Difference between revisions of "Corner Orientation"

m (Pure CO)
m (Removed apostrophe from my previous edit)
 
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'''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.
+
{{Substep Infobox
 +
|name=Corner Orientation
 +
|image=COinfo.png
 +
|proposers=
 +
|year=
 +
|anames=CO
 +
|variants=[[OCLL]]
 +
|subgroup=
 +
|algs=7
 +
|moves=
 +
|purpose=<sup></sup>
 +
* [[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 [[OLL#All edges flipped correctly|OLL with edges correctly oriented]] (OLL 21 - 27) and the last variation orients the corners ignoring edges (use any [[OLL]] that twists the same corners for that).
+
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).
  
== See also: ==
+
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 different 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]]
 
* [[Orientation]]
* [[Orient]]
 
 
* [[Permutation]]
 
* [[Permutation]]
 
* [[Edge Orientation]]
 
* [[Edge Orientation]]
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* [[Partial Corner Control]]
 
* [[Partial Corner Control]]
 
= Pure CO =
 
= Pure CO =
'''Usage:''' [[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 orienting the edges can be found at the [[ELL|ELL page]]). 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).
+
'''Usage:''' Besides that these cases are a group in [[L4C]], [[L3C]], [[ZBLL]], [[ZZLL]];
  
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]] (anti and mirrors included), the third section is for these combinations. 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.
+
[[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]]''.
  
Note that all of these algorithms are written in the Western [[notation]], where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z.
+
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 different 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 solvable using only two sides (RU [[2-gen]]). There are different sections for different 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}}
  
<strong>Click on an algorithm (not the camera icon) to watch an animation of it.</strong>
 
 
 
==Two corners unoriented==
 
==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"
 
{|border="0" width="100%" valign="top" cellpadding="3"
  
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|
 
|
 
=== U ===
 
=== U ===
[[File:Pure twist U.jpg]]
+
{{case |image=Pure twist U.jpg
 
+
|name=U, [[Headlights]], Superman
 +
|methods=[[L3C]], [[L4C]], [[BLD]]
 +
|optimal=13 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''Optimal 2-gen:'''
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R U2}}
+
{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)}}
{{Alg|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{Alg|R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)}}
  
 
'''Sune combos:'''
 
'''Sune combos:'''
 
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}
 
{{Alg|(R U2 R' U' R U' R') (L' U2 L U L' U L)}}
{{Alg|!}}
+
{{Alg|(R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)}}
  
 
'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}
 
{{Alg|F U' R2 U R2 U F U' F2 D R2 D' R2}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{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}}
 +
{{Alg|(F D' F' R' D' R) U (R' D R F D F') U'}}
  
 
|
 
|
  
 
=== T ===
 
=== T ===
[[File:Pure twist T.jpg]]
+
{{case |image=Pure twist T.jpg
 
+
|name=T
 +
|methods=[[L3C]], [[L4C]], [[BLD]]
 +
|optimal=13 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''Optimal 2-gen:'''
{{Alg|U R2 U' R U' R2 U R2 U R U' R' U' R U R2}}
+
{{Alg|(U) R2 U' R U' R2 U R2 U R U' R' U' R U R2}}
{{Alg|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{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:'''
 
'''Sune combos:'''
{{Alg|!}}
+
{{Alg|(L' U' L U' L' U2 L) (R U R' U R U2 R')}}
 +
{{Alg|(U2) (R' U' R U' R' U2 R) U2 (R U R' U R U2 R')}}
  
 
'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}
 
{{Alg|U R2 U' B R2 D' R2 D B2 U' B U R2}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{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}}
 +
{{Alg|(R' D R F D F') U (F D' F' R' D' R) U'}}
  
 
|-valign="top"
 
|-valign="top"
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=== L ===
 
=== L ===
[[File:Pure twist L.jpg]]
+
{{case |image=Pure twist L.jpg
 
+
|name=L, Bowtie
 +
|methods=[[L3C]], [[L4C]], [[BLD]]
 +
|optimal=12 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''Optimal 2-gen:'''
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' U'}}
+
{{Alg|R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')}}
{{Alg|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{Alg|(U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R}}
  
