Adjust the similarities and differences of permutation parity and the twist orientation of corners

Way of explanation

The Base 4PAIRs are placed in the shape as shown on the left.

"Similarity and difference of permutation parity" means "the permutation parity of the three corners, the Dog Tail Corner and the Remaining 2Corners, is different or the same as the permutation parity of the Basic 4PAIRs".


For the convenience of explanation, use to represent Hub Corner that does not consider the twisting orientation, and use to represent Dog Tail Corner that does not consider the twisting orientation.

The so-called two colors are "Opposite Color", which means that the colors of the center that is opposite to each other, that is, , are "Opposite Color", , are "Opposite Color", , are "Opposite Color".

Orientation Windows is only used for the other three corners of the non-Hub Corner on the U layer. Use the color on the Orientation Windows to observe the twist orientation of the corner, that is, the magenta observation facelet as shown on the left, and there is no need to pay attention to the twist orientation of the Hub Corner.


Goal

  • The similarities and differences of permutation parity are the same.
  • The color of the Dog Tail Corner on Orientation Windows is B(red) color, and the colors of the Remaining 2Corners on Orientation Windows are Opposite Color or the same color.
  • The relative position of the Hub Corner and the Dog Tail Corner is as shown on the right.

The meaning of the symbol used in the corners on the U layer

This method observes the twisting orientation of the corners on the U layer, as shown on the left, based on the magenta Orientation Windows used in the non-Hub Corner on the U layer. The absence of an arrow symbol on the corner of the U layer does not mean that the movement of that corner is not considered, but means that the corner will not move. The absence of a twist symbol on the corner of the U layer does not mean that the twist of that corner is not considered, but that the corner will not be twisted.


The arrow symbol as shown on the left not only represents the change of the position of the corner,
but also represents that the same color is maintained on Orientation Windows after the position of the corner is changed.

The red facelet on the corner shown on the right demonstrates how the arrow symbol makes a corner change.

The arrow symbol and the twist symbol as shown on the left are in the same corner position,
which means the corner that was originally in that position not only applies the rule of the arrow symbol, but also applies the original twist symbol rule at that position for the same corner.

Shown on the right demonstrates how the arrow symbol and the twist symbol in the same position make a corner change.


A series of Interchaging PAIRs Move

Here is a list of the different positions of the Hub Corner on the U layer, and the influence of R, D Layer Interchanging PAIRs Move of DIPODL (if you don't understand the term, try one of the move sequences R' D R2 D' R directly). As for the position change of the edge, that is, the influence of Interchanging PAIRs Move of DIPODL on the edge

Name The initial position of the Hub Corner
before the Interchanging PAIRs Move
After Interchanging PAIRs Move,
whether to change
the similarities and differences of permutation parity
After the Interchanging PAIRs Move,
the change of the corners on the U layer
oia Change
oib Change
oic No change
oid No change

Move seqence only include the U turn and the R turn do not change the position of each corner and the position of the Basic 4PAIRs in the end, so this series of move sequences will of course not change the similarities and differences of permutation parity and this series of move seqences can also be regarded as the same pair in the R, U layers do two times Interchanging PAIRs Move with different empty pairs to return to the original position. Only two of them are listed here.

Name Move sequence The twist change of the corner on the U layer.
The position change of the edge.
eia R' U' R2 U R2 U' R' U
eib R U R2 U' R2' U R U'

Observe the color on Orientation Windows to twist the corners in the same orientation

The above moves are all twisting the three corners in the same orientation on the U layer. You can make good use of the knowledge of twisting the three corners in the same orientation below, and observe with the color on Orientation Windows. The "color of the corner" described below is it means "the color of the corner on Orientation Windows".
Don't pay attention to the color of Hub Corner in this step.
On the U layer, only Dog Tail corner will have B(red) color and corners with F(orange) color must not be Dog Tail Corner.
There are 4 corners on the U layer, if three of them are twisted in the same orientation, excluding the Corner a, it is simply referred to as "Same Orientation Twist Excluding the corner a".

