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 2gen). There are diffrent sections for diffrent types of algorithms, first is optimal 2gen followed by 2gens 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 (26) 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 doublelayer 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
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!



T
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!



L
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!




Three corners unoriented
S
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!



S
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!



Four corners unoriented
H
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!



pi
Optimal 2gen:

Alg

!


Any other 2gen:

Alg

!


Sune combos:

Alg

!


HTM optimal:

Alg

!


Any other:

Alg

!


