Horoball Packings related to the 4-Dimensional Hyperbolic 24 Cell Honeycomb {3, 4, 3, 4}

Jenő Szirmai


In this paper we study the horoball packings related to the hyperbolic 24 cell in the extended hyperbolic space $\overline{\mathbf{H}}^4$
where we allow {\it horoballs in different types}
centered at the various vertices of the 24 cell.

We determine, introducing the notion of the generalized polyhedral density function, the locally densest horoball packing arrangement
and its density with respect to the above regular tiling. The maximal density is $\approx 0.71645$ which is equal to the known
greatest ball packing density in hyperbolic 4-space given in \cite{KSz14}.

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