2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137881We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n^2) ``moves'' between simple polygons. Each move is composed of a sequence of atomic moves called ``stretches'' and ``twangs''. These atomic moves walk between weakly simple ``polygonal wraps'' of S. These moves show promise to serve as a basis for generating random polygons.15 pages, 14 figures, 3 appendicesComputational GeometryDiscrete MathematicsF.2.2; G.2text