Lower bound on the translative covering density of octahedra

被引：0

作者：

Li, Yiming ^{[1
]}

Lian, Yanlu ^{[2
]}

Fu, Miao ^{[3
]}

Zhang, Yuqin ^{[4
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China

[3] CSSC Elect Technol Co Ltd, Syst Engn Res Inst, Beijing 100036, Peoples R China

[4] Tianjin Univ, Sch Math, Tianjin 300072, Peoples R China

来源：

ADVANCES IN GEOMETRY | 2024年 / 24卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Translative covering density; octahedron; tile; CAYLEY-GRAPHS; PACKING;

D O I：

10.1515/advgeom-2024-0006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on Zong's work [26] on translative packing densities of 3-dimensional convex bodies, we present a local method to estimate the density theta t(C-3) of the densest translative covering of an octahedron. As a consequence we prove that theta t(C-3) >= 1 + 6.6 x 10(-8), which is the first non-trivial lower bound for this density.

引用

页码：151 / 158

页数：8

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