New Lower Bounds for Optimal Horoball Packing Density in Hyperbolic $n$-space for $6\le n\le 9$

Abstract

Koszul type Coxeter simplex tilings exist in hyperbolic $n$-space ${\mathbb{H}}^n$ up to $n=9$, and their horoball packings achieve the highest known regular ball packing densities for $n=3,4,5$. In this paper we determine the optimal horoball packing densities of Koszul simplex tilings in dimensions $6\le n\le 9$, 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.

16 Pages, 6 Tables, 1 Figure. arXiv admin note: substantial text overlap with arXiv:1809.05411, arXiv:1401.6084

References in corpus (1)

• New Horoball Packing Density Lower Bound in Hyperbolic 5-space

Cited by in corpus (1)

• Optimal Horoball Packing Densities for Koszul-type tilings in Hyperbolic $3$-space