Sphere packings revisited

DOI10.1016/j.ejc.2005.05.001zbMath1091.52010OpenAlexW2153268570MaRDI QIDQ2493106

Károly Bezdek

Publication date: 9 June 2006

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2005.05.001

zbMATH Keywords

isoperimetric problemsVoronoi cellsKepler conjecture\(d\)-dimensional spaces of constant curvaturedodecahedral conjectureHadwiger numbersNewton numbersoctahedral conjecturepackings of congruent spherestouching numbers

Mathematics Subject Classification ID

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

Related Items (20)

On configurations of solid balls in 3-space: chromatic numbers and knotted cycles ⋮ Horoball packings to the totally asymptotic regular simplex in the hyperbolic \(n\)-space ⋮ Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space ⋮ New horoball packing density lower bound in hyperbolic 5-space ⋮ An integer parallelotope with small surface area ⋮ Hyperball packings in hyperbolic $3$-space ⋮ Optimal ball and horoball packings generated by 3-dimensional simply truncated Coxeter orthoschemes with parallel faces ⋮ Packing Coxeter honeycombs with sequences of spheres ⋮ An upper bound of the density for packing of congruent hyperballs in hyperbolic \(3\)-space ⋮ Horoball packings and their densities by generalized simplicial density function in the hyperbolic space ⋮ Coverings with congruent and non-congruent hyperballs generated by doubly truncated Coxeter orthoschemes ⋮ Packings with horo- and hyperballs generated by simple frustum orthoschemes ⋮ Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types ⋮ New lower bound for the optimal ball packing density in hyperbolic 4-space ⋮ Conic volume ratio of the packing cone associate to a convex body ⋮ Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings ⋮ The least dense hyperball covering of regular prism tilings in hyperbolic \(n\)-space ⋮ Decomposition method related to saturated hyperball packings ⋮ Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4} ⋮ Hyperball packings related to truncated cube and octahedron tilings in hyperbolic space

Uses Software

• kepler98

Cites Work

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