ReflectingOnPolygonSides2

Reflecting on polygon sides

The origin of the story is exposed in the file: ReflectingOnPolygonSides.html .

Given the generic quadrangle EFGH there are only 3 closed quadrangles, starting at a point O and comming back to that point after 4 successive reflections on the sides of the quadrangle at any order. Stated in another way: there are only 3 quadrangles whose medial lines (of the sides) are the sides of a given quadrangle.

Free movable is only the basic quadrangle EFGH. Switch to the selecti-tool (Ctrl+1), catch and modify it. It appears that from the three possible quadrangles one is convex the other non-convex and non-self-intersecting and the third is self-intersecting. Is this always the case for generic quadragles? I don't know yet.
There are some more questions that seem interesting e.g.:
a) Special (non generic) quadrangles.
b) Generalizations to 2n-gons.

http://users.math.uoc.gr/~pamfilos/