Difference between revisions of "Corner Orientation"
m (Removed apostrophe from my previous edit) |
|||
(87 intermediate revisions by 12 users not shown) | |||
Line 1: | Line 1: | ||
− | '''Corner Orientation''', abbrevaited '''CO''', the [[orientation]] of a [[cube]]'s [[corner]]s. There are three possible corner cubie orientations. CO is a [[ | + | {{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 [[OCLL]] (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). | ||
Line 5: | Line 18: | ||
The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation". | The separation of the corners to their correct layers on the [[Square-1]] is often wrongly named "corner orientation". | ||
− | == See also | + | '''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]] | ||
− | |||
* [[Permutation]] | * [[Permutation]] | ||
* [[Edge Orientation]] | * [[Edge Orientation]] | ||
Line 22: | Line 38: | ||
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). | 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 | + | 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 | + | ===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 | + | 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}} | |
− | |||
− | |||
==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). | 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). | ||
Line 38: | Line 52: | ||
| | | | ||
=== U === | === U === | ||
− | + | {{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)}} |
'''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|(R U2 R' U' R U' R') U2 (R' U2 R U R' U R) (U2)}} | ||
'''HTM optimal:''' | '''HTM optimal:''' | ||
Line 53: | Line 72: | ||
'''Any other:''' | '''Any other:''' | ||
− | {{Alg|(x | + | {{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 === | ||
− | + | {{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}} |
'''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|(L' U' L U' L' U2 L) (R U R' U R U2 R')}} | {{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:''' | ||
Line 73: | Line 101: | ||
'''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" | ||
Line 79: | Line 109: | ||
=== L === | === L === | ||
− | + | {{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')}} |
'''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|B' (R U2 R' U' R U' R') (L' U2 L U L' U L) B}} | {{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:''' <small>(12 move commutator)</small> | '''HTM optimal:''' <small>(12 move commutator)</small> | ||
Line 96: | Line 131: | ||
'''Any other:''' | '''Any other:''' | ||
{{Alg|R U' R' L' U2 L U L' U L R U2 R' U'}} | {{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}} | ||
| | | | ||
Line 106: | Line 143: | ||
| | | | ||
=== S === | === S === | ||
− | + | {{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}} | ||
'''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:''' | ||
Line 121: | Line 163: | ||
'''Any other:''' | '''Any other:''' | ||
− | {{Alg|(y) U2 R' U2 R U R' U R' d M' U2 M d' L2}} | + | {{Alg|(y) U2 R' U2 R U R' U R' d' M' U2 M d' L2 (y) }} |
| | | | ||
=== -S === | === -S === | ||
− | + | {{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}} | ||
'''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:''' | ||
Line 151: | Line 198: | ||
| | | | ||
=== H === | === H === | ||
− | + | {{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|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|(y) (R U R' U) (R U' R' U) (R U2 | + | {{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:''' | ||
Line 166: | Line 218: | ||
'''Any other:''' | '''Any other:''' | ||
+ | {{Alg|(r U2 R' U' R U R' U' R U' r') (M U' M' U2 M U' M')}} | ||
+ | {{Alg|(r' U2 R U R' U' R U R' U r) (M' U M U2 M' U M)}} | ||
+ | {{Alg|(L' U' L U' L' U L U' L' U2 L) (R U R' U R U' R' U R U2' R')}} | ||
{{Alg|F U R d' R U' R' d R' U R d' R U' R' d l' U' (x')}} | {{Alg|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}} | {{Alg|d R2 U2 R' (y x) M2 U M2 U (x' y') U2 R2 d' M2 U M2}} | ||
Line 174: | Line 227: | ||
=== pi === | === pi === | ||
− | + | {{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|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:''' | ||
Line 189: | Line 248: | ||
'''Any other:''' | '''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|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|(y2) F U R U' R' U R U' R' F' r U R' U' M U R U' R'}} | ||
Line 195: | Line 255: | ||
|} | |} | ||
− | |||
= OCLL-EPP = | = 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. | '''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 ( | + | '''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 | + | ===Algorithms=== |
− | + | {{Algnote}} | |
− | + | ==Two corners== | |
− | |||
− | ==Two corners | ||
− | |||
