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arXiv · 2310.18643

The Simultaneous Lattice Packing-Covering Constant of Octahedra

Yiming Li·Chuanming Zong
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Abstract

This paper proves that the simultaneous lattice packing-covering constant of an octahedron is $7/6$. In other words, $7/6$ is the smallest positive number $r$ such that for every octahedron $O$ centered at the origin there is a lattice $Λ$ such that $O+Λ$ is a packing in $\mathbb{E}^3$ and $rO+Λ$ is a covering of $\mathbb{E}^3$.

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Yiming Li, Chuanming Zong. 2025-01-18. The Simultaneous Lattice Packing-Covering Constant of Octahedra. https://doi.org/10.1515/advgeom-2025-0007

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