Lower bound on the translative covering density of octahedra
-
Yiming Li
,
Miao Fu
Abstract
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.
Funding statement: This work has been supported by the National Natural Science Foundation of China (NSFC12226006, NSFC11921001, NSFC11801410 and NSFC11971346), the Natural Key Research and Development Program of China (2018YFA0704701), the China Scholarship Council (No. 201906255029) and the Scientific Research Fund of Zhejiang Provincial Education Department (Y202250092), Y202351675) and the Natural Science Foundation of Zhejiang Provincial (LQ24A010008).
Acknowledgements
The authors are grateful to C. Zong for his supervision and discussion.
Communicated by: M. Henk
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Inequalities for f*-vectors of lattice polytopes
- Lower bound on the translative covering density of octahedra
- Variations on the Weak Bounded Negativity Conjecture
- Poisson Structures on moduli spaces of Higgs bundles over stacky curves
- Generalized Shioda–Inose structures of order 3
- Deformation cones of Tesler polytopes
- Some observations on conformal symmetries of G2-structures
- Characterization of the sphere and of bodies of revolution by means of Larman points
- Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
- The feet of orthogonal Buekenhout–Metz unitals
Articles in the same Issue
- Frontmatter
- Inequalities for f*-vectors of lattice polytopes
- Lower bound on the translative covering density of octahedra
- Variations on the Weak Bounded Negativity Conjecture
- Poisson Structures on moduli spaces of Higgs bundles over stacky curves
- Generalized Shioda–Inose structures of order 3
- Deformation cones of Tesler polytopes
- Some observations on conformal symmetries of G2-structures
- Characterization of the sphere and of bodies of revolution by means of Larman points
- Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
- The feet of orthogonal Buekenhout–Metz unitals
