ON FLIPS IN POLYHEDRAL SURFACES

Abstract

Let V be a finite point set in 3-space, and let [Formula: see text] be the set of triangulated polyhedral surfaces homeomorphic to a sphere and with vertex set V. Let abc and cbd be two adjacent triangles belonging to a surface [Formula: see text]; the flip of the edge bc would replace these two triangles by the triangles abd and adc. The flip operation is only considered when it does not produce a self-intersecting surface. In this paper we show that given two surfaces S1, [Formula: see text], it is possible that there is no sequence of flips transforming S1 into S2, even in the case that V consists of points in convex position.