Embedding a polytope in a lattice
type: Item
instance of: scholarly article
title: Embedding a polytope in a lattice
zbMATH Open document ID: 0824.52016
DOI: 10.1007/BF02574065
author: Yanyan Li
published in: Discrete \& Computational Geometry
publication date: 1995-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/131383
review text: The paper refers to the embeddability of the vertex sets of polytopes in lattices, i.e., to the theory of lattice polytopes. Using a certain similarity transform, the author proves e.g. the following results. If a \((4n-1)\)-dimensional polytope is similar to a lattice polytope in \(\mathbb{R}^{4n}\), then it is similar to a lattice polytope in \(\mathbb{R}^{4n- 1}\). Further on, an \(n\)-dimensional polytope \(P\) is similar to a lattice polytope in some \(\mathbb{R}^ N\) if and only if it is similar to a lattice polytope in \(\mathbb{R}^{2n+1}\), and if and only if \(\sin^ 2(<ABC)\) is rational for any three vertices \(A\), \(B\), \(C\) of \(P\).
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B20
zbMATH DE Number: 764247
zbMATH Keywords: simplex
zbMATH Keywords: similarly embeddable
zbMATH Keywords: lattice polytopes
zbMATH Keywords: similarity
MaRDI profile type: Publication
cites work: Triangles with Vertices on Lattice Points
cites work: Q4724693
cites work: Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert''
cites work: Regular Simplices and Quadratic Forms
cites work: Q5513521
description: scientific article; zbMATH DE number 764247