{"title":"Lower bound on the translative covering density of octahedra","authors":"Yiming Li, Yanlu Lian, Miao Fu, Yuqin Zhang","doi":"10.1515/advgeom-2024-0006","DOIUrl":null,"url":null,"abstract":"Based on Zong’s work [26] on translative packing densities of 3-dimensional convex bodies, we present a local method to estimate the density <jats:italic>θ<jats:sup>t</jats:sup> </jats:italic>(<jats:italic>C</jats:italic> <jats:sub>3</jats:sub>) of the densest translative covering of an octahedron. As a consequence we prove that <jats:italic>θ<jats:sup>t</jats:sup> </jats:italic>(<jats:italic>C</jats:italic> <jats:sub>3</jats:sub>) ≥ 1 + 6.6 × 10<jats:sup>–8</jats:sup>, which is the first non-trivial lower bound for this density.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2024-0006","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Based on Zong’s work [26] on translative packing densities of 3-dimensional convex bodies, we present a local method to estimate the density θt(C3) of the densest translative covering of an octahedron. As a consequence we prove that θt(C3) ≥ 1 + 6.6 × 10–8, which is the first non-trivial lower bound for this density.
期刊介绍：
Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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