 
'''Sune combos:'''
 
'''Sune combos:'''
{{Alg|!}}
+
{{Alg|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}}
 +
{{Alg|(U) F (R U2 R' U' R U' R') U2 (R' U2 R U R' U R) U2 F}}
  
'''HTM optimal:'''
+
'''HTM optimal:''' <small>(12 move commutator)</small>
{{Alg|U2 R' B D2 B' R U2 R' B D2 B' R}}
+
{{Alg|U2 (R' B D2 B' R) U2 (R' B D2 B' R)}}
{{Alg|!}}
+
{{Alg|(F L' D2 L F') U2 (F L' D2 L F') U2}}
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{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}}
 +
{{Alg|(F D' F' R' D' R) U2 (R' D R F D F') U2}}
  
 
|
 
|
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|
 
|
 
=== S ===
 
=== S ===
[[File:Pure twist S.jpg]]
+
{{case |image=Pure twist S.jpg
 
+
|name=S, Sune
 +
|methods=[[L3C]], [[L4C]], [[BLD]]
 +
|optimal=13 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''Optimal 2-gen:'''
 
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}
 
{{Alg|R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2}}
{{Alg|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{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:'''
 
'''Sune combos:'''
{{Alg|!}}
+
{{Alg|(U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)}}
  
 
'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}
 
{{Alg|U' B U' F U2 B2 D' R2 U D F' U' B}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }}
  
 
|
 
|
  
 
=== -S ===
 
=== -S ===
[[File:Pure twist aS.jpg]]
+
{{case |image=Pure twist aS.jpg
 
+
|name=-S, Antisune
 +
|methods=[[L3C]], [[L4C]], [[BLD]]
 +
|optimal=13 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''Optimal 2-gen:'''
 
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}
 
{{Alg|R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R}}
{{Alg|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{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:'''
 
'''Sune combos:'''
{{Alg|!}}
+
{{Alg|(U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)}}
  
 
'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}
 
{{Alg|U R' U L U' D' F2 D R2 U2 L' U R'}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{Alg|U2 R U2 R' U' R U' R d M U2 M' d L2}}
  
 
|}
 
|}
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|
 
|
 
=== H ===
 
=== H ===
[[File:Pure twist H.jpg]]
+
{{case |image=Pure twist H.jpg
 
+
|name=H
 +
|methods=[[L4C]], [[BLD]]
 +
|optimal=16 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''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)}}
{{Alg|!}}
+
{{Alg|R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')}}
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{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:'''
 
'''Sune combos:'''
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'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}
 
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
{{Alg|!}}
+
{{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 ===
 
=== pi ===
[[File:Pure twist pi.jpg]]
+
{{case |image=Pure twist pi.jpg
 
+
|name=pi, Bruno
 +
|methods=[[L4C]], [[BLD]]
 +
|optimal=15 [[HTM]]
 +
|text=
 +
}}
 
'''Optimal 2-gen:'''
 
'''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)}}
{{Alg|!}}
+
{{Alg|R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')}}
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
{{Alg|!}}
+
{{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:'''
 
'''Sune combos:'''
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'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}
 
{{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}}
 +
{{Alg|U R U2 R' U' R U' R' U2 R' U2 R U R' U R}}
 +
{{Alg|U R' U2 R U R' U R U2 R U2 R' U' 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}}
 +
{{Alg|U' R U R' U R U2 R' U2 R' U' R U' R' U2 R}}
 +
{{Alg|U' R' U' R U' R' U2' R U2 R U R' U R U2 R'}}
 +
 +
'''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}}
 +
{{Alg|U2 R' U' R U' R' U R U' R' U R U' R' U2 R}}
 +
{{Alg|U' R U2 R' U' R U R' U' R U R' U' R U' R'}}
 +
 +
'''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|!}}
 
{{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:'''
 
'''Any other:'''
Line 194: Line 385:
 
|}
 
|}
  
 +
==Four corners==
 +
{|border="0" width="100%" valign="top" cellpadding="3"
  
