Geometry and topology · Oct 6, 2026
The optimal order of convex-body covering density
Determines the optimal worst-case covering density as , for both lattice and unrestricted translative coverings. Every convex body in ℝn, n ≥ 2, admits a lattice covering of density at most ; centrally symmetric examples in every sufficiently large dimension require at least even without the lattice restriction, for absolute .
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model