English

Lower Bound on Translative Covering Density of Octahedron

Metric Geometry 2023-04-18 v1

Abstract

In this paper, we present the first nontrivial lower bound on the translative covering density of octahedron. To this end, we show the lower bound, in any translative covering of octahedron, on the density relative to a given parallelehedron. The resulting lower bound on the translative covering density of octahedron is 1+6.6×1081+6.6\times10^{-8}.

Keywords

Cite

@article{arxiv.2304.07833,
  title  = {Lower Bound on Translative Covering Density of Octahedron},
  author = {Yiming Li and Yanlu Lian and Miao Fu and Yuqin Zhang},
  journal= {arXiv preprint arXiv:2304.07833},
  year   = {2023}
}