Intrinsic volumes and f-vectors of random polytopes.
Imre Bárány (1989)
Mathematische Annalen
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Displaying similar documents to “Random polytopes in a convex polytope, independence of shape, and concentration of vertices.”
Intrinsic volumes and f-vectors of random polytopes.
On the Convex Hull of Uniform Random Points in a Simple d-Polytope.
J.A. Wieacker, F. Affentranger (1991)
Discrete & computational geometry
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Stellar Subdivisions of Boundary Complexes of Convex Polytopes.
G. Ewald, G.C. Shephard (1974)
Mathematische Annalen
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A purely combinatorial proof of the Hadwiger Debrunner conjecture.
Alon, N., Kleitman, D.J. (1997)
The Electronic Journal of Combinatorics [electronic only]
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Volume Approximation of Convex Bodies by Inscribed Polytopes.
Peter M. Gruber (1988)
Mathematische Annalen
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Characterizing certain staircase convex sets in .
Breen, Marilyn (2010)
Beiträge zur Algebra und Geometrie
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The Mayer-Vietoris and IC Equations for Convex Polytopes.
J. Fine (1995)
Discrete & computational geometry
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Expectation of Random Polytopes.
Peter M. Gruber (1996)
Manuscripta mathematica
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On Ray Shooting in Convex Polytopes.
J. Matousek, O. Schwarzkopf (1993)
Discrete & computational geometry
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Recent Results on Random Polytopes
Rolf Schneider (2008)
Bollettino dell'Unione Matematica Italiana
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This is a survey over recent asymptotic results on random polytopes in d-dimensional Euclidean space. Three ways of generating a random polytope are considered: convex hulls of finitely many random points, projections of a fixed high-dimensional polytope into a random d-dimensional subspace, intersections of random closed halfspaces. The type of problems for which asymptotic results are described is different in each case.
Coating by cubes.
Bezdek, K., Hausel, T. (1994)
Beiträge zur Algebra und Geometrie
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Random Polytopes in the d- Dimensional Cube.
Z. Füredi (1986)
Discrete & computational geometry
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A. D. Alexandrov's uniqueness theorem for convex polytopes and its refinements.
Panina, Gaiane (2008)
Beiträge zur Algebra und Geometrie
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Rigidity and flexibility of virtual polytopes
G. Panina (2003)
Open Mathematics
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All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.