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.
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页码：151 / 158
页数：8
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