[[Category:Puzzle Theory]]
+
|-valign="top"
[[Category:Cubing Terminology]]
+
|
[[Category:Sub Steps]]
+
=== 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__
 
__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|y R U2 R' (U' R U R') U' (R U' R')|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|R U2' R2' U' R2 U' R2' U2' R|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}}

Latest revision as of 09:16, 12 March 2017

Corner Orientation
COinfo.png
Information
Proposer(s):
Proposed:
Alt Names: CO
Variants: OCLL
Subgroup:
No. Algs: 7
Avg Moves:
Purpose(s):
Previous state: unknown
Next state: unknown

Previous cube state -> Corner Orientation step -> Next cube state


The Corner Orientation step is the step between the Previous cube state and the Next cube state.

Corner Orientation, abbrevaited CO, the orientation of a cube's corners. There are three possible corner cubie orientations. CO is a substep in many methods.

For the last layer of the 3x3x3 cube there are three main variations used for the seven cases of CO, one that is named 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 different variations of CO;

  • Pure CO: orients corners preserving edge orientation and both corner and edge permutation.
  • OCLL-EPP: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

See also

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 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 different start of the last layer that gives a easier case in the end).

Algorithms

All cases here have long algorithms, 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 solvable using only two sides (RU 2-gen). There are different sections for different 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.

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms)

Click on an algorithm (not the camera icon) to watch an animation of it.

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).

U

Pure twist U.jpg

Name: U, Headlights, Superman
Used in: L3C, L4C, BLD
Optimal moves: 13 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U2 R' U R' U2 R U2 R U R' U' R' U R (U2)


Any other 2-gen:

Speedsolving Logo tiny.gif Alg R' U2 R U' R U2 R' U2 R' U' R U R U' R' (U2)


Sune combos:

Speedsolving Logo tiny.gif Alg (R U2 R' U' R U' R') (L' U2 L U L' U L)
Speedsolving Logo tiny.gif Alg (R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)


HTM optimal:

Speedsolving Logo tiny.gif Alg F U' R2 U R2 U F U' F2 D R2 D' R2


Any other:

Speedsolving Logo tiny.gif Alg (x) U2 R' U' R U' R' L' U2 L U L' U L R (x')
Speedsolving Logo tiny.gif Alg (z') (U R U' R')2 L' (R U R' U')2 L (z)
Speedsolving Logo tiny.gif Alg (y2) (R U R' U')2 L' (U R U' R')2 L
Speedsolving Logo tiny.gif Alg (F D' F' R' D' R) U (R' D R F D F') U'


T

Pure twist T.jpg

Name: T
Used in: L3C, L4C, BLD
Optimal moves: 13 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg (U) R2 U' R U' R2 U R2 U R U' R' U' R U R2


Any other 2-gen:

Speedsolving Logo tiny.gif Alg (U2) R U R' U' R' U R U2 R U2 R' U R' U2 R
Speedsolving Logo tiny.gif Alg (U2) R' U' R U' R' U2 R U2 R U R' U R U2 R'


Sune combos:

Speedsolving Logo tiny.gif Alg (L' U' L U' L' U2 L) (R U R' U R U2 R')
Speedsolving Logo tiny.gif Alg (U2) (R' U' R U' R' U2 R) U2 (R U R' U R U2 R')


HTM optimal:

Speedsolving Logo tiny.gif Alg U R2 U' B R2 D' R2 D B2 U' B U R2


Any other:

Speedsolving Logo tiny.gif Alg (z') (R U R' U')2 L' (U R U' R')2 L (z)
Speedsolving Logo tiny.gif Alg (y2) (U R U' R')2 L' (R U R' U')2 L
Speedsolving Logo tiny.gif Alg (R' D R F D F') U (F D' F' R' D' R) U'


L

Pure twist L.jpg

Name: L, Bowtie
Used in: L3C, L4C, BLD
Optimal moves: 12 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U' R' U2 R' U2 R U R' U R U2 R U2 R' (U')


Any other 2-gen:

