Overview

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 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. This text should be of interest to researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Full Product Details

Author:   Tibor Bisztriczky ,  Peter McMullen ,  Rolf Schneider ,  Asia Ivic Weiss
Publisher:   Springer
Imprint:   Springer
Edition:   1994 ed.
Volume:   440
Dimensions:   Width: 15.50cm , Height: 2.90cm , Length: 23.50cm
Weight:   1.002kg
ISBN:  

9780792330165

ISBN 10:   0792330161
Pages:   507
Publication Date:   31 July 1994
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Abstract.- Recent results on Coxeter groups.- The evolution of Coxeter-Dynkin diagrams.- Polyhedra with hollow faces.- A hierarchical classification of Euclidean polytopes with regularity properties,.- Modern developments in regular polytopes.- Classification of locally toroidal regular polytopes.- Convex.- Face numbers and subdivisions of convex polytopes.- Approximation by convex polytopes.- Some aspects of the combinatorial theory of convex polytopes.- On volumes of non-Euclidean polytopes.- Manifolds in the skeletons of convex polytopes,tightness, and generalized Heawood inequalities.- Generalized stress and motions.- Polytopes and Brunn-Minkowski theory.- A survey of Eulerian posets.- Computational.- On recent progress in computational synthetic geometry.- The ridge graph of the metric polytope and some relatives.- On the complexity of some basic problems in Computational Convexity: II. Volume and mixed volumes.- The diameter of polytopes and related applications.- Problems.- Contributed problems.- Three problems about 4-polytopes.

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