The Generalization of the reflection of a triangle [La généralisation de la réflexion d'un triangle].




The blue spheres display the intersection points of the blue lines with the continuation of the red sides.


Instead of using three points {P(1),P(2),P(3)} defining a triangle, one use a set of N points {P(1),P(2),...,P(N)} defining the polygon {P(1),P(2),...,P(N),P(1)}. Starting with i=1, for each subset of three points {P(i),P(i+1),P(i+2)}, the red point P(i) is transformed into a green point using the "blue" symmetry about the red {P(i+1),P(i+2)} side. At last, this process is iterated by incrementing the index 'i' (+1).


See some related bidimensionnal visualizations (possibly including this one), the blue spheres (if any) displaying the intersection points of the blue lines with the red sides:

 





See some related tridimensionnal visualizations (possibly including this one), the blue spheres (if any) displaying the intersection points of the blue lines with the red faces:

 



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