Lectures on Polytopes

ISBN-10: 038794365X
ISBN-13: 9780387943657
Edition: 1995 (Revised)
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Description: Based on a graduate course given at the Technische Universitt, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides  More...

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Book details

List price: $49.95
Copyright year: 1995
Publisher: Springer
Publication date: 5/3/2012
Binding: Paperback
Pages: 370
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 1.188
Language: English

Based on a graduate course given at the Technische Universitt, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures - introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids) - discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction) - show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) They should provide interesting and enjoyable reading for researchers as well as students.

Preface
Preface to the Second Printing
Introduction and Examples
Polytopes, Polyhedra, and Cones
Faces of Polytopes
Graphs for Polytopes
Steinitz' Theorem for 3-Polytopes
Schlegel Diagrams for 4-Polytopes
Duality, Gale Diagrams, and Applications
Fans, Arrangements, Zonotopes, and Tilings
Shellability and the Upper Bound Theorem
Fiber Polytopes, and Beyond
References
Index

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