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 [9, Open Problem 5.3].

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Adrian Dumitrescu, Evan Hilscher
• Keywords: Adjacent Vertices, DM 2010, Polygons, Pop Operations