Difference between revisions of "Corner Orientation"

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(→‎Pure CO: Making a section for cases ignoring CP, lesser alg categorys here because it is basicly only useful for speed...)
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{{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'}}
 
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}
 
{{Alg|(y' x) U' L U2 R' U2 L' U2 R U' (x' y') M' U' M U2 M' U' M U2}}
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|}
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= 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.
 +
 +
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.
 +
 +
<strong>Click on an algorithm (not the camera icon) to watch an animation of it.</strong>
 +
 +
==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"
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|-valign="top"
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|
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=== U (EPP) ===
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[[File:OCLL-EPP U.jpg]]
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 +
'''Optimal 2-gen:'''
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{{Alg|R U2 R' U R' U2 R U2 R U R' U' R' U R U2}}
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 +
'''HTM optimal:'''
 +
{{Alg|!}}
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 +
'''Any other:'''
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{{Alg|!}}
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 +
|
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 +
=== T (EPP) ===
 +
[[File:OCLL-EPP T.jpg]]
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 +
'''Optimal 2-gen:'''
 +
{{Alg|!}}
 +
 +
'''HTM optimal:'''
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{{Alg|!}}
 +
 +
'''Any other:'''
 +
{{Alg|!}}
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 +
|-valign="top"
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|
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 +
=== L (EPP) ===
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[[File:OCLL-EPP L.jpg]]
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 +
'''Optimal 2-gen:'''
 +
{{Alg|!}}
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 +
'''HTM optimal:'''
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{{Alg|!)}}
 +
 +
'''Any other:'''
 +
{{Alg|!}}
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 +
|
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|}
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 +
==Three corners unoriented==
 +
{|border="0" width="100%" valign="top" cellpadding="3"
 +
 +
|-valign="top"
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|
 +
=== S (EPP) ===
 +
[[File:OCLL-EPP S.jpg]]
 +
 +
'''Optimal 2-gen:'''
 +
{{Alg|!}}
 +
 +
'''HTM optimal:'''
 +
{{Alg|!}}
 +
 +
'''Any other:'''
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{{Alg|}}
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|
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=== -S (EPP) ===
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[[File:OCLL-EPP aS.jpg]]
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 +
'''Optimal 2-gen:'''
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{{Alg|!}}
 +
 +
'''HTM optimal:'''
 +
{{Alg|!}}
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 +
'''Any other:'''
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{{Alg|!}}
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 +
|}
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==Four corners unoriented==
 +
{|border="0" width="100%" valign="top" cellpadding="3"
 +
 +
|-valign="top"
 +
|
 +
=== H (EPP) ===
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[[File:OCLL-EPP H.jpg]]
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 +
'''Optimal 2-gen:'''
 +
{{Alg|R U R2 U' R2 U' R U2 R U2 R U' R2 U' R2 U R U}}
 +
 +
'''HTM optimal:'''
 +
{{Alg|R U2 F2 R' U' F R' U2 F' U2 R2 F U R' F U2}}
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'''Any other:'''
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{{Alg|!}}
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|
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=== pi (EPP) ===
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[[File:OCLL-EPP pi.jpg]]
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'''Optimal 2-gen:'''
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{{Alg|!}}
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 +
'''HTM optimal:'''
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{{Alg|U R L' D' R2 U2 R' D R2 U2 L U' L2 B2 L2}}
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'''Any other:'''
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{{Alg|!}}
  
 
|}
 
|}

Revision as of 17:27, 23 August 2010

Corner Orientation, abbrevaited CO, the orientation of a cube's corners. There are three possible corner cubie orientations. CO is a sub step 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".

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 diffrent 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 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.

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.

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

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 !


Sune combos:

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


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)


T

Pure twist T.jpg

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 !


Sune combos:

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


L

Pure twist L.jpg

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 !


Sune combos:

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


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'


Three corners unoriented

S

Pure twist S.jpg

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 !


Sune combos:

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


-S

Pure twist aS.jpg

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 !


Sune combos:

Speedsolving Logo tiny.gif Alg (y2) (R U2 R' U' R U R' U' R U' R') (y) (L' U2 L U L' U L) U2


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

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


Any other 2-gen:

Speedsolving Logo tiny.gif 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:

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


pi

Pure twist pi.jpg

Optimal 2-gen:

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 !


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 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


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 diffrent 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 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.

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.

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 (EPP)

OCLL-EPP U.jpg

Optimal 2-gen:

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


HTM optimal:

Speedsolving Logo tiny.gif Alg !


Any other:

Speedsolving Logo tiny.gif Alg !


T (EPP)

OCLL-EPP T.jpg

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg !


Any other:

Speedsolving Logo tiny.gif Alg !


L (EPP)

OCLL-EPP L.jpg

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg !)


Any other:

Speedsolving Logo tiny.gif Alg !


Three corners unoriented

S (EPP)

OCLL-EPP S.jpg

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg !


Any other:

Speedsolving Logo tiny.gif Alg [1]


-S (EPP)

OCLL-EPP aS.jpg

Optimal 2-gen:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

Speedsolving Logo tiny.gif Alg !


Any other:

Speedsolving Logo tiny.gif Alg !


Four corners unoriented

H (EPP)

OCLL-EPP H.jpg

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


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 !


pi (EPP)

OCLL-EPP pi.jpg

Optimal 2-gen:

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 !