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Convex Polytopes

"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise bea...

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Bibliographic Details
Main Author: Grünbaum, Branko
Other Authors: Ziegler, Günter M. (Editor)
Format: eBook
Language:English
Published: New York, NY Springer New York 2003, 2003
Edition:2nd ed. 2003
Series:Graduate Texts in Mathematics
Subjects:
Convex Geometry 
Convex And Discrete Geometry
Discrete Geometry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Notation and prerequisites
  • 1.1 Algebra
  • 1.2 Topology
  • 1.3 Additional notes and comments
  • 2 Convex sets
  • 2.1 Definition and elementary properties
  • 2.2 Support and separation
  • 2.3 Convex hulls
  • 2.4 Extreme and exposed points; faces and poonems
  • 2.5 Unbounded convex sets
  • 2.6 Polyhedral sets
  • 2.7 Remarks
  • 2.8 Additional notes and comments
  • 3 Polytopes
  • 3.1 Definition and fundamental properties
  • 3.2 Combinatorial types of polytopes; complexes
  • 3.3 Diagrams and Schlegel diagrams
  • 3.4 Duality of polytopes
  • 3.5 Remarks
  • 3.6 Additional notes and comments
  • 4 Examples
  • 4.1 The d-simplex
  • 4.2 Pyramids
  • 4.3 Bipyramids
  • 4.4 Prisms
  • 4.5 Simplicial and simple polytopes
  • 4.6 Cubical polytopes
  • 4.7 Cyclic polytopes
  • 4.8 Exercises
  • 4.9 Additional notes and comments
  • 5 Fundamental properties and constructions
  • 5.1 Representations of polytopes as sections or projections
  • 5.2 The inductive construction of polytopes
  • 5.3 Lower semicontinuity of the functions fk(P)
  • 5.4 Gale-transforms and Gale-diagrams
  • 5.5 Existence of combinatorial types
  • 5.6 Additional notes and comments
  • 6 Polytopes with few vertices
  • 6.1 d-Polytopes with d + 2 vertices
  • 6.2 d-Polytopes with d + 3 vertices
  • 6.3 Gale diagrams of polytopes with few vertices
  • 6.4 Centrally symmetric polytopes
  • 6.5 Exercises
  • 6.6 Remarks
  • 6.7 Additional notes and comments
  • 7 Neighborly polytopes
  • 7.1 Definition and general properties
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