Lower bound on the translative covering density of octahedra

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2024-08-13 DOI:10.1515/advgeom-2024-0006

Yiming Li, Yanlu Lian, Miao Fu, Yuqin Zhang

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 (C 3) of the densest translative covering of an octahedron. As a consequence we prove that θt (C 3) ≥ 1 + 6.6 × 10–8, which is the first non-trivial lower bound for this density.

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八面体平移覆盖密度下限

基于宗庆后关于三维凸体平移堆积密度的研究[26]，我们提出了一种局部方法来估计八面体最密平移覆盖的密度θt (C 3)。因此，我们证明了 θt (C 3) ≥ 1 + 6.6 × 10-8，这是该密度的第一个非难下限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

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.