Extremal Problems Concerning Numbers of Faces
In chapters 8 and 9 we obtained information on the f-vectors of d-polytopes, and of some special classes of d-polytopes, by determining the affine hull of all the f-vectors of polytopes in the class considered. In other words, we were concerned with the linear relations satisfied by the f-vectors of all polytopes belonging to a certain class. Chapter 10 reports on the present knowledge about non-linear relations existing between the components of f-vectors of certain classes of polytopes. As will be seen, results in this direction are still rather incomplete—despite the considerable interest and efforts devoted to some aspects of these problems.
KeywordsExtremal Problem Convex POLYTOPES Simplicial Manifold Affine Hull Simplicial Sphere
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