Decomposition method related to saturated hyperball packings

Jenő Szirmai

Abstract


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.


Keywords


Hyperbolic geometry, hyperball packings, Dirichlet-Voronoi cell, packing density, Coxeter tilings

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DOI: https://doi.org/10.26493/1855-3974.1485.0b1

ISSN: 1855-3974

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