{|border="0" width="100%" valign="top" cellpadding="3" | {|border="0" width="100%" valign="top" cellpadding="3" | ||
Line 213: | Line 271: | ||
| | | | ||
=== U (EPP) === | === U (EPP) === | ||
− | + | {{case |image=OCLL-EPP U.jpg | |
− | + | |name=U, Headlights, Superman | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=9 [[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|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:''' | '''HTM optimal:''' | ||
− | {{Alg| | + | {{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:''' | '''Any other:''' | ||
− | {{Alg| | + | {{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) === | === T (EPP) === | ||
− | + | {{case |image=OCLL-EPP T.jpg | |
− | + | |name=T | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=8 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg| | + | {{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:''' | '''HTM optimal:''' | ||
− | {{Alg| | + | {{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:''' | '''Any other:''' | ||
− | {{Alg| | + | {{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" | |-valign="top" | ||
Line 242: | Line 321: | ||
=== L (EPP) === | === L (EPP) === | ||
− | + | {{case |image=OCLL-EPP L.jpg | |
− | + | |name=L, Bowtie | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=8 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg| | + | {{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:''' | '''HTM optimal:''' | ||
− | {{Alg| | + | {{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:''' | '''Any other:''' | ||
− | {{Alg| | + | {{Alg|U' F U R' U' R F' R' U R}} |
+ | {{Alg|R U R U' L' U R' U' M' (x')}} | ||
| | | | ||
|} | |} | ||
− | ==Three corners | + | ==Three corners== |
{|border="0" width="100%" valign="top" cellpadding="3" | {|border="0" width="100%" valign="top" cellpadding="3" | ||
Line 262: | Line 350: | ||
| | | | ||
=== S (EPP) === | === S (EPP) === | ||
− | + | {{case |image=OCLL-EPP S.jpg | |
− | + | |name=S, Sune | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=8 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg| | + | {{Alg|U2 R' U' R U' R U R2 U R2 U2 R'}} |
'''HTM optimal:''' | '''HTM optimal:''' | ||
− | {{Alg| | + | {{Alg|R U' L' U R' U' L U}} |
'''Any other:''' | '''Any other:''' | ||
− | {{Alg|}} | + | {{Alg|!}} |
| | | | ||
=== -S (EPP) === | === -S (EPP) === | ||
− | + | {{case |image=OCLL-EPP aS.jpg | |
− | + | |name=-S, Antisune | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=8 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg| | + | {{Alg|U2 R U2 R2 U' R2 U' R' U R' U R}} |
'''HTM optimal:''' | '''HTM optimal:''' | ||
− | {{Alg| | + | {{Alg|U' L' U R U' L U R'}} |
'''Any other:''' | '''Any other:''' | ||
Line 289: | Line 385: | ||
|} | |} | ||
− | ==Four corners | + | ==Four corners== |
{|border="0" width="100%" valign="top" cellpadding="3" | {|border="0" width="100%" valign="top" cellpadding="3" | ||
Line 295: | Line 391: | ||
| | | | ||
=== H (EPP) === | === H (EPP) === | ||
− | + | {{case |image=OCLL-EPP H.jpg | |
− | + | |name=H | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=12 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg|R U | + | {{Alg|R U R' U' R' U2 R' U R U' R U2 R2 U2 R' U'}} |
'''HTM optimal:''' | '''HTM optimal:''' | ||
− | {{Alg|R U2 | + | {{Alg|R' F2 R2 U2 R' F2 R U2 R2 F2 R U2}} |
'''Any other:''' | '''Any other:''' | ||
− | {{Alg| | + | {{Alg|F (R U R' U')3 F'}} |
| | | | ||
=== pi (EPP) === | === pi (EPP) === | ||
− | + | {{case |image=OCLL-EPP pi.jpg | |
− | + | |name=pi, Bruno | |
+ | |methods=2-look [[L4C]] | ||
+ | |optimal=12 [[HTM]] | ||
+ | |text= | ||
+ | }} | ||
'''Optimal 2-gen:''' | '''Optimal 2-gen:''' | ||
− | {{Alg| | + | {{Alg|R U' R U R' U R' U' R2 U R' U' R U' R2 U}} |
'''HTM optimal:''' | '''HTM optimal:''' | ||
− | {{Alg|U R | + | {{Alg|R F' D2 F R' U' R F' D2 F R' U}} |
'''Any other:''' | '''Any other:''' | ||
− | {{Alg| | + | {{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 | + | [[Category:Puzzle theory]] |
− | [[Category: | + | [[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}} |
Revision as of 09:16, 12 March 2017
|
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
- Orientation
- Permutation
- Edge Orientation
- Corner Permutation
- OCLL
- Winter Variation
- CLS
- Partial Corner Control
Pure CO
Usage: Besides that these cases are a group in L4C, L3C, ZBLL, ZZLL;
3OP is a blindfold method that orients the pieces before they are placed into position, the algorithms here solves the corner orientation in at the most 3 steps, first, if needed two pieces, one in the top layer and one in the bottom layer to fix orientation parity and then 2-4 corners in the top layer and then the same for the bottom layer. Algs for pure orientation of the edges can be found at the ELL 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).
