Difference between revisions of "Corner Orientation"

(Pure CO)
(Pure CO)
Line 28: Line 28:
 
[[File:Pure twist U.jpg]]
 
[[File:Pure twist U.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|
 
|
Line 36: Line 50:
 
[[File:Pure twist T.jpg]]
 
[[File:Pure twist T.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|-valign="top"
 
|-valign="top"
Line 45: Line 73:
 
[[File:Pure twist L.jpg]]
 
[[File:Pure twist L.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|
 
|
Line 59: Line 101:
 
[[File:Pure twist S.jpg]]
 
[[File:Pure twist S.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|
 
|
Line 67: Line 123:
 
[[File:Pure twist aS.jpg]]
 
[[File:Pure twist aS.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|}
 
|}
Line 80: Line 150:
 
[[File:Pure twist H.jpg]]
 
[[File:Pure twist H.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
  
 
|
 
|
Line 88: Line 172:
 
[[File:Pure twist pi.jpg]]
 
[[File:Pure twist pi.jpg]]
  
 +
'''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:'''
 +
{{Alg|!}}
 +
 +
'''Sune combos:'''
 +
{{Alg|!}}
 +
 +
'''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:'''
 +
{{Alg|!}}
 +
 
|}
 
|}
  

Revision as of 19:26, 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

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). The first alg given for each case is optimal in 2-gen and the second is optimal in Half Turn Metric, using as many sides that is needed for that (2-6).

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
Speedsolving Logo tiny.gif Alg !


Any other 2-gen:

Speedsolving Logo tiny.gif Alg !


Sune combos:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

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


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
Speedsolving Logo tiny.gif Alg !


Any other 2-gen:

Speedsolving Logo tiny.gif Alg !


Sune combos:

Speedsolving Logo tiny.gif Alg !


HTM optimal:

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


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'
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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'
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


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
Speedsolving Logo tiny.gif Alg !


Any other:

Speedsolving Logo tiny.gif Alg !