Ebook: Polytopes: Abstract, Convex and Computational

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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Content:
Front Matter....Pages i-xix
Recent Results on Coxeter Groups....Pages 1-19
The Evolution of Coxeter-Dynkin Diagrams....Pages 21-42
Polyhedra with Hollow Faces....Pages 43-70
A Hierarchical Classification of Euclidean Polytopes with Regularity Properties....Pages 71-96
Modern Developments in Regular Polytopes....Pages 97-124
Classification of Locally Toroidal Regular Polytopes....Pages 125-154
Face Numbers and Subdivisions of Convex Polytopes....Pages 155-171
Approximation by Convex Polytopes....Pages 173-203
Some Aspects of the Combinatorial Theory of Convex Polytopes....Pages 205-229
On Volumes of Non-Euclidean Polytopes....Pages 231-239
Manifolds in the Skeletons of Convex Polytopes, Tightness, and Generalized Heawood Inequalities....Pages 241-247
Generalized Stress and Motions....Pages 249-271
Polytopes and Brunn-Minkowski Theory....Pages 273-299
A Survey of Eulerian Posets....Pages 301-333
On Recent Progress in Computational Synthetic Geometry....Pages 335-358
The Ridge Graph of the Metric Polytope and Some Relatives....Pages 359-372
On the Complexity of Some Basic Problems in Computational Convexity....Pages 373-466
The Diameter of Polytopes and Related Applications....Pages 467-492
Front Matter....Pages 493-493
Contributed Problems....Pages 493-497
Three Problems About 4-Polytopes....Pages 499-502
Back Matter....Pages 503-507

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Content:
Front Matter....Pages i-xix
Recent Results on Coxeter Groups....Pages 1-19
The Evolution of Coxeter-Dynkin Diagrams....Pages 21-42
Polyhedra with Hollow Faces....Pages 43-70
A Hierarchical Classification of Euclidean Polytopes with Regularity Properties....Pages 71-96
Modern Developments in Regular Polytopes....Pages 97-124
Classification of Locally Toroidal Regular Polytopes....Pages 125-154
Face Numbers and Subdivisions of Convex Polytopes....Pages 155-171
Approximation by Convex Polytopes....Pages 173-203
Some Aspects of the Combinatorial Theory of Convex Polytopes....Pages 205-229
On Volumes of Non-Euclidean Polytopes....Pages 231-239
Manifolds in the Skeletons of Convex Polytopes, Tightness, and Generalized Heawood Inequalities....Pages 241-247
Generalized Stress and Motions....Pages 249-271
Polytopes and Brunn-Minkowski Theory....Pages 273-299
A Survey of Eulerian Posets....Pages 301-333
On Recent Progress in Computational Synthetic Geometry....Pages 335-358
The Ridge Graph of the Metric Polytope and Some Relatives....Pages 359-372
On the Complexity of Some Basic Problems in Computational Convexity....Pages 373-466
The Diameter of Polytopes and Related Applications....Pages 467-492
Front Matter....Pages 493-493
Contributed Problems....Pages 493-497
Three Problems About 4-Polytopes....Pages 499-502
Back Matter....Pages 503-507
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