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Lattice 3-Polytopes with Few Lattice Points

Abstract: We extend White's classification of empty tetrahedra to the complete classification of lattice 3-polytopes with five lattice points, showing that, apart from infinitely many of width one, there are exactly nine equivalence classes of them with width two and none of larger width. We also prove that, for each $n\in\mathbb{N}$, there is only a finite number of (classes of) lattice 3-polytopes with $n$ lattice points and of width larger than one. This implies that extending the present classification to larger sizes makes sense, which is the topic of subsequent papers of ours.

 Fuente: SIAM J. Discrete Math., 30(2), 669-686.

 Editorial: Society for Industrial and Applied Mathematics

 Año de publicación: 2016

 Nº de páginas: 17

 Tipo de publicación: Artículo de Revista

 DOI: 10.1137/15M1014450

 ISSN: 0895-4801,1095-7146

 Proyecto español: BES-2012-058920

 Url de la publicación: https://doi.org/10.1137/15M1014450