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 θ t ( C 3 ) of the densest translative covering of an octahedron. As a consequence we prove that θ t ( C 3 ) ≥ 1 + 6.6 × 10 –8 , which is the first non-trivial lower bound for this density.