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AfteRain
 
How to evaluate a symmetry rank:
A symmetry rank is a number of possible symmetry operations which can be performed
in order to match the figure with itself.
A square has the highest possible rank. It can be selfmatched in four different ways
using reflection operations  from top to bottom, from left to right, and in two diagonal
directions.
It also can be selfmatched by rotating it around it's center in three different angles 
90, 180, and 270 degrees. Rotation in 360 or more degrees and negative degrees are considered illegal.
So we can say that the square's symmetry rank is 7.
This simple table will help you estimate the symmetry rank of your configuration:
Your figure's name 
YourFigureName 
Reflection from top to bottom 
Yes (No) 
Reflection from left to right 
Yes (No) 
Reflection from left bottom to right top 
Yes (No) 
Reflection from left top to right bottom 
Yes (No) 
Rotation by 90 degrees 
Yes (No) 
Rotation by 180 degrees 
Yes (No) 
Rotation by 270 degrees 
Yes (No) 
Symmetry Rank 
Number of "Yes" 
Examples:
For a rectangle the scores will look like this:
Your figure's name 
rectangle 
Reflection from top to bottom 
Yes 
Reflection from left to right 
Yes 
Reflection from left bottom to right top 
No 
Reflection from left top to right bottom 
No 
Rotation by 90 degrees 
No 
Rotation by 180 degrees 
Yes 
Rotation by 270 degrees 
No 
Symmetry Rank 
3 
For a FourEars figure the scores will look like this:
Your figure's name 
FourEars 
Reflection from top to bottom 
No 
Reflection from left to right 
No 
Reflection from left bottom to right top 
Yes 
Reflection from left top to right bottom 
Yes 
Rotation by 90 degrees 
No 
Rotation by 180 degrees 
Yes 
Rotation by 270 degrees 
No 
Symmetry Rank 
3 
For a Propeller figure the scores will look like this:
Your figure's name 
Propeller 
Reflection from top to bottom 
No 
Reflection from left to right 
No 
Reflection from left bottom to right top 
No 
Reflection from left top to right bottom 
No 
Rotation by 90 degrees 
Yes 
Rotation by 180 degrees 
Yes 
Rotation by 270 degrees 
Yes 
Symmetry Rank 
3 
