On flips in polyhedral surfaces

Oswin Aichholzer, Lyuba S. Alboul, Ferran Hurtado

Research output: Contribution to journalArticlepeer-review


Let V be a finite point set in 3-space, and let S (V) 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 S (V) 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 S 1, S2 (V), 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.

Original languageEnglish
Pages (from-to)303-311
Number of pages9
JournalInternational journal of foundations of computer science
Issue number2
Publication statusPublished - 2002


  • flip
  • Schönhardt's polyhedron
  • Triangulated polyhedral surface
  • triangulation

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

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