Flipping your lid
Hee-Kap Ahn, Prosenjit K. Bose, Jurek Czyzowicz, Nicolas Hanusse, Evangelos Kranakis, Pat Morin · Canadian Conference on Computational Geometry · 2001
Given a polygon P, a flipturn involves reflecting a pocket p of P through the midpoint of the lid of p. In 1973, Joss and Shannon (published in Grunbaum (1995)) showed that any polygon on n vertices will become convex after a sequence of at most (n - 1)! flipturns. They conjectured that this bound was not tight, and that n2=4 flipturns would always be sufficient. In this work, we show that any polygon on n vertices will be convex after any sequence of at most n(n - 3)=2 flipturns.