchurch'''
::[http://www.speedsolving.com/forum/member.php?u=765 Dene]

==South America==

===Brazil===
:[http://www.speedsolving.com/forum/member.php?u=11 Pedro]

[[Category:Cubing Community]]

List of cubing memes

2011-01-19T17:53:30Z

Riffz: /* I'm calling you out! Time to make a malt liquor video! (February 2010) */

Memes created by the cubing community, mostly on the [[Speedsolving Forums]]. See also the [http://www.speedsolving.com/forum/showthread.php?26846-Speedsolving-wiki-List-of-Cubing-Memes corresponding Speedsolving thread].

== Smerbia (2008) ==
* Also see: [[Smerbia]]
* Since 2008, Andrew Nelson has represented the country of Smerbia for the [[Negative Time Solving Contest]]. See [http://cubefreak.net/other/negative/past.html Negative Time Solving Contest results archive]
* [http://caltech.cubingusa.com/utahopen2009/list.php Pre-registration page for Utah Open 2009], where 6 competitors signed up as Smerbians.
* [http://www.speedsolving.com/forum/showthread.php?13827-Country! Smerbia Thread]
* [http://www.urbandictionary.com/define.php?term=Smerbia Urban Dictionary Page]
* [http://www.facebook.com/pages/Smerbia/60556512413 Facebook page for Smerbia]
* [http://caltech.cubingusa.com/berkeleyfall2009/index.php Smerbia Open 2009 on CubingUSA]

== Or you could just use Petrus (August, 2009) ==
"Or you could just use Petrus" represents the largest quote tree in Speedsolving.com history. The evidence for the original piece of art was erased at the discretion of the forum moderators but the memory remains firm. The thread is still hilarious and well worth a read.

[http://www.speedsolving.com/forum/showthread.php?13377-A-new-method-to-solve-the-F2L-of-the-Rubik-s-Cube-! This is the original thread with the quote tree removed]

Later examples found on Speedsolving.com include: [http://www.speedsolving.com/forum/showthread.php?13652-Should-I-stick-with-Petrus&p=207282&viewfull=1#post207282 August 2009], [http://www.speedsolving.com/forum/showthread.php?15005-jsut-had-to-put-this-video-in-the-forums/page2 August 2009], [http://www.speedsolving.com/forum/showthread.php?22013-Best-time-with-Petrus-F2L-beginners-OLL-PLL/page3 June 2010]

== I accidentally a 5x5 (2008?) ==
This was an extension of the existing meme "I accidentally the whole coke bottle" from 4chan. It was brought to the Speedsolving Forums through a post in the accomplishment thread (?), and it is unsure whether this was intentional or not. Several users caught on and would post "I accidentally a _______" without a verb.

Examples on the Speedsolving Forums:
* [http://www.speedsolving.com/forum/showthread.php?25738-I-solve-with-two-hands-sometimes.-(7.84-single-and-10.41-avg5) "I accidentally the last solve"]
* [http://www.speedsolving.com/forum/showthread.php?24429-Race-to-Sub-15-quot-Newer-quot&p=483543&viewfull=1#post483543 "i accidentally the last round"]
* [http://www.speedsolving.com/forum/showthread.php?20834-ZZ-ZB-Home-Thread&p=405079&viewfull=1#post405079 "I accidentally the whole cube over"]
Other examples:
* I accidentally the whole database." - Tyson Mao

* [http://knowyourmeme.com/memes/i-accidentally I Accidentally meme at Know Your Meme]

== i can't go because i live in ___ but you should do ___. just a suggestion (October 2009) ==
Third post into the Speedsolving thread [http://www.speedsolving.com/forum/showthread.php?16231-Belleview-Open-2009-(unofficial) Belleview Open 2009 (unofficial)], user ianini posted the following message: "i can't go because i live in California but you should do a megmnix [sic] round. just a suggestion". Rather than merely pointing out the absurdity of suggesting an event for a competition he was not attending, other users (first none other than Dene) soon started parodying his phrase, forming an ever-extending quote tree. Here are the first few examples:
* i can't go because i live in New Zealand but you should do 6 and 7. just a suggestion
* i can't go because i live in California but you should do magic BLD. just a suggestion
* i can't go because i live in New Jersey but you should do a 2x2 bdl [sic] round. just a suggestion
* i can't go because i live in New York but you should do a tehtreball [sic] round. just a suggestion
* i can't go because i live in great britain but you should do a [[ball-in-cup]] round. just a suggestion
* i can't go because i live in Texas but you should do a mini chess tournament as a side event. just a suggestion
* i can't go because i live in Canada but you should do a fihgt [sic] to the deth. just a suggestion
These posts mirrored the capitalization and punctuation, and in some cases the misspelling of the event name, in the original message. The most nested quote tree ([http://www.speedsolving.com/forum/showthread.php?16231-Belleview-Open-2009-(unofficial)&p=261921&viewfull=1#post261921 this message]) consisted of 25 of these messages. This quote tree won the award for the "best quote tree" in the 2009 Forum Awards.

