Generating Smooth Lattice Polytopes

  • Christian Haase
  • Benjamin Lorenz
  • Andreas Paffenholz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


A lattice polytope P is the convex hull of finitely many lattice points in ℤ d . 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.


lattice polytopes smooth polytopes classification polymake 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christian Haase
    • 1
  • Benjamin Lorenz
    • 1
  • Andreas Paffenholz
    • 1
  1. 1.Freie Universität BerlinBerlinGermany

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