Lattice 3-polytopes with few lattice points
type: Item
instance of: scholarly article
publication date: 2014-09-23T00:00:00Z
publication date: 2016-04-15T00:00:00Z
arXiv ID: 1409.6701
arXiv classification: math.CO
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52B20
DOI: 10.1137/15M1014450
DOI: 10.48550/ARXIV.1409.6701
author: M. Blanco
author: Francisco Santos
MaRDI profile type: Publication
zbMATH Open document ID: 1341.52023
published in: SIAM Journal on Discrete Mathematics
full work available at URL: https://arxiv.org/abs/1409.6701
zbMATH DE Number: 6569180
zbMATH Keywords: lattice 3-polytopes
zbMATH Keywords: unimodular equivalence
zbMATH Keywords: lattice points
zbMATH Keywords: finiteness
cites work: Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three
cites work: Minkowski length of 3D lattice polytopes
cites work: The finiteness threshold width of lattice polytopes
cites work: Lattice 3-polytopes with six lattice points
cites work: Lattice polytopes with distinct pair-sums
cites work: Triangulations. Structures for algorithms and applications
cites work: Lattice vertex polytopes with interior lattice points
cites work: Toric Fano three-folds with terminal singularities
cites work: Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
cites work: On the classification of convex lattice polytopes
cites work: Projecting lattice polytopes without interior lattice points
cites work: Unimodular triangulations of dilated 3-polytopes
cites work: Integral Polyhedra in Three Space
cites work: Lattice Tetrahedra
OpenAlex ID: W4237179050
title: Lattice 3-polytopes with few lattice points
review text: In this paper the authors develop an extension of White's theorem on empty tetrahedra. They provide a 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. Additionally the authors prove a general theorem: for every positive integer \(n\) there is only a finite number of (integer congruence classes of) lattice 3-polytopes with \(n\) lattice points and of width larger than one.
reviewed by: Oleg Karpenkov
description: scientific article; zbMATH DE number 6569180
alternative label: Lattice 3-Polytopes with Few Lattice Points