Difference between revisions of "Corner Orientation"

m (T)
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'''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:'''
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'''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|!}}
 
  
 
'''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:'''
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'''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:'''
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'''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:'''
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'''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:'''
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'''HTM optimal:'''
 
'''HTM optimal:'''
 
{{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|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
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'''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:'''
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'''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:'''
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'''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:'''
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'''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:'''
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'''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|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
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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:'''
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'''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|!}}
 
  
 
'''Any other 2-gen:'''
 
'''Any other 2-gen:'''
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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}}
{{Alg|!}}
 
  
 
'''Any other:'''
 
'''Any other:'''
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|}
 
|}
 
  
 
[[Category:Puzzle Theory]]
 
[[Category:Puzzle Theory]]

Revision as of 20:18, 9 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 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).

See also:

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 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).

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 (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

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 !


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 !


HTM optimal:

Speedsolving Logo tiny.gif Alg U2 R' B D2 B' R U2 R' B D2 B' R


Any other:

Speedsolving Logo tiny.gif Alg !


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 !


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 !


-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 !


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 !


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 !


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 !


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 !