An Introduction to Convex Polytopes

Graduate Texts in Mathematics #90

by Arne Brondsted

1 Convex Sets.- A7;1. The Affine Structure of ?d.- A7;2. Convex Sets.- A7;3. The Relative Interior of a Convex Set.- A7;4. Supporting Hyperplanes and Halfspaces.- A7;5. The Facial Structure of a Closed Convex Set.- A7;6. Polarity.- 2 Convex Polytopes.- A7;7. Polytopes.- A7;8. Polyhedral Sets.- A7;9. Polarity of Polytopes and Polyhedral Sets.- A7;10. Equivalence and Duality of Polytopes.- A7;11. Vertex-Figures.- A7;12. Simple and Simplicial Polytopes.- A7;13. Cyclic Polytopes.- A7;14. Neighbourly Polytopes.- A7;15. The Graph of a Polytope.- 3 Combinatorial Theory of Convex Polytopes.- A7;16. Eulerߣs Relation.- A7;17. The Dehn-Sommerville Relations.- A7;18. The Upper Bound Theorem.- A7;19. The Lower Bound Theorem.- A7;20. McMullenߣs Conditions.- Appendix 1 Lattices.- Appendix 2 Graphs.- Appendix 3 Combinatorial Identities.- Bibliographical Comments.- List of Symbols.

176 pages, Paperback

First published January 1, 1982