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Official Rules Symmetry rank
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 self-matched in four different ways using reflection operations - from top to bottom, from left to right, and in two diagonal directions.
It also can be self-matched 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

  
  
   

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