Cauchy's Theorem for Orthogonal Polyhedra of Genus 0

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Biedl T., Genc B.

17th Annual European Symposium on Algorithms, Copenhagen, Denmark, 7 - 09 September 2009, vol.5757, pp.71-72 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 5757
  • Doi Number: 10.1007/978-3-642-04128-0_7
  • City: Copenhagen
  • Country: Denmark
  • Page Numbers: pp.71-72
  • Hacettepe University Affiliated: No


A famous theorem by Cauchy states that the dihedral angles of a convex polyhedron are determined by the incidence structure and face-polygons alone. In this paper, we prove the same for orthogonal polyhedra of genus 0 as long as no face has a hole. Our proof yields a linear-time algorithm to find the dihedral angles.