Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types - Mathematics > Metric GeometryReport as inadecuate




Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types - Mathematics > Metric Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: The goal of this paper to determine the optimal horoball packing arrangementsand their densities for all four fully asymptotic Coxeter tilings Coxeterhoneycombs in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs arerequired to lie at vertices of the regular polyhedral cells constituting thetiling. We allow horoballs of different types at the various vertices. Ourresults are derived through a generalization of the projective methodology forhyperbolic spaces. The main result states that the known B\-or\-oczky-Floriandensity upper bound for -congruent horoball- packings of $\mathbb{H}^3$ remainsvalid for the class of fully asymptotic Coxeter tilings, even if packingconditions are relaxed by allowing for horoballs of different types underprescribed symmetry groups. The consequences of this remarkable result arediscussed for various Coxeter tilings.



Author: Robert Thijs Kozma, Jenő Szirmai

Source: https://arxiv.org/







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