Speedsolving Logo tiny.gif Alg (U') R U2 R' U2 R' U' R U R U' R' U2 R' U2 R


Sune combos:

Speedsolving Logo tiny.gif Alg B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B
Speedsolving Logo tiny.gif Alg (U) F (R U2 R' U' R U' R') U2 (R' U2 R U R' U R) U2 F


HTM optimal: (12 move commutator)

Speedsolving Logo tiny.gif Alg U2 (R' B D2 B' R) U2 (R' B D2 B' R)
Speedsolving Logo tiny.gif Alg (F L' D2 L F') U2 (F L' D2 L F') U2


Any other:

Speedsolving Logo tiny.gif Alg R U' R' L' U2 L U L' U L R U2 R' U'
Speedsolving Logo tiny.gif Alg y' R' U L U' R U2 y' R' U' R F' R' U R U2
Speedsolving Logo tiny.gif Alg (F D' F' R' D' R) U2 (R' D R F D F') U2


Three corners unoriented

S

Pure twist S.jpg

Name: S, Sune
Used in: L3C, L4C, BLD
Optimal moves: 13 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R' U R' U R2 U R' U R2 U R' U R U2 R U2 R2


Any other 2-gen:

Speedsolving Logo tiny.gif Alg R U R2 U' R2 U R U R' U' R U R U R U' R' (U)
Speedsolving Logo tiny.gif Alg (R U R' U') R' U' R' U' (R U R' U') R2 U2 R2 U2 R' (U')


Sune combos:

Speedsolving Logo tiny.gif Alg (U') (R' U2 R U R' U' R U R' U R) (U) (R U2 R' U' R U' R') (U2)


HTM optimal:

Speedsolving Logo tiny.gif Alg U' B U' F U2 B2 D' R2 U D F' U' B


Any other:

Speedsolving Logo tiny.gif Alg (y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y)


-S

Pure twist aS.jpg

Name: -S, Antisune
Used in: L3C, L4C, BLD
Optimal moves: 13 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R2 U2 R' U R' U2 R' U R' U' R2 U' R2 U' R' U R


Any other 2-gen:

Speedsolving Logo tiny.gif Alg R2 U2 R' U2 R' U' R U' R2 U' R U' R2 U' R U' R
Speedsolving Logo tiny.gif Alg (U2) R U' R2 U' R U' R' U2 R' U2 R' U' R U' R2 (U)


Sune combos:

Speedsolving Logo tiny.gif Alg (U2) (R U2 R' U' R U R' U' R U' R') (U') (R' U2 R U R' U R) (U)


HTM optimal:

Speedsolving Logo tiny.gif Alg U R' U L U' D' F2 D R2 U2 L' U R'


Any other:

Speedsolving Logo tiny.gif Alg U2 R U2 R' U' R U' R d M U2 M' d L2


Four corners unoriented

H

Pure twist H.jpg

Name: H
Used in: L4C, BLD
Optimal moves: 16 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R (U)
Speedsolving Logo tiny.gif Alg R' U' R2 U R2 U R' U2 R' U2 R' U R2 U R2 U' R' (U')


Any other 2-gen:

Speedsolving Logo tiny.gif 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:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2


Any other:

Speedsolving Logo tiny.gif Alg (r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')
Speedsolving Logo tiny.gif Alg (r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)
Speedsolving Logo tiny.gif Alg (L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')
Speedsolving Logo tiny.gif Alg F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')
Speedsolving Logo tiny.gif Alg d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2


pi

Pure twist pi.jpg

Name: pi, Bruno
Used in: L4C, BLD
Optimal moves: 15 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U R2 U' R2 U' R2 U2 R2 U' R' U R U2 R' (U)
Speedsolving Logo tiny.gif Alg R' U' R2 U R2 U R2 U2 R2 U R U' R' U2 R (U')


Any other 2-gen:

Speedsolving Logo tiny.gif Alg (y) R U2 R' U' R U R2 U2 R2 U R2 U R2 U' R' (U')
Speedsolving Logo tiny.gif Alg (y') R' U2 R U R' U' R2 U2 R2 U' R2 U' R2 U R (U)


Sune combos:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2


Any other:

Speedsolving Logo tiny.gif Alg (y) R' U' (R' F R F') (R U' R' U) (R' F R F') R U' R' U2 R
Speedsolving Logo tiny.gif Alg B (U L U' L') (U L U') L2 (x') U' M' U L U' M (x)
Speedsolving Logo tiny.gif Alg (y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'
Speedsolving Logo tiny.gif 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

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms)

Click on an algorithm (not the camera icon) to watch an animation of it.

