Cauchy's Theorem for Orthogonal Polyhedra of Genus 0

Biedl T., Genc B.

17th Annual European Symposium on Algorithms, Copenhagen, Danimarka, 7 - 09 Eylül 2009, cilt.5757, ss.71-72 identifier identifier

  • Cilt numarası: 5757
  • Doi Numarası: 10.1007/978-3-642-04128-0_7
  • Basıldığı Şehir: Copenhagen
  • Basıldığı Ülke: Danimarka
  • Sayfa Sayıları: ss.71-72


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.