The least dense hyperball covering to the regular prism tilings in the hyperbolic n-space

2013/12/09 by Jenő Szirmai, Jenö Szirmai, Szirmai, Jenö · 2 citations
Mathematics · #52B15 #52C17 #52C22 #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #Metric Geometry (math.MG) #math.MG #msc:52B15 #msc:52C17 #msc:52C22

paper · pdf · doi:10.48550/arxiv.1312.2328

18 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1306.4221

arxiv created 2013/12/09 · openalex publication_date 2013/12/09 · arxiv updated 2013/12/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

After having investigated the densest packings by congruent hyperballs to the regular prism tilings in the n-dimensional hyperbolic space ℍⁿ (n ∈ ℕ, n ≥ 3) we consider the dual covering problems and determine the least dense hyperball arrangements and their densities.

Citations

• The optimal hyperball packings related to the smallest compact arithmetic 5-orbifolds

Cited by

• Packings with horo- and hyperballs generated by simple frustum orthoschemes
• Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings

Related

• Hyperball packings related to octahedron and cube tilings in hyperbolic\n space
• Hyperball packings in hyperbolic 3-space
• Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings
• Upper bound of density for packing of congruent hyperballs in hyperbolic 3-space
• Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic n-space