2018/03/13 by Jenő Szirmai, Szirmai, Jenő · 1 citation
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
paper · pdf · doi:10.48550/arxiv.1803.04948
openalex publication_date 2018/03/13 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In this paper we study congruent and non-congruent hyperball (hypersphere)\npackings of the truncated regular octahedron and cube tilings. These are\nderived from the Coxeter simplex tilings p,3,4 (7\≤ p \∈ \ℕ)\nand p,4,3 (5\≤ p \∈ \ℕ) in 3-dimensional hyperbolic space\n\ℍ3. We determine the densest hyperball packing arrangement and its\ndensity with congruent and non-congruent hyperballs related to the above\ntilings in \ℍ3.\n We prove that the locally densest congruent or non-congruent hyperball\nconfiguration belongs to the regular truncated cube with density \≈\n0.86145. This is larger than the B "or "oczky-Florian density upper bound for\nballs and horoballs. Our locally optimal non-congruent hyperball packing\nconfiguration cannot be extended to the entire hyperbolic space \ℍ3,\nbut we determine the extendable densest non-congruent hyperball packing\narrangement related to a regular cube tiling with density \≈ 0.84931.\n