Cauchy's Theorem for Orthogonal Polyhedra of Genus 0

A famous theorem by Cauchy states that a convex polyhedron is determined by its 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.

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Therese C. Biedl, Burkay Genc
• Keywords: Algorithms, Cauchy States, Convex Polyhedron, ESA 2009, Famous Theorem