Classification of smooth lattice polytopes with few lattice points

Details Classification of smooth lattice polytopes with few lattice points Classification of smooth lattice polytopes with few lattice points

2010-01-04

arxiv.org/abs/1001.0514v1

Mathematics

Combinatorics

25 pages plus 2 pages containing the polytopes and 16 pages of polymake extension and data files

Scientific paper

After giving a short introduction on smooth lattice polytopes, I will present a proof for the finiteness of smooth lattice polytopes with few lattice points. The argument is then turned into an algorithm for the classification of smooth lattice polytopes in fixed dimension with an upper bound on the number of lattice points. Additionally I have implemented this algorithm for dimension two and three and used it, together with a classification of smooth minimal fans by Tadao Oda, to create lists of all smooth 2-polytopes and 3-polytopes with at most 12 lattice points.

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