论文信息 - An Introduction to Convex Polytopes

An Introduction to Convex Polytopes

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

A. Brøndsted

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