== lolben (2009) ==
"lolben" is a phrase used to flame or lightly ridicule users on the Speedsolving Forums. It is applied almost exclusively to user ben1996123 ([http://worldcubeassociation.org/results/p.php?i=2009WHIT01 Ben Whitmore]).

ben1996123 posted several videos in late 2009 and early 2010 that were severely flamed for being blatantly rehearsed (e.g. [http://www.speedsolving.com/forum/showthread.php?18905-8.16-second-3x3-solve-%28with-scramble-and-solution%29 8.16 second 3x3 solve (with scramble and solution)]). These videos showed extremely fast, some sub-9, single times with correspondingly ridiculously easy solutions, along with poor fingertricks and blatantly rehearsed reactions afterward. Understandably, the forums had its haxxor detector on max mode. ben1996123's defense, which started by providing Cube Explorer-generated scrambles and solutions, degenerated into rants protesting that his solves were genuine. Subsequent posts by ben1996123 were also flamed, until the community realized the futility of long flames. Instead, the term "lolben" was coined to flame with ease.

The term is now used whenever users encounter an erroneous claim, a fake video, or even just a funny moment. As Waffo says, "tl;dr - lolben because lolben is lol."

An Example of a lolben moment:
[[File:Lolben.jpg]]

== I'm calling you out! Time to make a malt liquor video! (February 2010)==

A drunk man uploaded a video on Youtube calling out Sa967St (Sarah Strong) after he saw a video of her official 10.21 3x3 solve. Throughout the video he drinks a 40oz bottle of malt liquor while trying to reason out why she should quit cubing and make a malt liquor video. He repeates the lines "I'm calling you out", "time to make a malt liquor video", "run down to your nearest store and get yoruself a 40", and several others. She made a [http://www.speedsolving.com/forum/showthread.php?19072-Drunk-guy-calling-me-out thread] for the video on the speedsolving forum. The user removed the video off of Youtube after many members of the speedcubing community commented on his video.

On Sarah's 19th birthday (19 is the legal drinking age in Ontario, Canada), user Reisen Bunny made a [http://www.speedsolving.com/forum/showthread.php?26635-SELA-IS-LEGAL-DRINKING-AGE-NEEDS-TO-MAKE-MALT-LIQUOR-VIDEO thread] to remind her that she needs to run down to the nearest store and get herself a 40. The thread had a poll asking if she should make a malt liquor video, and over 40 people votes 'yes'.

Sarah is yet to make a malt liquor video.

== OrtegaZB (February 2010) ==
Late February, Thom Barlow introduced his method for solving the 2x2 cube basing of the Ortega Method called [http://www.speedsolving.com/forum/showthread.php?19420-OrtegaZB/ "OrtegaZB"]. Upon reading the description, many people immediately picked up that it was just CLL. It was pretty obvious that Thom was just joking and many people joined in on the fun while others were not entertained by the thread even though it was just for fun. Joey Gouly said so himself "This thread really was just for fun! Me and thom were just cubing (in a pub), and came up with the idea!" Perhaps another alcohol fueled Thom Barlow moment.

== F R U R' U' F' is a Y- perm (2010) ==
?

== Speedcubin? (June-July 2010) ==
Speedcubin.

This meme from come a thread titled [http://www.speedsolving.com/forum/showthread.php?22233-Speedcubin "Speedcubin?"] from the user goatseforever. The post asked "Speedcubin?" and the thread had a poll with eight options of "Speedcubin", all identical. This was clearly a troll thread (goatseforever has made many in the past), but several users decided to have fun with it and post about which Speedcubin was best. The thread had over 250 replies but it was closed about a week after it was posted. This thread was the "catch of the day" in the very first episode of the Cubecast Podcast.

== Andrew Kang loves skewbs (July 2010) ==
In the third episode of the [http://www.cubecastpodcast.com Cubecast Podcast] Andrew Kang, the host, revealed that he absolutely loves skewbs. Andrew's love for the skewb event is one of the biggest on-going themes of the podcast, as it gets brought up several times each episode. He also knows everything there is to know about skewbs, and other cube-shaped puzzles that do not turn like a 3x3x3.

