A Rigidity Criterion for Non-Convex Polyhedra |
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Authors: | Jean-Marc Schlenker |
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Institution: | (1) Laboratoire Emile Picard, UMR CNRS 5580, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France |
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Abstract: | Let P be a (non-necessarily convex) embedded polyhedron in R3,
with its vertices on the boundary of an
ellipsoid. Suppose that the interior of
$P$ can be decomposed into convex polytopes without adding any vertex.
Then P is infinitesimally rigid.
More generally, let P be a polyhedron bounding a domain which is
the union of polytopes C1, . . ., Cn with disjoint
interiors, whose vertices are the vertices of P. Suppose that there
exists an ellipsoid which contains no vertex of P but intersects all
the edges of the Ci. Then P is infinitesimally rigid.
The proof is based on some geometric properties of hyperideal hyperbolic
polyhedra. |
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Keywords: | |
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