Polytope Enumeration

Chapter

Abstract

We describe an efficient method of enumerating all (d;2d) polytopes, where d is the polytope dimension. To our knowledge, this is the first algorithm which produces all known polytopes with their f-vector representation. Our algorithm is based on key insights on the behavior of cutting plane and vertex separation phenomenon. We have implemented our algorithm (in serial as well as parallel versions) and experimental results are given at the end of this paper. As an example we can compute all (4;8) polytopes in minutes.

Keywords

Compaction 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.West LinnUSA

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