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Journal for Geometry and Graphics 23 (2019), No. 2, 157--165 Copyright Heldermann Verlag 2019 Euclidean Realizations of Triangulated Polyhedra Pacal Honvault LMPA CNRS, Université Littoral Côte d'Opale, 62228 Calais, France pascal.honvault@univ-littoral.fr [Abstract-pdf] Let $C=(d_0,\ldots,d_n)$ be an admissible degree sequence for a triangulated polyhedron $P_n$ with $n+1$ vertices. We give necessary and sufficient conditions on its Euclidean parameters (angles, lenghts, $\ldots$) for beeing realized in the usual 3D-space. Keywords: Polyhedron, combinatorics, triangulation, Euclidean parameters, quaternions. MSC: 52B05; 51N20, 52-04 [ Fulltext-pdf (234 KB)] |