Rigid Ball-Polyhedra in Euclidean $$3$$ -Space
نویسندگان
چکیده
منابع مشابه
Rigid Ball-Polyhedra in Euclidean 3-Space
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 ballpolyhedron 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 ba...
متن کاملGlobally Rigid Ball-Polyhedra in Euclidean 3-Space
The rigidity theorems of Alexandrov (1950) and Stoker (1968) are classical results in the theory of convex polyhedra.We prove analogues of them for ball-polyhedra, which are intersections of finitely many congruent balls in Euclidean 3-space.
متن کاملRigidity of ball-polyhedra in Euclidean 3-space
In this paper we introduce ball-polyhedra as finite intersections of congruent balls in Euclidean 3-space. We define their duals and study their face-lattices. Our main result is an analogue of Cauchy’s rigidity theorem. © 2004 Elsevier Ltd. All rights reserved.
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In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
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We study two notions. One is that of lens-convexity. A set of circumradius not greater than one is lens-convex if, for any pair of its points, it contains every shorter unit circular arc connecting them. The other objects of study are bodies obtained as an intersection of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on convex polyhedral set...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2012
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-012-9480-y