A permutation denotes location and orientation changes of cube parts.
Tick this checkbox to enable support for permutations by the notation.
When this checkbox is ticked, then a couple of entry fields are shown below the checkbox. You must fill in all text fields, to denote a valid notation.
Ticking this checkbox also enables the following checkboxes: Sequence, Repetition, Inversion, Conjugation, Commutation, Rotationand Delimiter.
Use these text fields to specify the keywords used to denote a cube face. You must fill in all fields.
The face names are used whithin a permutation cycle to describe the locations of cube parts.
The keywords entered here may be ambiguous with keywords entered on the Twists tab of the notation editor.
Please note: The keywords entered here may be ambiguous with twist keywords only, if the «Cycle Begin» and «Cycle End» keywords are not ambiguous with other keywords of the notation.
Use these text fields to specify the keywords used to denote an orientation change of a cube part. You must fill in all fields.
When used as a prefix for the first item in a permutation cycle, then «Plus» denotes an orientation change by plus one tick, «Plus Plus» denotes an orientation change by plus two ticks, «Minus» denotes an orientation change by minus one tick.
When used as a prefix for the second item or one of the following items in a permutatation cycle, then «Plus» denotes an orientation at tick 1, «Plus Plus» denotes an orientation at tick 2, «Minus» denotes an orientation at tick -1.
Use these text fields to specify the keywords used to denote the begin and end of a permutation cycle. You must fill in both fields.
«Cycle Begin» denotes
the begin of a permutation cycle.
«Cycle End» denotes the
end of a permutation cycle.
The keywords entered here may be ambiguous with keywords entered for Grouping expressions.
Please note: The keywords entered here may be ambiguous with the «Grouping Begin» and «Grouping End» keywords, if none of the «Faces» and «Orientation» keywords are ambiguous with other keywords of the notation.
Use this text field to specify the keywords used to delimit part location names whithin a permutation cycle. You must enter a keyword into this field.
Use these radio buttons to specify the location of the orientation keywords.
«Before Cycle Begin» denotes, that the orientation keyword is prepended to a permutation cycle.
«After Cycle Begin» denotes, that the orientation keyword is inserted after the permutation cycle begin keyword.
«After Cycle End» denotes, that the orientation keyword is appended to a permutation cycle.
«Before Cycle End» denotes, that the orientation keyword is inserted before the permutation cycle end keyword.
Example 1:
If you fill in the text fields as shown in the table below, then faces are identified using the six lowercase keywords «r», «u», «f», «l», «d», «b», orientation changes are described using the symbols «+», «-», «++», cycles are delimited by «(», «)», and part location names are delimited by «,», cycle orientation symbols are positioned before the cycle begin keyword.
Faces: | r |
u |
f |
l |
d |
b |
Orientation | Plus: | + |
Plus Plus: | ++ |
||
Minus: | - |
|||||
Cycle | Begin: | ( |
End: | ) |
||
Delimiter: | , |
|||||
Position | Before Cycle Begin |
Here's an example permutation. This permutation was achieved, by twisting the right face of the cube by 90 ° clockwise, and by twisting the middle layer of the cube as seen from above by 90 ° clockwise.
(urf,bru,drb,frd)
+(lf,bl,rb,rd) +(ur,rf)
+(f,-l,++b,+r)
This example is identical to example 1, except for the position of the permutation sign.
Faces: | r |
u |
f |
l |
d |
b |
Orientation | Plus: | + |
Plus Plus: | ++ |
||
Minus: | - |
|||||
Cycle | Begin: | ( |
End: | ) |
||
Delimiter: | , |
|||||
Position | After Cycle Begin |
Here's the same example permutation as used by example 1.
(urf,bru,drb,frd)
(+lf,bl,rb,rd) (+ur,rf)
(+f,l-,b++,r+)
This example is identical to example 1, except for the position of the permutation sign.
Faces: | r |
u |
f |
l |
d |
b |
Orientation | Plus: | + |
Plus Plus: | ++ |
||
Minus: | - |
|||||
Cycle | Begin: | ( |
End: | ) |
||
Delimiter: | , |
|||||
Position | Before Cycle End |
Here's the same example permutation as used by example 1.
(urf,bru,drb,frd)
(lf,bl,rb,rd+) (ur,rf+)
(f,-l,++b,+r+)
This example is identical to example 1, except for the position of the permutation sign.
Faces: | r |
u |
f |
l |
d |
b |
Orientation | Plus: | + |
Plus Plus: | ++ |
||
Minus: | - |
|||||
Cycle | Begin: | ( |
End: | ) |
||
Delimiter: | , |
|||||
Position | After Cycle End |
Here's the same example permutation as used by example 1.
(urf,bru,drb,frd)
(lf,bl,rb,rd)+ (ur,rf)+
(f,l-,b++,r+)+