== Famous [insert adjective] Rubik (2010) ==
After seeing a newspaper article about himself containing the phrase "Famous Deaf Rubik," Shane Rowland started to use it to refer to himself. His reasoning was that he was "famous" among the deaf community for solving and collecting Rubik's puzzles. Of course this does not make any sense in English, and some cubers spread around "Famous [adjective] Rubik" to parody Shane's title.

* [http://www.facebook.com/pages/Shane-Rowland-Famous-Deaf-Rubik/119220994785897 Facebook page on Shane Rowland - Famous Deaf Rubik]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?25955-It-s-done!-famous-giant-rubik It's done! famous giant rubik]
* nlCuber22's signature: "approved orangina provider for all famous rubiks" (accessed January 17, 2011)
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?26293-10.69-OH-single 10.69 OH single (contains "famous kitten rubik's")]

== I DEMAND TWO ROUNDS OF [insert event]! (Summer 2010) ==
Two threads were posted in the speedsolving forum about [[Haiyan Zhuang]] getting banned from WCA competitions for unsportsman-like behavior. One of the things he did was demand more rounds of BLD, in order to have more attempts to try to break his (former) 3x3 BLD world record. After the community learned about how Haiyan threatened people at competitions, "I DEMAND TWO [or more] ROUNDS OF [insert event]" became a joke to parody Haiyan.

Examples on the Speedsolving Forums:
* [http://www.speedsolving.com/forum/showthread.php?24151-WCA-Competition-stats&p=461438&viewfull=1#post461438 "I DEMAND 3 ROUNDS PYRA." (September 2010)]
* [http://www.speedsolving.com/forum/showthread.php?25872-Princeton-Fall-2011&p=494194&viewfull=1#post494194 "I DEMAND 3 ROUNDS OF OH" (November 2010)]

Non-Example (note date)?
* [http://www.speedsolving.com/forum/showthread.php?20935-Ohio-Open-2010-June-5th-Columbus-OH&p=374636&viewfull=1#post374636 "I DEMAND EIGHT ROUNDS OF FEET SOLVING" (May 2010)]

== Orangina (August 2010) ==
After the second day of [[US Nationals 2010]], a small group of cubers went to the store in the student centre to obtain mass amounts of soda (or pop to some people) and junk food. Upon browsing the selection, Sarah Strong was puzzled when she saw a bottle of Orangina and she asked "What's Orangina?", pronouncing it incorrectly (oh-ran-gy-nah). The group proceeded to break into hysterical laughter. As the laughing receded, one of the cubers in the group told her that the name of the drink is actually pronounced oh-ran-GEE-nah and so was the start of the meme. That night, Chris Tran, Sarah Strong, Waffo, and several others spammed the US Nationals 2010 thread of this discovery as they posted pictures of Orangina ads from the same hotel room. On the third day of US Nationals 2010, Orangina was the joke among that small group, and Ethan Crislip bought several 1L bottles of the carbonated beverage just to try it. Waffo wanted to time it and his first attempt at the bottle was 5x.xx. Soon after Felix Lee and Chris Tran followed Waffo's attempt but were unable to break it. The chugging drew in a crowd as Waffo attempted another 1L of Orangina only a few hours after his first attempt, racing with Sarah Strong, Ryan Reese, and Stachu Korick. He broke his previous UWR with a 48.46 and threw up mere minutes later. Waffo still practices Orangina chugging to date.

After US Nationals was over, Orangina was a wide spread story on the Speedsolving Forums as people changed they avatars to Orangina logos and bottles for quite a while. Many people have tried to take Waffo's throne at a competition but were unable to beat the 48.46 set at US Nationals 2010.

Waffo holds the current UWR for chugging a 1L glass bottle of Orangina (starting with the cap off) at 30.02 seconds.

* YouTube: [http://www.youtube.com/watch?v=aZNe8sgbdIo Waffle 48.46 Orangina UWR (former)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?26006-Orangina-Fail..... Orangina Fail.....]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?26778-my-first-time...-(hi-waffo)/page2 my first time... (hi waffo)]

== Same thing happened to me with some other pants (2010) ==
This meme originated from a Skype conversation between Stachu Korick and Waffo. They were talking about Lady Gaga and Waffo was saying how he didn't have a good first impressioin of her music, but after he listened to a variety of her songs he liked her music more. Stachu agreed and meant to reply "same thing happed to me with some other bands", but instead of "bands" he typed "pants". Waffo found this typo hilarious and spammed some threads on the speedsolving forum with "same thing happened to me with some other pants". [[Dan Cohen]] banned him for one day for spamming. Waffo recieved a message from him saying "You have been banned for the following reason: Too many pants."
Regardless of him being temporarily banned, this meme gets brought up on occasion. Some users mistook this phrase for something along the lines of "same thing happened to me in someone else's pants", and posts like that also come up on occasion.

