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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


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

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