Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types

@article{Kozma2012OptimallyDP,
title={Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types},
author={Robert Thijs Kozma and JenHo Szirmai},
journal={Monatshefte f{\"u}r Mathematik},
year={2012},
volume={168},
pages={27-47}
}
• Published 5 July 2010
• Mathematics
• Monatshefte für Mathematik
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 $${\mathbb{H}^3}$$. 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…
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