The goal of this paper is to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space H 3 . Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result states that the known Böröczky-Florian density upper bound for "congruent horoball" packings of H 3 remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.

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Koszul type Coxeter Simplex tilings exist in hyperbolic space H n for 2 ≤ n ≤ 9, and their horoball packings have the highest known regular ball packing densities for 3 ≤ n ≤ 5. In this paper we determine the optimal horoball packings of Koszul type Coxeter simplex tilings of n-dimensional hyperbolic space for 6 ≤ n ≤ 9, which give new lower bounds for packing density in each dimension. The symmetries of the packings are given by Coxeter simplex groups.