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- W3099681155 abstract "A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is locally rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles." @default.
- W3099681155 created "2020-11-23" @default.
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- W3099681155 date "2012-11-28" @default.
- W3099681155 modified "2023-09-27" @default.
- W3099681155 title "Rigid Ball-Polyhedra in Euclidean $$3$$ -Space" @default.
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- W3099681155 doi "https://doi.org/10.1007/s00454-012-9480-y" @default.
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