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Polytopes - Abstract, Convex and Computational

Proceedings of the NATO Advanced Study Institute, Scarborough, Ontario, Canada, August 20-September 3, 1993

By: T. Bisztriczky, NATO Advanced Study Institute on Polytop, Tibor Bisztriczky (Editor)

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Hardcover | 1 July 1994

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530 Pages

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23.39 x 15.6 x 2.87

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The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject.
The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex.
With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes.
For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

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Non-Fiction Mathematics Topology Geometry Algebraic Geometry Mathematical Foundation Set Theory Computing & I.T.Computer Science Groups & Group Theory Analytic Geometry Computer Programming & Software Development

Algorithms & Data Structures Databases Data Capture & Analysis Algebra

Preface
Acknowledgements
Participants
Scientific Programme
Recent results on Coxeter groups	p. 1
The evolution of Coxeter-Dynkin diagrams	p. 21
Polyhedra with hollow faces	p. 43
A hierarchical classification of Euclidean polytopes with regularity properties	p. 71
Modern developments in regular polytopes	p. 97
Classification of locally toroidal regular polytopes	p. 125
Face numbers and subdivisions of convex polytopes	p. 155
Approximation by convex polytopes	p. 173
Some aspects of the combinatorial theory of convex polytopes	p. 205
On volumes of non-Euclidean polytopes	p. 231
Manifolds in the skeletons of convex polytopes, tightness, and generalized Heawood inequalities	p. 241
Generalized stress and motions	p. 249
Polytopes and Brunn-Minkowski theory	p. 273
A survey of Eulerian posets	p. 301
On recent progress in computational synthetic geometry	p. 335
The ridge graph of the metric polytope and some relatives	p. 359
On the complexity of some basic problems in Computational Convexity: II. Volume and mixed volumes	p. 373
The diameter of polytopes and related applications	p. 467
Contributed problems	p. 493
Three problems about 4-polytopes	p. 499
Index	p. 503
Table of Contents provided by Blackwell. All Rights Reserved.

Polytopes - Abstract, Convex and Computational

Proceedings of the NATO Advanced Study Institute, Scarborough, Ontario, Canada, August 20-September 3, 1993

At a Glance

Hardcover

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