I generaly find the definition of polygon as a "polygonal chain", but I barely find another definition that defines a convex polygon as the intersection of a finite number of half-planes and defines polygon as the union of a finite number of convex polygons.
The first one is used everywhere but I find it vague, like with proofs of convexity or to tell if a point is in a polygon. The second one explains this, but doesnt talk at all about the vertices or edges, and when I find this definition it is just assumed that those exists.
Does anyone has any reference of a robust definition?