Hyperball packings in hyperbolic $3$-space

zbMath1474.52030arXiv1405.0248MaRDI QIDQ3388354

Jenő Szirmai

Publication date: 5 May 2021

Full work available at URL: https://arxiv.org/abs/1405.0248

zbMATH Keywords

hyperbolic geometrypacking densityCoxeter tilingshyperball packings

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Symmetry properties of polytopes (52B15)

Related Items (6)

Hyperbolic space groups with truncated simplices as fundamental domains ⋮ Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space ⋮ Optimal ball and horoball packings generated by 3-dimensional simply truncated Coxeter orthoschemes with parallel faces ⋮ An upper bound of the density for packing of congruent hyperballs in hyperbolic \(3\)-space ⋮ Unnamed Item ⋮ Decomposition method related to saturated hyperball packings

Cites Work

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• Horoball packings and their densities by generalized simplicial density function in the hyperbolic space
• A candidate for the densest packing with equal balls in Thurston geometries
• The regular \(p\)-gonal prism tilings and their optimal hyperball packings in the hyperbolic 3-space
• The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic \(d\)-space
• On the volume of hyperbolic polyhedra
• Ausfüllungen der hyperbolischen Ebene durch kongruente Hyperzykelbereiche
• The projective interpretation of the eight 3-dimensional homogeneous geometries
• Highly saturated packings and reduced coverings
• Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types
• New lower bound for the optimal ball packing density in hyperbolic 4-space
• Horoball packings to the totally asymptotic regular simplex in the hyperbolic \(n\)-space
• Sphere packings revisited
• Coxeter groups as automorphism groups of solid transitive 3-simplex tilings
• Packing of spheres in spaces of constant curvature
• The optimal hyperball packings related to the smallest compact arithmetic 5-orbifolds
• Über die dichteste Kugelpackung im hyperbolischen Raum
• The least dense hyperball covering of regular prism tilings in hyperbolic \(n\)-space

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