The local optimality of the double lattice packing

DOI10.1007/s00454-016-9792-4zbMath1359.52024arXiv1509.02241OpenAlexW3099210340MaRDI QIDQ312160

Yoav Kallus, Wöden Kusner

Publication date: 14 September 2016

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02241

zbMATH Keywords

optimizationpolygondensitydouble lattice packing

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Convex sets in (2) dimensions (including convex curves) (52A10) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Uses Software

• Flyspeck
• kepler98

Cites Work

• The 3-ball is a local pessimum for packing
• Improved sphere packing lower bounds from Hurwitz lattices
• Upper bound on the packing density of regular tetrahedra and octahedra
• Double-lattice packings of convex bodies in the plane
• New upper bounds on sphere packings. I
• Notions of denseness
• Über die dichteste gitterförmige Lagerung kongruenter Bereiche in der Ebene und eine besondere Art konvexer Kurven
• Pessimal packing shapes
• The sphere packing problem in dimension \(24\)
• Computing upper bounds for the packing density of congruent copies of a convex body
• Existenzsätze für Lagerungen im Euklidischen Raum
• Research Problems in Discrete Geometry
• Strict Periodic Extreme Lattices
• A Note on Sphere Packings in High Dimension
• Dense Packing of Space with Various Convex Solids
• Nonlinear Programming
• Recent Progress in Sphere Packing
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