Lower bound on the translative covering density of octahedra.

Based on Zong's work [26] on translative packing densities of 3-dimensional convex bodies, we present a local method to estimate the density θt(C3) of the densest translative covering of an octahedron. As a consequence we prove that θt(C3) ≥ 1 + 6.6 × 10–8, which is the first non-trivial lower bound for this density. [ABSTRACT FROM AUTHOR]