Lattice-like translation ball packings in Nil space

2012 ◽  
Vol 80 (3-4) ◽  
pp. 427-440 ◽  
Author(s):  
JENO SZIRMAI
Keyword(s):  
Ball Packings

scholarly journals Lorentzian Coxeter systems and Boyd–Maxwell ball packings

2014 ◽  
Vol 174 (1) ◽  
pp. 43-73 ◽  
Author(s):  
Hao Chen ◽  
Jean-Philippe Labbé
Keyword(s):  
Ball Packings ◽  
Coxeter Systems

Optimal ball packings for crystallographic groups of the cubic crystal system and their Dirichlet-Voronoi cells

2006 ◽  
Vol 221 (1) ◽  
Author(s):  
István Prok ◽  
Jenö Szirmai
Keyword(s):  
Euclidean Space ◽  
Crystallographic Groups ◽  
Cubic Crystal ◽  
Voronoi Cells ◽  
Crystal System ◽  
Ball Packings

AbstractIn this paper we look for densest ball packings of Euclidean space E

About four‐ball packings

Mathematika ◽  
1993 ◽  
Vol 40 (2) ◽  
pp. 226-232
Author(s):  
Károly Böröczky
Keyword(s):  
Ball Packings

scholarly journals Density bounds for outer parallel domains of unit ball packings

2015 ◽  
Vol 288 (1) ◽  
pp. 209-225 ◽  
Author(s):  
Károly Bezdek ◽  
Zsolt Lángi
Keyword(s):  
Unit Ball ◽  
Ball Packings

scholarly journals Top dense hyperbolic ball packings and coverings for complete coxeter orthoscheme groups

2018 ◽  
Vol 103 (117) ◽  
pp. 129-146
Author(s):  
Emil Molnár ◽  
Jenő Szirmai
Keyword(s):  
Hyperbolic Space ◽  
Coxeter Group ◽  
Upper Bound ◽  
Dihedral Angles ◽  
Ball Packings ◽  
Ball Packing ◽  
Packing Densities

In n-dimensional hyperbolic space Hn (n > 2), there are three types of spheres (balls): the sphere, horosphere and hypersphere. If n = 2, 3 we know a universal upper bound of the ball packing densities, where each ball?s volume is related to the volume of the corresponding Dirichlet-Voronoi (D-V) cell. E.g., in H3 a densest (not unique) horoball packing is derived from the {3,3,6} Coxeter tiling consisting of ideal regular simplices T? reg with dihedral angles ?/3. The density of this packing is ??3 ? 0.85328 and this provides a very rough upper bound for the ball packing densities as well. However, there are no ?essential" results regarding the ?classical" ball packings with congruent balls, and for ball coverings either. The goal of this paper is to find the extremal ball arrangements in H3 with ?classical balls". We consider only periodic congruent ball arrangements (for simplicity) related to the generalized, so-called complete Coxeter orthoschemes and their extended groups. In Theorems 1.1 and 1.2 we formulate also conjectures for the densest ball packing with density 0.77147... and the loosest ball covering with density 1.36893..., respectively. Both are related with the extended Coxeter group (5,3,5) and the so-called hyperbolic football manifold. These facts can have important relations with fullerenes in crystallography.

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