On convexification of polygons by pops

Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, and show that any polygon from this family cannot be convexified by pop operations. This family contains simple as well as non-simple (i.e., self-intersecting) polygons, as desired. We thereby answer in the negative an open problem posed by Demaine and O’Rourke (2007) [9, Open Problem 5.3].