Fundamental Properties and Constructions

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


Despite the simplicity of the notion of a polytope, our understanding of what properties a polytope may, or may not, have is severely hampered by the difficulty of producing polytopes having certain desired features. One example of such a difficulty will help to focus the problem. Let us consider 4-polytopes with 8 vertices; with some patience, combining the different types of polytopes considered in Chapter 4, the reader will probably find 4-polytopes with 8 vertices and 16 edges, or with any number of edges between 18 and 28. Now he may ask himself whether it is possible to complete the list by a polytope with 17 edges. But how is one to start looking for such a polytope?


Convex Hull Fundamental Property Convex POLYTOPES Combinatorial Type Abstract Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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