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  • 1 Institute of Mathematics, Department of Geometry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
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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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Acta Mathematica Hungarica
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  • Impact Factor (2019): 0.588
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  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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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
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Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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