Two corners

U (EPP)

OCLL-EPP U.jpg

Name: U, Headlights, Superman
Used in: 2-look L4C
Optimal moves: 9 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg U' R' U2 R' U2 R U R' U R U2 R U2 R' U' R
Speedsolving Logo tiny.gif Alg U R U2 R' U' R U' R' U2 R' U2 R U R' U R
Speedsolving Logo tiny.gif Alg U R' U2 R U R' U R U2 R U2 R' U' R U' R'


HTM optimal:

Speedsolving Logo tiny.gif Alg R2 D' R U2 R' D R U2 R
Speedsolving Logo tiny.gif Alg R2 F2 R' B2 R F2 R' B2 R'
Speedsolving Logo tiny.gif Alg (z' y') U2 R2 U' L2 U R2 U' L2 U' (y z)


Any other:

Speedsolving Logo tiny.gif Alg R U2 R2 U L U' R2 U L' U R'
Speedsolving Logo tiny.gif Alg R' U2 R F' R' F U2 F' R F



T (EPP)

OCLL-EPP T.jpg

Name: T
Used in: 2-look L4C
Optimal moves: 8 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R' U' R' U R U2 R U2 R' U R' U2 R U2 R U
Speedsolving Logo tiny.gif Alg U' R U R' U R U2 R' U2 R' U' R U' R' U2 R
Speedsolving Logo tiny.gif Alg U' R' U' R U' R' U2' R U2 R U R' U R U2 R'


HTM optimal:

Speedsolving Logo tiny.gif Alg R' F' R B' R' F R B
Speedsolving Logo tiny.gif Alg (x) R' U' R D' R' U R D (x')
Speedsolving Logo tiny.gif Alg (x') R' D' R U' R' D R U (x)
Speedsolving Logo tiny.gif Alg (y') r U R' U' r' F R F'
Speedsolving Logo tiny.gif Alg (y) l U L' U' R' U L U' (x)


Any other:

Speedsolving Logo tiny.gif Alg F U F' R' F U' F' U R U'
Speedsolving Logo tiny.gif Alg (y') R U R' U' L' U R U' M' (x')


L (EPP)

OCLL-EPP L.jpg

Name: L, Bowtie
Used in: 2-look L4C
Optimal moves: 8 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R' U' R2 U2 R2 U R U' R U R2 U2 R2 U' R' U
Speedsolving Logo tiny.gif Alg U2 R' U' R U' R' U R U' R' U R U' R' U2 R
Speedsolving Logo tiny.gif Alg U' R U2 R' U' R U R' U' R U R' U' R U' R'


HTM optimal:

Speedsolving Logo tiny.gif Alg R B' R' F R B R' F'
Speedsolving Logo tiny.gif Alg (y) F R' F' r U R U' r'
Speedsolving Logo tiny.gif Alg (x') U' R U L' U' R' U r


Any other:

Speedsolving Logo tiny.gif Alg U' F U R' U' R F' R' U R
Speedsolving Logo tiny.gif Alg R U R U' L' U R' U' M' (x')


Three corners

S (EPP)

OCLL-EPP S.jpg

Name: S, Sune
Used in: 2-look L4C
Optimal moves: 8 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg U2 R' U' R U' R U R2 U R2 U2 R'


HTM optimal:

Speedsolving Logo tiny.gif Alg R U' L' U R' U' L U


Any other:

Speedsolving Logo tiny.gif Alg !


