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?


Hull Pyramid 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

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

Personalised recommendations