English

Lower Bound on Translative Covering Density of Tetrahedra

Metric Geometry 2025-09-16 v1

Abstract

In this paper, we present the first nontrivial lower bound on the translative covering density of tetrahedra. To this end, we show the lower bound, in any translative covering of tetrahedra, on the density relative to a given cube. The resulting lower bound on the translative covering density of tetrahedra is 1+1.227×1031+1.227\times10^{-3}.

Keywords

Cite

@article{arxiv.2206.13252,
  title  = {Lower Bound on Translative Covering Density of Tetrahedra},
  author = {Yiming Li and Miao Fu and Yuqin Zhang},
  journal= {arXiv preprint arXiv:2206.13252},
  year   = {2025}
}