Contact numbers for congruent sphere packings in Euclidean 3-space

DOI10.1007/s00454-012-9405-9zbMath1259.52013arXiv1102.1198OpenAlexW2170193516MaRDI QIDQ452008

Károly Bezdek

Publication date: 19 September 2012

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

Full work available at URL: https://arxiv.org/abs/1102.1198

zbMATH Keywords

isoperimetric inequalitydensitycontact numbercongruent sphere packingspherical cap packingtruncated Voronoi cellunion of balls

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (6)

On contact numbers of totally separable unit sphere packings ⋮ Contact graphs of unit sphere packings revisited ⋮ Density bounds for outer parallel domains of unit ball packings ⋮ Towards a proof of the 24-cell conjecture ⋮ Kissing number in non-Euclidean spaces of constant sectional curvature ⋮ Selected Open Problems in Discrete Geometry and Optimization

Uses Software

• kepler98

Cites Work

• On the maximum number of touching pairs in a finite packing of translates of a convex body
• Average kissing numbers for non-congruent sphere packings
• A proof of the Kepler conjecture
• Kreislagerungen auf Flächen konstanter Krümmung
• Das Problem der dreizehn Kugeln
• The isoperimetric inequality
• On a stronger form of Roger's lemma and the minimum surface area of Voronoi cells in unit ball packings
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