Reducing to R, U face rotations group

Foreword

Here is a way to send back all other non-R, U face rotations, so after that you only can use the U, R face rotations to complete the cube, so that the RUP method can be a reducing group method, and this method should be simple and easy to use.

Bad edge, good edge

Only rotate U, R face will have bad edge, good edge. The so-called bad edge is that you only rotate R, U face can never twist this edge right. The so-called good edge is that you only rotate R, U face can twist this edge right.

To twist the bad edge into a good edge, turn the 2 bad edge with rotating R, U face only, to the position of the two edge of figure in Fig. 1 below, and then do the Move 1, F R' F', then these two bad edges are turned into good edges.

Unless there is no bad edges, do it until there will be only 2 bad edges left.

Fig. 1

Move 1

Find the Alien Line

Now the face D is , first turn the two corners with to the two positions DRF, DRB, who is in the position DRF or who is in the position DRB does not matter. Because the face U is , the remaining four corners do not consider , and only consider the other colors. If it is found that two adjacent corners have the same non- color, assume it is , we use the U face rotation to turn the two corners to the side, as in the following Example 1, you will found that the positions of the adjacent two corners with are exchanged with each other. The two corners with adjacent on the face are in the correct position, and the two rest corners on the face are just swapped with each other. The X symbol indicates that the two adjacent corners positions are exchanged with each other, and no X symbol indicates that the two adjacent corners are in the correct position.

There will be three lines, two of which are exchanged, and one is different from the other two, the position of the corners on this line is correct, not exchanged. The line that is different from the other two is the Alien Line. The two corners in the Alien Line are what we are searching for. In the following Example 1, position UFL, UFR are the two corners.

Example 1

Some examples of Alien Line

In the following, the corners of the same color have an X symbol indicating that the two adjacent corners positions are exchanged with each other, and no X symbol indicates that the two adjacent corners are in the correct position, and each Example has three lines of the same color. The excahnged situation of position of the corners in one of the sections is different from the other two. The following is indicated by . This is the Alien Line we are searching for.

If there is no , it means there is no Alien Line.

Example 2

Example 3

Example 4

Example 5

Example 6

Return other non-R, U face rotations

There are 2 bad edges left, and there are also Alien Line.: The following four optional ones can be completed. Turn the two corners on the Alen Line and the remaining two bad edges with only R, U face rotations to the lower position, and will send back other non-R, U face rotations according to the description.

Use the sequence F R ' F ' to solve

Move 2

Use the sequence F' U F to solve

Move 3

Use the sequence B' R B to solve

Move 4

Use the sequence B U' B' to solve

Move 5
2 bad edges left, but Alien Line: Turn the two bad edges with the R, U face ratations only, to the position below, and will send back other non-R, U faces ratations with the sequence F R2 U R U' F'.

Move 6
No bad edges, but there are Alien Line: Turn the two corners on the Alien Line with only the R, U face rotaions to the position below, and will send back the other non-R, U face rotations with the sequence F R' U R U' F'.

Move 7
No bad edges, no Alen Line: Has already completed sending back other non-R, U face rotations.

Can replace the corners in the Alien Line

If indicates an Alien Line, in fact you can not only use the two corners in the Alien Line.

According to the position of the , you can see that the figure below matches the position of your Alien Line.

Replacing the two corners of Alien Line with the other two corners of the same color will also have the reducing group effect.

There are alternative corners that will make it easier to combine the bad edges only with R, U face rotations.

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

As shown in the following Example 7, the Alen Line position will be in UFL, UFR, according to this position, the color of Fig. 5 above is just in these two positions. According to Fig. 5 above, you can use the two corners of position ULB, DRF, or two corners of position URB, DRB to replace the two corners in the original Alien Line

The two corners at position URB, DRB have already just connected a bad edge, so we use the two corners at position URB, DRB will be better than the original two corners.

Example 7

The first turn is the state before the Move 4
The 2~4th turns is the Move 4

next: Reducing to the group of retaining 2 pairs The RUP Method

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