The color of Dog Tail Corner is B(red) color, and the color of Remaining 2Corners are Opposite Color or the same color is the completed state.
Here, only three corners are twisted in the same orientation each time to reach the minimum number of times to complete the state, to classify all the twist orientations of corners on the U layer, and divide them into "Completed State", "1 Time Can Be Completed", "Within 1 Time Can Not Be Completed" these three categories. Collectively referred to as "Category of Completion Times".

Discrimination method of "Category of Completion Times"

  • "Completed State" if and only if there is B(red) color on Orientation Windows, and the colors of the other two facelets are Opposite Color or the same color.
  • "1 Time Can Be Completed" if and only if there is no B(red) color on Orientation Windows.
  • "Within 1 Time Can Not Be Completed" if and only if there is B(red) color on Orientation Windows, and the colors of the other two facelets are not Opposite Color or the same color.

Under "1 Time Can Be Completed", one corner can not be twisted at all in the process of twisting in the same orientation to Completed State, then this corner is called "No Twist Required Corner"

For example of "1 Time Can Be Completed" as shown on the right, is the "No Twist Required Corner"


Under "1 Time Completion", look for the "No Twist Required Corner"

  • If there is no F(orange) color or there are two facelets with F(orange) color on Orientation Windows, then there must be two facelets on the Orientation Windows that are Opposite Color or the same color.
    • There are two facelets on the Orientation Windows that are Opposite Color or the same color, and these two facelets just belong to the Remaining 2Corners, then the Hub Corner is the "No Twist Required Corner"
    • There are two facelets on the Orientation Windows that are Opposite Color or the same color. The remaining facelet and that two facelets are not Opposite Color or the same color and belong to the Remaining 2Corners, then the corner to which this facelet belongs is the "No Twist Required Corner"
  • Only one facelet of Orientation Windows is F(orange) color.
    • If the other two facelets on Orientation Windows are not Opposite Color or the same color, the corner with F(orange) color on Orientation Windows is the "No Twist Required Corner"
    • If the other two facelets on Orientation Windows are Opposite Color or the same color, then the one facelet of that two belongs to Remaining 2Corners, and the corner to which that facelet belongs is the "No Twist Required Corner"

"Category of Completion Times" for the three twist orientations of the twisting corners in the same orientation.

  • Doing "Same Orientation Twist Excluding Dog Tail Corner", the "Category of Completion Times" of each three twisting results of the three twisting orientations of the twisting corner in the same orientation are all the same. If the "Category of Completion Times" is "1 Time Can Be Completed", even the position of the "No Twist Required Corner" is the same.
  • Do "Same Orientation Twist Excluding corner a", and corner a is not Dog Tail Corner, and the other two corners are corner b and corner c. The "Category of Completion Times" of each three twisting results of the three twisting orientations of the twisting corner in the same orientation will only be one of the following two
    • "Completed State", "1 Time Can Be Completed" and the No Twist Required Corner is corner a, "1 Time Can Be Completed" and the No Twist Required Corner is corner a.
    • "Within 1 Time Can Not Be Completed", "1 Time Can Be Completed" and the No Twist Required Corner is corner b, "1 Time Can Be Completed" and the No Twist Required Corner is corner c.

How to use

The above moves show that the similarities and differences of permutation parity will be changed together with the twist orientation of the corner and the position of Dog Tail Corner. Without changing the similarities and differences of permutation parity, the twisting orientation of the corner and the position movement of Dog Tail Corner can be done independently. Therefore, the basic elementary level and the most inflexible approach can be

Stage one
Use move sequence oia or oib to adjust the similarities and differences of permuted parity to be the same.
Stage two
Use eia or eib to adjust the color of Dog Tail Corner on the Orientation Windows to B(red) color, and the colors of the Remaining 2Corners on the Orientation Windows to Opposite Color or the same color.
Stage three
Use oic or oid to adjust the relative position of Dog Tail Corner to Hub Corner.

Therefore, only the moves listed above are sufficient if they are only required to be solved.

A more advanced approach is to take into account the twist orientation of the corner and the position of the Dog Tail Corner while adjusting the similarities and differences of permutation parity, and make good use of "No Twist Required Corner" instead of following the above three stages. Use the above moves more skillfully to reduce the overall number of move sequence. You can also use S2 to adjust the edge and select the appropriate Interchanging PAIRs Move so that the next step does not need to break Parallel PAIR.