  Given a polygon $P$ in the plane, a {\em 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 \cite[Open
Problem 5.3]{DO07}.
