Generating smooth lattice polytopes

Authors:
Christian Haase;Benjamin Lorenz;Andreas Paffenholz
Affiliations:
Freie Universität Berlin, Berlin, Germany;Freie Universität Berlin, Berlin, Germany;Freie Universität Berlin, Berlin, Germany
Venue:
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Year:
2010

Citing 3
Cited 0

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Abstract

A lattice polytope P is the convex hull of finitely many lattice points in Zd. It is smooth if each cone in the normal fan is unimodular. It has recently been shown that in fixed dimension the number of lattice equivalence classes of smooth lattice polytopes in dimension d with at most N lattice points is finite. We describe an algorithm to compute a representative in each equivalence class, and report on results in dimension 2 and 3 for N ≤ 12. Our algorithm is implemented as an extension to the software system polymake.