Extremal Problems Concerning Numbers of Faces

  • Branko Grünbaum
Part of the Graduate Texts in Mathematics book series (GTM, volume 221)


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.


Extremal Problem Convex POLYTOPES Simplicial Manifold Affine Hull Simplicial Sphere 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Branko Grünbaum
    • 1
  1. 1.Department of MathematicsUniversity of Washington, SeattleSeattleUSA

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