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New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space

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Abstract

In this paper we consider ball packings in \(4\)-dimensional hyperbolic space. We show that it is possible to exceed the conjectured \(4\)-dimensional realizable packing density upper bound due to L. Fejes-Tóth (Regular Figures, Macmillian, New York, 1964). We give seven examples of horoball packing configurations that yield higher densities of \(0.71644896\dots \), where horoballs are centered at ideal vertices of certain Coxeter simplices, and are invariant under the actions of their respective Coxeter groups.

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Authors and Affiliations

  1. Department of Mathematics, SUNY Stony Brook, Stony Brook, NY, 11794-3651, USA

    Robert Thijs Kozma

  2. Institute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, 1521, Budapest, Hungary

    Jenő Szirmai

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  1. Robert Thijs Kozma
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  2. Jenő Szirmai
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Correspondence to Robert Thijs Kozma.

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Kozma, R.T., Szirmai, J. New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-Space. Discrete Comput Geom 53, 182–198 (2015). https://doi.org/10.1007/s00454-014-9634-1

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  • DOI: https://doi.org/10.1007/s00454-014-9634-1

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