文摘
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.