## Overview of algorithms to orient and position last edge of top layer, and to orient the middle layer edges.

### Explanation

#### Situation

The following algorithms are based upon the following state of the cube:

The front side looks like (where red is the front color, and yellow the bottom color): The back side looks like (where orange is the back color, and yellow the bottom color): So the bottom layer (yellow) is completed solved, and the top layer (white) is solved except for one edge.
The not solved edge of the top layer is cubie D in the two images.

#### Goal

Next goal is to position the last top layer edge (D). After that only the middle layer edges are not solved yet.
In this case you could position the last top layer edge with 6 moves (EL'E'L2E'L').

But you could already make sure that the middle layer edges are oriented correctly at the same time!
This will take 6 to 11 moves (average 8 moves). So in max. 5 moves extra (average is 2 moves), you can make the last phase much easier. Because after this, the middle layer edges only need to be positioned, to solve the cube.

#### Description

The left face of the cube shows letters A, B and C.
Based upon the orientation of these edges, you can find out how to orient the middle layer edges.
There are 8 different situations, A, B and C can all be oriented correctly or incorrectly.
A, B and C are oriented correctly:
- if the color is the same as the color of the center between A and C
or
- if the color is the same as the center at the opposite side.

#### Algorithms

 Edge A Edge B Edge C Algorithm C C C E'L'E'LELE'L' (8,8) C C I L2E'L'EL'E'L'EL (9,10) C I C EL'E'L2E'L' (6,7) C I I LELE'L'E'L' (7,7) I C C E'LELE'LEL (8,8) I C I LE'LELEL'E'L'EL' (11,11) I I C LEL'E'LE'L' (7,7) I I I LE'LE'LEL2EL' (9,10)

#### Mirrored positions

The above images can also be mirrored vertically. In that case the edge at position D has the same position, but the edge needs to be positioned in the bottom layer instead of the top layer.
The algorithms you can use, are still the same, with one exception: L becomes L', and L' becomes L.

#### All top and bottom layer edges are already in place

It is also possible that all top and bottom layer edges are already in place.
In that case there are two possibilities:
• The last top layer edge is twisted
• The last top layer edge is not twisted

Last top layer edge is twisted

There could be 1 or 3 twisted edges in the middle layer. You can solve these situations as follows:

 Number of twisted edges Action 1 Move the middle layer, so that the FL edge is not twisted, and the FR edge is twisted. Then do the following algorithm: RU2R'E2R2E'R'U2R' (9,13,16) 3 Move the middle layer, so that the FL edge is not twisted, and the FR edge is twisted. Then do the following algorithm: LELELEL (7,7,10)

Last top layer edge is not twisted

There could be 0, 2 or 4 twisted edges in the middle layer. You can solve these situations as follows:

 Number of twisted edges Position of twisted edges Action 0 - No action. Move on to positioning the edges. 2 Next to each other Move the middle layer, so that the two twisted edges are at FL and FR. Then do the following algorithm: R2FMF'R2FM'F' (8, 10, 12) or L'EL'EL2E'L'E'L (9,10,14) 2 Opposite each other Move the middle layer, so that the two twisted edges are at FL and BR. Then do the following algorithm: FMF'R2FM'F'R2 (8,10,12) or LEL'EL2E'L'E'L' (9,10,14) 4 - Do the following algorithm: LEL2F2L'E2LF2L2E'L' (11,16,20) or RF2R2ERE2RF2R2ER (11,16,20) or F'U'FERERERERF'UF (14,14,18)

Good luck!