OK here is the setup...

lets say you draw a polygon of n sides, but extend those line segments into infinite lines.

a polygon of 5 or 6 sides will generate what I will call a secondary triangle as the 'opposing' lines are not parallel (72degrees in a pentagon vs 90deg in a n=4 square).

a polygon of 7 or 8 sides will generate secondary triangles, but also 'tertiary triangles' due to intersections

a polygon on 9 or 10 sides will generate quaternary triangles

a polygon of 11 or 12 sides will generate 5th order triangles etc

my question is:

why does increasing n inodd number of sidesgenerate a higher order intersectional triangle?

does this pattern occur indefinitely? .. or do other intersections become possible with more and more acute angles whereby other polygon sides start to intersect?

many thanks-

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