>>14057947I'm not sure if a polygon is a meaningful idea if it has no area. For example, one could consider the triangle with sides 1, 1, 2, which would look like a line segment. Is it a triangle at that point, or a line segment? Perhaps both.
I don't think a regular bigon could exist. I thought the idea of regular polygons was the enclosure of an area by non-intersecting line segments whose ends are connected. I can't think of how this could be done by one line segment, or even two. I think we need three. And I believe this is because of the issue of height. If we consider our first line segment in the drawing of a polygon as a horizontal line in the 2D Euclidian plane (giving our future polygon some horizontal extension), we still need some vertical extension. For this, we require one side that goes up or down, and one side that comes back down or up by the same amount.
This requires three sides in total.
QE Sneed
