Review of Convex Polyhedra by A . D . Alexandrov Robert Connelly
نویسندگان
چکیده
منابع مشابه
On the infinitesimal rigidity of weakly convex polyhedra
The main motivation here is a question: whether any polyhedron which can be subdivided into convex pieces without adding a vertex, and which has the same vertices as a convex polyhedron, is infinitesimally rigid. We prove that it is indeed the case for two classes of polyhedra: those obtained from a convex polyhedron by “denting” at most two edges at a common vertex, and suspensions with a natu...
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 کاملThe Rigidity of Certain Cabled Frameworks and the Second-Order Rigidity of Arbitrarily Triangulated Convex Surfaces
It had been suspected that any (connected) polyhedral surface, convex or not, (with its triangular faces, say, held rigid) was rigid, but this has turned out to be false (see Connelly [7]). W e extend Cauchy’s theorem to show that any convex polyhedral surface, no matter how it is triangulated, is rigid. Note that vertices are allowed in the relative interior of the natural faces and edges. Her...
متن کاملMSC 52A20, 52A38, 52B11, 52B55, 49Q20, 65D17, 68U07 Blaschke Addition and Convex Polyhedra
This is an extended version of a talk on October 4, 2004 at the research seminar “Differential geometry and applications” (headed by Academician A. T. Fomenko) at Moscow State University. The paper contains an overview of available (but far from well-known) results about the Blaschke addition of convex bodies, some new theorems on the monotonicity of the volume of convex bodies (in particular, ...
متن کاملModelling Decision Problems Via Birkhoff Polyhedra
A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...
متن کامل