Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types

Details Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types

2010-07-05

arxiv.org/abs/1007.0722v1

Mathematics

Metric Geometry

26 pages, 10 figures

Scientific paper

10.1007/s00605-012-0393-x

The goal of this paper 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 result states that the known B\"or\"oczky--Florian density upper bound for "congruent horoball" packings of $\mathbb{H}^3$ remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.

Affiliated with

Also associated with

No associations

Rating

Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-596715