Vertex classification of planar C-polygons

Given a convex domain C, a C-polygon is an intersection of \(n\ge 2\) $n\ge 2$ homothets of C. If the homothets are translates of C then we call the intersection a translative C-polygon. This paper proves that if C is a strictly convex domain with m singular boundary points, then the number of singular boundary points a C-polygon has is between n and \(2(n-1)+m\) $2(n-1)+m$ . For a translative C-polygon we show the number of singular boundary points is between n and \(n+m\) $n+m$ .