2018/03/13 by Jenő Szirmai, Szirmai, Jenő · 3 citations
Materials Science · Mathematics · #52B15 #52C17 #52C22 #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #Supramolecular Self-Assembly in Materials #math.MG #msc:52B15 #msc:52C17 #msc:52C22
paper · pdf · doi:10.48550/arxiv.1803.04948
33 pages, 12 figures. arXiv admin note: text overlap with arXiv:1510.03208, arXiv:1505.03338
arxiv created 2018/03/13 · openalex publication_date 2018/03/13 · arxiv updated 2018/03/14 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In this paper we study congruent and non-congruent hyperball (hypersphere) packings of the truncated regular octahedron and cube tilings. These are derived from the Coxeter simplex tilings \p,3,4\ (7≤ p ∈ ℕ) and \p,4,3\ (5≤ p ∈ ℕ) in 3-dimensional hyperbolic space ℍ3. We determine the densest hyperball packing arrangement and its density with congruent and non-congruent hyperballs related to the above tilings in ℍ3. We prove that the locally densest congruent or non-congruent hyperball configuration belongs to the regular truncated cube with density ≈ 0.86145. This is larger than the Böröczky-Florian density upper bound for balls and horoballs. Our locally optimal non-congruent hyperball packing configuration cannot be extended to the entire hyperbolic space ℍ3, but we determine the extendable densest non-congruent hyperball packing arrangement related to a regular cube tiling with density ≈ 0.84931.