New lower bounds for optimal horoball packing density in hyperbolic n-space for $$6 \le n \le 9$$

Abstract

AbstractKoszul type Coxeter simplex tilings exist in hyperbolic n-space $$\mathbb {H}^n$$ H n up to $$ n = 9$$ n = 9 , and their horoball packings achieve the highest known regular ball packing densities for $$n = 3, 4, 5$$ n = 3 , 4 , 5 . In this paper we determine the optimal horoball packing densities of Koszul simplex tilings in dimensions $$6 \le n \le 9$$ 6 ≤ n ≤ 9 , which give new lower bounds for optimal packing density in each dimension. The symmetries of the packings are given by Coxeter simplex groups, and a parameter related to the Busemann function gives an isometry invariant description of different optimal horoball packing configurations.