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Enumeration of Lattice 3-Polytopes by Their Number of Lattice Points

Abstract: We develop a procedure for the complete computational enumeration of lattice 3-polytopes of width larger than one, of which there are finitely many for each given number of lattice points. We also implement an algorithm for doing this and enumerate those with at most 11 lattice points (there are 216,453 of them). In order to achieve this we prove that if P is a lattice 3-polytope of width larger than one and with at least seven lattice points then it fits in one of three categories that we call boxed, spiked and merged. Boxed polytopes have at most 11 lattice points; in particular they are finitely many, and we enumerate them completely with computer help. Spiked polytopes are infinitely many but admit a quite precise description (and enumeration). Merged polytopes are computed as a union (merging) of two polytopes of width larger than one and strictly smaller number of lattice points.

 Fuente: Discrete and Computational Geometry, 2018, 60(3), 756-800

 Editorial: Springer New York LLC

 Fecha de publicación: 01/10/2018

 Nº de páginas: 45

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00454-017-9932-5

 ISSN: 0179-5376,1432-0444

 Proyecto español: MTM2011-22792 ; MTM2014-54207-P ; BES-2012-058920

 Url de la publicación: https://doi.org/10.1007/s00454-017-9932-5