Weakly sporadic F-hollow lattice 3-polytopes
Description
A database containing all weakly sporadic F-hollow lattice 3-polytopes.
Data Description
The text files "weakly_sporadic_non_sporadic_lattice_width1_degree_leq_1.txt", "weakly_sporadic_non_sporadic_lattice_width1_degree2.txt" and "weakly_sporadic_non_sporadic_lattice_width2.txt" contain vertex data for the weakly sporadic F-hollow lattice 3-polytopes which are not sporadic, i.e. they have a lattice projection onto a F-hollow polytope of smaller dimension. The data are sorted by the degree of the polytopes and their lattice width. Each line of the file contains the vertices of one polytope.The text files "sporadic_mu_4_over_3.txt", "sporadic_mu_5_over_4.txt" and "sporadic_mu_7_over_6.txt" contain vertex data for the sporadic F-hollow lattice 3-polytopes, i.e. they have no lattice projection onto a F-hollow polytope of smaller dimension. The data are sorted by the minimal multiplier, which is either 4/3, 5/4 or 7/6. The text files "sporadic_236.txt", "sporadic_244.txt" and "sporadic_333.txt" contain vertex data for the sporadic F-hollow lattice 3-polytopes, which are affine unimodular equivalent to a lattice subpolytope of the simplex with vertices (0,0,0), (i,0,0), (0,j,0), (0,0,k) in the file "spradic_ijk.txt". Note that a sporadic F-hollow lattice 3-polytope can be a subpolytope of more than one of the simplices. Each line of the file contains the vertices of one polytope.
References
The data in "weakly_sporadic_non_sporadic_lattice_width1_degree2.txt" consist of Gorenstein polytopes of index 2 classified in: Victor Batyrev, Dorothee Juny: "Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension.", Mosc. Math. J. 10, No. 2, 285-316 (2010).The data for the sporadic examples were generated from subpolytopes of maximal hollow lattice 3-polytopes, which were classified in: Gennadiy Averkov, Christian Wagner, Robert Weismantel: "Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three." Math. Oper. Res. 36, No. 4, 721-742 (2011). and: Gennadiy Averkov, Jan Krümpelmann, Stefan Weltge: "Notions of maximality for integral lattice-free polyhedra: the case of dimension three." Math. Oper. Res. 42, No. 4, 1035-1062 (2017).
Files
sporadic_236.txt
Files
(283.0 kB)
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Additional details
Related works
- Is supplement to
- Preprint: arXiv:2412.11163 (arXiv)
References
- Victor Batyrev, Dorothee Juny: "Classification of Gorenstein toric del Pezzo varieties in arbitrary dimension.", Mosc. Math. J. 10, No. 2, 285-316 (2010).
- Gennadiy Averkov, Christian Wagner, Robert Weismantel: "Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three." Math. Oper. Res. 36, No. 4, 721-742 (2011).
- Gennadiy Averkov, Jan Krümpelmann, Stefan Weltge: "Notions of maximality for integral lattice-free polyhedra: the case of dimension three." Math. Oper. Res. 42, No. 4, 1035-1062 (2017).