2016/01/14 by R. Kozma, Kozma, Robert T., Jenő Szirmai +1
Computer Science · Materials Science · Mathematics · #52B15 #52C17 #52C22 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1601.03620
openalex publication_date 2016/01/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Four packings of hyperbolic 3-space are known to yield the optimal packing density of 0.85328…. They are realized in the regular tetrahedral and cubic Coxeter honeycombs with Schläfli symbols \3,3,6 \ and \4,3,6\. These honeycombs are totally asymptotic, and the packings consist of horoballs (of different types) centered at the ideal vertices. We describe a method to visualize regular horoball packings of extended hyperbolic 3-space ℍ3 using the Beltrami-Klein model and the Coxeter group of the packing. We produce the first known images of these four optimal horoball packings.