Cauchy Rigidity of C -polyhedra
نویسندگان
چکیده
We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and bounded non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings as well as that of certain hyperideal hyperbolic polyhedra. The proof follows the pattern of Cauchy’s proof of the rigidity of convex Euclidean polyhedra. The trick in applying Cauchy’s argument in this setting is in constructing hyperbolic polygons around each vertex in a c-polyhedron on which a generalized Cauchy arm lemma may be applied.
منابع مشابه
Rigidity of Circle Polyhedra in the 2-sphere and of Hyperideal Polyhedra in Hyperbolic 3-space
We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and proper non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings in the ...
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