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.
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Haase, C., Lorenz, B., Paffenholz, A. (2010). Generating Smooth Lattice Polytopes. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_51
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DOI: https://doi.org/10.1007/978-3-642-15582-6_51
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