Lectures on Polytopes

1995
ISBN: 978-0-387-94365-7
Verlag: Springer

Buch, Englisch, Band 152, 370 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 587 g

Reihe: Graduate Texts in Mathematics

Based on a graduate course given at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward exposition 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, 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Ziegler, Günter M.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines

Inhaltsverzeichnis

and Examples.- Polytopes, Polyhedra, and Cones.- Faces of Polytopes.- Graphs of 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.- Fiber Polytopes, and Beyond.