Acta Mathematica Hungarica
Volume/Issue:
Volume 136: Issue 1-2
Horoball packings and their densities by generalized simplicial density function in the hyperbolic space
Author:
Jenő SzirmaiInstitute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

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Pages:
39–55
Online Publication Date:
07 Mar 2012
Publication Date:
01 Jul 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-012-0205-8
Keywords:
hyperbolic geometry; horoball packing; optimal simplicial density; 52C17; 52C22; 52B15
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Abstract

The aim of this paper is to determine the locally densest horoball packing arrangements and their densities with respect to fully asymptotic tetrahedra with at least one plane of symmetry in hyperbolic 3-space extended with its absolute figure, where the ideal centers of horoballs give rise to vertices of a fully asymptotic tetrahedron. We allow horoballs of different types at the various vertices. Moreover, we generalize the notion of the simplicial density function in the extended hyperbolic space (n≧2), and prove that, in this sense, the well known Böröczky–Florian density upper bound for “congruent horoball” packings ofdoes not remain valid to the fully asymptotic tetrahedra.

The density of this locally densest packing is ≈0.874994, may be surprisingly larger than the Böröczky–Florian density upper bound ≈0.853276 but our local ball arrangement seems not to have extension to the whole hyperbolic space.

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  • [10] Szirmai, J. 2007 The densest geodesic ball packing by a type of Nil lattices Beiträge Alg. Geom. (Contr. Alg. Geom.) 48 383–397.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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