Horoball packings related to hyperbolic 24 cell

2015/02/07 by Jenő Szirmai, Szirmai, Jenő · 1 citation
Mathematics · #52B15 #52C17 #52C22 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52B15 #msc:52C17 #msc:52C22

paper · pdf · doi:10.48550/arxiv.1502.02107

24 pages, 6 figures. arXiv admin note: text overlap with arXiv:1401.6084

arxiv created 2015/02/07 · arxiv updated 2015/02/10

Abstract

In this paper we study the horoball packings related to the hyperbolic 24 cell in the extended hyperbolic space H⁴ where we allow \it horoballs in different types centered at the various vertices of the 24 cell. We determine, introducing the notion of the generalized polyhedral density function, the locally densest horoball packing arrangement and its density with respect to the above regular tiling. The maximal density is ≈ 0.71645 which is equal to the known greatest ball packing density in hyperbolic 4-space given in \citeKSz14.

Citations

• New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-space

Cited by

• Structure and Visualization of Optimal Horoball Packings in 3-dimensional Hyperbolic Space

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