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Polytope Enumeration

  • Sandeep Koranne
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

Face Lattice Hierarchical Representation Simple Polytopes Combinatorial Graph Face Poset 
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, LLC 2009

Authors and Affiliations

  1. 1.West LinnUSA

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