-S (EPP)

OCLL-EPP aS.jpg

Name: -S, Antisune
Used in: 2-look L4C
Optimal moves: 8 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg U2 R U2 R2 U' R2 U' R' U R' U R


HTM optimal:

Speedsolving Logo tiny.gif Alg U' L' U R U' L U R'


Any other:

Speedsolving Logo tiny.gif Alg !


Four corners

H (EPP)

OCLL-EPP H.jpg

Name: H
Used in: 2-look L4C
Optimal moves: 12 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'


HTM optimal:

Speedsolving Logo tiny.gif Alg R' F2 R2 U2 R' F2 R U2 R2 F2 R U2


Any other:

Speedsolving Logo tiny.gif Alg F (R U R' U')3 F'


pi (EPP)

OCLL-EPP pi.jpg

Name: pi, Bruno
Used in: 2-look L4C
Optimal moves: 12 HTM

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg R U' R U R' U R' U' R2 U R' U' R U' R2 U


HTM optimal:

Speedsolving Logo tiny.gif Alg R F' D2 F R' U' R F' D2 F R' U


Any other:

Speedsolving Logo tiny.gif Alg R' U L U' R U L2 U R U' L U R' U2
Speedsolving Logo tiny.gif Alg L U' R' U L' U' R2 U' L' U R' U' L U2



OLC Algorithms

Orient Last Corners (OLC), also known as Orient Last 4 Corners (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.

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms)

Click on an algorithm (not the camera icon) to watch an animation of it.

OLC 1

Probability 4/27

O27.gif

Name: S, Sune, Swimming Left
Used in: ZZ-reduction
Optimal moves: {{{optimal}}}

Speedsolving Logo tiny.gif OLL R U' L' U R' U' L
Speedsolving Logo tiny.gif OLL y2 R' U L U' R U L'
Speedsolving Logo tiny.gif OLL U R U' L' U R' U' L


OLC 2

Probability 4/27

O26.gif

Name: -S, Antisune, Swimming Right
Used in: ZZ-reduction
Optimal moves: ? HTM

Speedsolving Logo tiny.gif OLL L' U R U' L U R'


OLC 3

Probability 2/27

O21.gif

Name: H, Double Sune, Flip, Cross
Used in: ZZ-reduction
Optimal moves: ? HTM, ? STM

Speedsolving Logo tiny.gif OLL y F (R U R' U')3 F'
Speedsolving Logo tiny.gif OLL y R U2 R' (U' R U R') U' (R U' R')
Speedsolving Logo tiny.gif OLL R U2 R' F R' F' R F2 L F L' F


OLC 4

Probability 4/27

O22.gif

Name: pi, Bruno, wheel, T-shirt
Used in: ZZ-reduction
Optimal moves: ? HTM

Speedsolving Logo tiny.gif OLL f (R U R' U') F f' (R U R' U') F'
Speedsolving Logo tiny.gif OLL R U2' R2' U' R2 U' R2' U2' R
Speedsolving Logo tiny.gif OLL y U L' U2 L2 U L2 U L2 U2 L' U2


OLL 23

Probability 4/27

O23.gif

Name: U, Headlights, Superman
Used in: OCLL, OLL
Optimal moves: 9 HTM

Speedsolving Logo tiny.gif OLL R2' D' R U2 R' D R U2 R
Speedsolving Logo tiny.gif OLL y' F L' D2 L U2 L' D2 L U2 F'
Speedsolving Logo tiny.gif OLL y' B L2 B R2 B F2 R2 B L2 F2
Speedsolving Logo tiny.gif OLL y' B' F2 R2 B L2 B' R2 B L2 F2
Speedsolving Logo tiny.gif OLL L2 D L' U2 L D' L' U2 L'
Speedsolving Logo tiny.gif OLL (y2) R' F2 R U2 R U2 R' F2 R U2 R'
Speedsolving Logo tiny.gif OLL (y2) R2 D R' U2 R D' R' U2 R'
Speedsolving Logo tiny.gif OLL R2 D R' U2' R D' R' U2 R'
Speedsolving Logo tiny.gif OLL F R U' R' U R U R' U R U' R' F'
Speedsolving Logo tiny.gif OLL (R' U' R U') R' U2 R2 U (R' U R U2 R')
Speedsolving Logo tiny.gif OLL l2 U' R D2 R' U R D2 R
Speedsolving Logo tiny.gif OLL l2' U' z' U R2 U' L U R2 U z'
Speedsolving Logo tiny.gif OLL y2 R2' B2 R F2' R' B2 R F2' R
Speedsolving Logo tiny.gif OLL (x) R' B2' (R U' R' U) B2' (U' R U)
Speedsolving Logo tiny.gif OLL y' F' L2 F' R2 B2 F' R2 F' L2 B2


