Abstract We determine the optimal horoball packing densities for Koszul-type Coxeter simplex tilings in hyperbolic 3-space. Using a parametrization of horoballs by the Busemann function and the symmetry of the tilings, we obtain families of packings that attain the universal simplicial density upper bound d₃ () = (2 3 (3) \!) ^-1 0. 853276, d 3 (∞) = (2 3 Λ (π 3) ) - 1 ≈ 0. 853276, where Λ denotes the Lobachevsky function. These results show that extremal packing densities in H³ H 3 are realized by multiple explicit Coxeter tilings and are closely tied to special values of L -functions and hyperbolic manifold volumes.
T. et al. (Thu,) studied this question.