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arXiv · 1401.6084

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

Robert Thijs Kozma·Jenő Szirmai
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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, 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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Robert Thijs Kozma, Jenő Szirmai. 2014-08-22. New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-space. https://doi.org/10.1007/s00454-014-9634-1

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