Corner Orientation
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:
 Orientation
 Orient
 Permutation
 Edge Orientation
 Corner Permutation
 OCLL
 Winter Variation
 CLS
 Partial Corner Control
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 24 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 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, 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 (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
UOptimal 2gen:

TOptimal 2gen:
 
LOptimal 2gen:

Three corners unoriented
SOptimal 2gen:

SOptimal 2gen:

Four corners unoriented
HOptimal 2gen:

piOptimal 2gen:
