1 Convex Sets. - & 00A7;1. The Affine Structure of ?d. - & 00A7;2. Convex Sets. - & 00A7;3. The Relative Interior of a Convex Set. - & 00A7;4. Supporting Hyperplanes and Halfspaces. - & 00A7;5. The Facial Structure of a Closed Convex Set. - & 00A7;6. Polarity. - 2 Convex Polytopes. - & 00A7;7. Polytopes. - & 00A7;8. Polyhedral Sets. - & 00A7;9. Polarity of Polytopes and Polyhedral Sets. - & 00A7;10. Equivalence and Duality of Polytopes. - & 00A7;11. Vertex-Figures. - & 00A7;12. Simple and Simplicial Polytopes. - & 00A7;13. Cyclic Polytopes. - & 00A7;14. Neighbourly Polytopes. - & 00A7;15. The Graph of a Polytope. - 3 Combinatorial Theory of Convex Polytopes. - & 00A7;16. Euler& 2019;s Relation. - & 00A7;17. The Dehn-Sommerville Relations. - & 00A7;18. The Upper Bound Theorem. - & 00A7;19. The Lower Bound Theorem. - & 00A7;20. McMullen& 2019;s Conditions. - Appendix 1 Lattices. - Appendix 2 Graphs. - Appendix 3 Combinatorial Identities. - Bibliographical Comments. - List of Symbols. Language: English