Three corners unoriented
SOptimal 2-gen:
|
-S
Optimal 2-gen:
|
Four corners unoriented
HOptimal 2-gen:
|
piOptimal 2-gen:
|
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)
Optimal 2-gen:
|
T (EPP)Optimal 2-gen:
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
L (EPP)Optimal 2-gen:
|
Three corners
S (EPP)Optimal 2-gen:
|
-S (EPP)Optimal 2-gen:
|
Four corners
H (EPP)Optimal 2-gen:
|
pi (EPP)Optimal 2-gen:
|
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
Name: S, Sune, Swimming Left |
OLL | R U' L' U R' U' L |
OLL | y2 R' U L U' R U L' |
OLL | U R U' L' U R' U' L |
OLC 2
Probability 4/27
Name: -S, Antisune, Swimming Right |
OLL | L' U R U' L U R' |
OLC 3
Probability 2/27
Name: H, Double Sune, Flip, Cross |
OLL | y F (R U R' U')3 F' |
OLL | y R U2 R' (U' R U R') U' (R U' R') |
OLL | R U2 R' F R' F' R F2 L F L' F |
OLC 4
Probability 4/27
Name: pi, Bruno, wheel, T-shirt |
OLL | f (R U R' U') F f' (R U R' U') F' |
OLL | R U2' R2' U' R2 U' R2' U2' R |
OLL | y U L' U2 L2 U L2 U L2 U2 L' U2 |
OLL 23
Probability 4/27
Name: U, Headlights, Superman |
OLL | R2' D' R U2 R' D R U2 R |
OLL | y' F L' D2 L U2 L' D2 L U2 F' |
OLL | y' B L2 B R2 B F2 R2 B L2 F2 |
OLL | y' B' F2 R2 B L2 B' R2 B L2 F2 |
OLL | L2 D L' U2 L D' L' U2 L' |
OLL | (y2) R' F2 R U2 R U2 R' F2 R U2 R' |
OLL | (y2) R2 D R' U2 R D' R' U2 R' |
OLL | R2 D R' U2' R D' R' U2 R' |
OLL | F R U' R' U R U R' U R U' R' F' |
OLL | (R' U' R U') R' U2 R2 U (R' U R U2 R') |
OLL | l2 U' R D2 R' U R D2 R |
OLL | l2' U' z' U R2 U' L U R2 U z' |
OLL | y2 R2' B2 R F2' R' B2 R F2' R |
OLL | (x) R' B2' (R U' R' U) B2' (U' R U) |
OLL | y' F' L2 F' R2 B2 F' R2 F' L2 B2 |
OLL 24
Probability 4/27
Name: T, chameleon, shark, Hammerhead, Little Horse, stingray |
OLL | r U R' U' L' U R U' x' |
OLL | r U R' U' r' F R F' |
OLL | (y' x') R U R' D R U' R' D' |
OLL | (y') F R U R' U' R U' R' U' R U R' F' |
OLL | (y x) D' R' U R D R' U' R x' |
OLL | (y x) D L U' L' D' L U L' x' |
OLL | (y x') U' R' D R U R' D' R x |
OLL | (y2) R' F' L F R F' L' F |
OLL | (y2) R' F' r U R U' r' F |
OLL | (y2) l' U' L U R U' r' F |
OLL | (y') l U l' F R B' R' F' |
OLL 25
Probability 4/27
Name: L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship |
OLL | y' F' r U R' U' r' F R |
OLL | R U2 R' U' (R U R' U') (R U R' U') R U' R' |
OLL | R U R' U (R U' R' U) (R U' R' U) R U2 R' |
OLL | y2 R' F R B' R' F' R B |
OLL | y2 F R' F' L F R F' L' |
OLL | y F' L F R' F' L' F R |
OLL | y' F' r U R' U' r' F R |
OLL | y' x U R' U' L U R U' r' |
OLL | R' F' L' F R F' L F |
OLL | y2 R U2' R D R' U2 R D' R2' |
OLL | y2 F R' F' r U R U' r' |
OLL | y2 l' U R D' R' U' R D x' |
OLL | y2 x' L' U' R' U L U' R U |
OLL | x' D R U R' D' R U' l' |
OLL | x' U L' U' R U L U' l' |
OLL | x' R' D R U' R' D' R U x |
OLL | x R' U R D' R' U' R D x' |
OLL | y2 x L U' L' D L U L' D' x' |
OLL | l' U' L' U R U' L U x' |
OLL | U r U R U' L' U R' U' x' |
OLL | R U2 R' U' (R U R' U')2 R U' R' |
OLL | y2 L' R U R' U' L U R U' R' |
OLL | F R B R' F' l U' l' |
OLL | U R U2 R' L' U' L U' R U' R' L' U2 L |
OLL | y R U R' U' R' F R U R U' R' F' |