Lower Bound on Translative Covering Density of Tetrahedra

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 $1+1.227\times 10^{-3}$.

References in corpus (1)

• Upper bound on the packing density of regular tetrahedra and octahedra