Geodesic
Decomposition method related to saturated hyperball packings
Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 349-358.

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In this paper we study the problem of hyperball (hypersphere) packings in 3-dimensional hyperbolic space. We introduce a new definition of the non-compact saturated ball packings with generalized balls (horoballs, hyperballs) and describe to each saturated hyperball packing, a new procedure to get a decomposition of 3-dimensional hyperbolic space ℍ3 into truncated tetrahedra. Therefore, in order to get a density upper bound for hyperball packings, it is sufficient to determine the density upper bound of hyperball packings in truncated simplices.
DOI : 10.26493/1855-3974.1485.0b1
Keywords: Hyperbolic geometry, hyperball packings, Dirichlet-Voronoi cell, packing density, Coxeter tilings 
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Jenő Szirmai. Decomposition method related to saturated hyperball packings. Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 349-358. doi : 10.26493/1855-3974.1485.0b1. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1485.0b1/

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