OLL 24

Probability 4/27

O24.gif

Name: T, chameleon, shark, Hammerhead, Little Horse, stingray
Used in: OCLL, OLL
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif OLL r U R' U' L' U R U' x'
Speedsolving Logo tiny.gif OLL r U R' U' r' F R F'
Speedsolving Logo tiny.gif OLL (y' x') R U R' D R U' R' D'
Speedsolving Logo tiny.gif OLL (y') F R U R' U' R U' R' U' R U R' F'
Speedsolving Logo tiny.gif OLL (y x) D' R' U R D R' U' R x'
Speedsolving Logo tiny.gif OLL (y x) D L U' L' D' L U L' x'
Speedsolving Logo tiny.gif OLL (y x') U' R' D R U R' D' R x
Speedsolving Logo tiny.gif OLL (y2) R' F' L F R F' L' F
Speedsolving Logo tiny.gif OLL (y2) R' F' r U R U' r' F
Speedsolving Logo tiny.gif OLL (y2) l' U' L U R U' r' F
Speedsolving Logo tiny.gif OLL (y') l U l' F R B' R' F'


OLL 25

Probability 4/27

O25.gif

Name: L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship
Used in: OCLL, OLL
Optimal moves: 8 HTM

Speedsolving Logo tiny.gif OLL y' F' r U R' U' r' F R
Speedsolving Logo tiny.gif OLL R U2 R' U' (R U R' U') (R U R' U') R U' R'
Speedsolving Logo tiny.gif OLL R U R' U (R U' R' U) (R U' R' U) R U2 R'
Speedsolving Logo tiny.gif OLL y2 R' F R B' R' F' R B
Speedsolving Logo tiny.gif OLL y2 F R' F' L F R F' L'
Speedsolving Logo tiny.gif OLL y F' L F R' F' L' F R
Speedsolving Logo tiny.gif OLL y' F' r U R' U' r' F R
Speedsolving Logo tiny.gif OLL y' x U R' U' L U R U' r'
Speedsolving Logo tiny.gif OLL R' F' L' F R F' L F
Speedsolving Logo tiny.gif OLL y2 R U2' R D R' U2 R D' R2'
Speedsolving Logo tiny.gif OLL y2 F R' F' r U R U' r'
Speedsolving Logo tiny.gif OLL y2 l' U R D' R' U' R D x'
Speedsolving Logo tiny.gif OLL y2 x' L' U' R' U L U' R U
Speedsolving Logo tiny.gif OLL x' D R U R' D' R U' l'
Speedsolving Logo tiny.gif OLL x' U L' U' R U L U' l'
Speedsolving Logo tiny.gif OLL x' R' D R U' R' D' R U x
Speedsolving Logo tiny.gif OLL x R' U R D' R' U' R D x'
Speedsolving Logo tiny.gif OLL y2 x L U' L' D L U L' D' x'
Speedsolving Logo tiny.gif OLL l' U' L' U R U' L U x'
Speedsolving Logo tiny.gif OLL U r U R U' L' U R' U' x'
Speedsolving Logo tiny.gif OLL R U2 R' U' (R U R' U')2 R U' R'
Speedsolving Logo tiny.gif OLL y2 L' R U R' U' L U R U' R'
Speedsolving Logo tiny.gif OLL F R B R' F' l U' l'
Speedsolving Logo tiny.gif OLL U R U2 R' L' U' L U' R U' R' L' U2 L
Speedsolving Logo tiny.gif OLL y R U R' U' R' F R U R U' R' F'