# Corner Orientation

 Corner Orientation Information Proposer(s): unknown Proposed: unknown Alt Names: CO Variants: OCLL Subgroup: unknown No. Algs: unknown Avg Moves: unknown Purpose(s): Speedsolving, BLD, FMC Previous state: unknown Next state: unknown
 Previous cube state -> Corner Orientation step -> Next cube state The Corner Orientation step is the step between the Previous cube state and the Next cube state.

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

Algorithms; at this page you can find algortihms for two diffrent variations of CO;

• Pure CO: orients corners preserving edge orientation and both corner and edge permutation.
• OCLL-EPP: orients corners preserving edge orientation and permutation for the edges but not the corners (this method is seldomly used).

# 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. (how to add algorithms) 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

 Name: U, Headlights, Superman Used in: L3C, L4C, BLD Optimal moves: 13 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

HTM optimal:

Any other:

### T

 Name: T Used in: L3C, L4C, BLD Optimal moves: 13 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

HTM optimal:

Any other:

### L

 Name: L, Bowtie Used in: L3C, L4C, BLD Optimal moves: 12 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

HTM optimal: (12 move commutator)

Any other:

## Three corners unoriented

### S

 Name: S, Sune Used in: L3C, L4C, BLD Optimal moves: 13 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

HTM optimal:

Any other:

### -S

 Name: -S, Antisune Used in: L3C, L4C, BLD Optimal moves: 13 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

HTM optimal:

Any other:

## Four corners unoriented

### H

 Name: H Used in: L4C, BLD Optimal moves: 16 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

 Alg !

HTM optimal:

Any other:

### pi

 Name: pi, Bruno Used in: L4C, BLD Optimal moves: 15 HTM

Optimal 2-gen:

Any other 2-gen:

Sune combos:

 Alg !

HTM optimal:

Any other:

# OCLL-EPP

Orientation of the corners of the last layer - edges permutation preserved; orients the last layer corners preserving edge permutation but ignoring corner permutation.

Usage; to solve the last four corners in two looks if the edges are solved (3-look LLEF, OCLL-EPP and CPLL, total 26 algs. 4-look EO, EP, OCLL-EPP and CPLL, total 16 algs).

Average movecount is 9.63 turns optimally, CPLL is 9.12 turns optimally wich gives 19 moves on average for solving L4C in 2-looks like this.

### Algorithms

 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. (how to add algorithms) Click on an algorithm (not the camera icon) to watch an animation of it.

## Two corners

### U (EPP)

 Name: U, Headlights, Superman Used in: 2-look L4C Optimal moves: 9 HTM

Optimal 2-gen:

HTM optimal:

Any other:

### T (EPP)

 Name: T Used in: 2-look L4C Optimal moves: 8 HTM

Optimal 2-gen:

HTM optimal:

 Alg R' F' R B' R' F R B

Any other:

### L (EPP)

 Name: L, Bowtie Used in: 2-look L4C Optimal moves: 8 HTM

Optimal 2-gen:

HTM optimal:

 Alg R B' R' F R B R' F'

Any other:

## Three corners

### S (EPP)

 Name: S, Sune Used in: 2-look L4C Optimal moves: 8 HTM

Optimal 2-gen:

HTM optimal:

 Alg R U' L' U R' U' L U

Any other:

 Alg !

### -S (EPP)

 Name: -S, Antisune Used in: 2-look L4C Optimal moves: 8 HTM

Optimal 2-gen:

HTM optimal:

 Alg U' L' U R U' L U R'

Any other:

 Alg !

## Four corners

### H (EPP)

 Name: H Used in: 2-look L4C Optimal moves: 12 HTM

Optimal 2-gen:

HTM optimal:

Any other:

 Alg F (R U R' U')3 F'

### pi (EPP)

 Name: pi, Bruno Used in: 2-look L4C Optimal moves: 12 HTM

Optimal 2-gen:

HTM optimal:

Any other:

## OLC Algorithms

Orient Last Corners (OLC), also known as Orient Last 4 Corners (OL4C), is a subset of OLL used in ZZ-reduction following Phasing that orients corners while preserving edge permutation (2 opposite edges or all 4). This results in a limited PLL set of 9 cases, down from 21 in full PLL.

Of the 7 orientation cases in ZZ, 4 do not commonly preserve edge permutation (Sune, Antisune, Pi, Double-Sune). The other 3 commonly preserve edges (Headlights, Chameleon, Triple-Sune).

Odds of skipping this step are 1/27.

 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. (how to add algorithms) Click on an algorithm (not the camera icon) to watch an animation of it.

### OLC 1

Probability 4/27

 Name: S, Sune, Swimming Left Used in: ZZ-reduction Optimal moves: {{{optimal}}}
 OLL R U' L' U R' U' L
 OLL y2 R' U L U' R U L'
 OLL U R U' L' U R' U' L

### OLC 2

Probability 4/27

 Name: -S, Antisune, Swimming Right Used in: ZZ-reduction Optimal moves: ? HTM
 OLL L' U R U' L U R'

### OLC 3

Probability 2/27

 Name: H, Double Sune, Flip, Cross Used in: ZZ-reduction Optimal moves: ? HTM, ? STM
 OLL y F (R U R' U')3 F'

### OLC 4

Probability 4/27

 Name: pi, Bruno, wheel, T-shirt Used in: ZZ-reduction Optimal moves: ? HTM

### OLL 23

Probability 4/27

 Name: U, Headlights, Superman Used in: OCLL, OLL Optimal moves: 9 HTM

### OLL 24

Probability 4/27

 Name: T, chameleon, shark, Hammerhead, Little Horse, stingray Used in: OCLL, OLL Optimal moves: 8 HTM
 OLL r U R' U' r' F R F'

### OLL 25

Probability 4/27

 Name: L, Bowtie, Triple-Sune, Side-winder, Diagonals, Spaceship Used in: OCLL, OLL Optimal moves: 8 HTM
 OLL R' F' L' F R F' L F
 OLL F R B R' F' l U' l'