* Sarah Strong's signature: "[9:34:25 PM] Stachu: same thing happened to me with some other pants"

== 3q (October 2010) ==
The user Zhizhou Zhang posted [http://www.speedsolving.com/forum/showthread.php?24988-who-can-help-me-with-roux-method&p=473401&viewfull=1#post473401 3q very much] in a thread he made asking for help with the Roux method. His native language is Chinese. 3 is pronounced like "san" or "sun" in Chinese (and also in Japanese), so 3q sounds like "sun-Q", which is like "thank you" with an east Asian accent. It may not be too funny for those who did not see the post, but when user Blah, Chester Lian, posted a reply to it, several other people caught on. The most amusing part about this was that Zhizhou Zhang used it casually, forgetting that not everyone on the speedsolving forum knows Chinese. 3q gets brought up on occasion on the forums, but only a handful of people understand it.

== Zeroing (November 2010) ==
Supposedly [[Feliks Zemdegs]]'s secret method, zeroing is a hoax started by the following post by Anthony Brooks on the Speedsolving Forums: [http://www.speedsolving.com/forum/showthread.php?25488-National-IQ-test-Channel-9-Feliks-Zemdegs-s-solve&p=484856&viewfull=1#post484856 post]: "Feliks got the nickname Faz because of the method he uses actually. FAZ stands for F2L After Zeroing. What's "zeroing" you might ask? Only Faz knows at this point. It's apparently his secret weapon, but he won't share. :-("

* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?25517-Predict-Faz-s-secret! Predict Faz's secret!]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?25515-Feliks-Zemdegs-Melbourne-Cube-Day-WRs Feliks Zemdegs Melbourne Cube Day WRs]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?25576-Zeroing-Tutorial-Discussion-(Text-Video!) Zeroing Tutorial/Discussion (Text+Video!)]

== Alot Profile Picture Takeover (November 2010) ==
An Alot is an "imaginary creature that kind of looks like a cross between a bear, a yak and a pug" introduced in the blog [http://hyperboleandahalf.blogspot.com/2010/04/alot-is-better-than-you-at-everything.html Hyperbole and a Half's page on Alot].

On November 22, 2010, user TheRubiksGod created the thread [http://www.speedsolving.com/forum/showthread.php?25696-I-Will-Make-Your-Avatar-D "I Will Make Your Avatar :D"] on the [[Speedsolving Forums]]. Prompted by [[Lucas Garron]]'s [http://www.speedsolving.com/forum/showthread.php?25696-I-Will-Make-Your-Avatar-D&p=490306&viewfull=1#post490306 reply] linking Hyperbole and a Half, the thread turned into a request for Alot of ___ avatars. Many of these were made by [[Shelley Chang]]. Within a week, many prominent users on Speedsolving had changed their profile to some type of Alot.

[[Category:Cubing Community]]

Corner Orientation

2010-09-09T02:02:03Z

Riffz: /* U */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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|!}}

'''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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__

Corner Orientation

2010-09-09T02:01:11Z

Riffz: /* T */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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)}}

|

=== 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|!}}

'''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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__

Corner Orientation

2010-09-09T01:59:29Z

Riffz: /* T */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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)}}

|

=== 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|!}}

'''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)}}

|-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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__

Corner Orientation

2010-09-09T01:57:18Z

Riffz: /* U */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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)}}

|

=== 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|!}}

'''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|!}}

|-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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__

Corner Orientation

2010-09-09T01:55:36Z

Riffz: /* T */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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)}}

|

=== 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|!}}

'''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|!}}

|-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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__

Corner Orientation

2010-09-09T01:54:56Z

Riffz: /* T */

{{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 [[sub step]] 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]]
* [[Orient]]
* [[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|!}}

'''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)}}

|

=== 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|!}}

'''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|(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|!}}

'''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'}}

|
|}

==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|!}}

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

|

=== -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|!}}

'''Sune combos:'''
{{Alg|(y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2}}

'''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}}

'''Any other 2-gen:'''
{{Alg|(y) (R U R' U) (R U' R' U) (R U2' R') (R2 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|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}}
{{Alg|(r U2 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|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}}

'''Any other 2-gen:'''
{{Alg|!}}

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

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

'''Any other:'''
{{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 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|(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' R' L}}

|-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|(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|(y) U L U' R' U L' U' R}}

'''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|!}}

|

=== 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}}

|}

[[Category:Puzzle Theory]]
[[Category:Cubing Terminology]]
[[Category:Sub Steps]]

__NOTOC__