Abstract
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.
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Biedl, T., Genc, B. (2009). Cauchy’s Theorem for Orthogonal Polyhedra of Genus 0. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_7
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DOI: https://doi.org/10.1007/978-3-642-04128-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04127-3
Online ISBN: 978-3-642-04128-0
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