Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4}

Abstract

In this paper we study the horoball packings related to the hyperbolic 24 cell honeycomb by Coxeter-Schl?fli symbol {3,4,3,4} in the extended hyperbolic 4-spaceH 4 where we allow horoballs in different types centered at the various vertices of the 24 cell. Introducing the notion of the generalized polyhedral density function, we determine the locally densest horoball packing arrangement and its density with respect to the above regular tiling. The maximal density is ? 0:71645 which is equal to the known greatest horoball packing density in hyperbolic 4-space, given in [13].