Lectures on polytopes

Günter M. Ziegler

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

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

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書名 Lectures on polytopes
著作者等 Ziegler, Gunter M
Ziegler Gunter M.
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1995
版表示 Softcover reprint of the original 1st ed. 1995
ページ数 ix, 370 p.
大きさ 25 cm
ISBN 038794365X
NCID BA24036607
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言語 英語
出版国 アメリカ合衆国