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.
KeywordsFace Lattice Hierarchical Representation Simple Polytopes Combinatorial Graph Face Poset
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