Symmetry breaking operations: Polar

 

 
Horizontal line segments become circular arcs.
Vertical line segments become rays emanating from the origin.
Diagonal line segments become spiral arcs.
 
Inverse Polar  
Straight line segments become arch sections.
Circles around the origin become horzontal lines.
Off center circles become ovals.
 
Point Inversion  
 
 
 
 

Symmetry preserving operations

Reflection

 

Rotation
Scaling
Symmetry creating operations Truncating reflection
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