Geodesic ball packings in \(S^{2} \times R\) space for generalized Coxeter space groups

DOI10.1007/s13366-011-0023-0zbMath1235.52029OpenAlexW1968649137MaRDI QIDQ717839

Jenő Szirmai

Publication date: 7 October 2011

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-011-0023-0

zbMATH Keywords

tilingspace groupThurston geometriesgeodesic ball packing

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Non-Euclidean differential geometry (53A35) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (14)

Densest geodesic ball packings to \({\mathbf S^2 \times \mathbf R}\) space groups generated by screw motions ⋮ Horoball packings to the totally asymptotic regular simplex in the hyperbolic \(n\)-space ⋮ Interior angle sums of geodesic triangles in $S^2 \times R$ and $H^2 \times R$ geometries ⋮ Non-periodic geodesic ball packings generated by infinite regular prism tilings in \(\widetilde{\mathbf{SL}_2\mathbf{R}}\) space ⋮ Hyperbolic Space Forms with Crystallographic Applications and Visualizations ⋮ The sum of the interior angles in geodesic and translation triangles of Sl2(R)~ geometry ⋮ Geodesic and translation ball packings generated by prismatic tessellations of the universal cover of \(\mathrm{SL}_2(\mathbb R)\) ⋮ Fibre-like cylinders, their packings and coverings in \(\widetilde{\mathbf{SL}_2 \mathbf{R}}\) space ⋮ On lattice coverings of Nil space by congruent geodesic balls ⋮ A candidate for the densest packing with equal balls in Thurston geometries ⋮ Simply transitive geodesic ball packings to \(\mathbf{S}^2\times \mathbf{R}\) space groups generated by glide reflections ⋮ Packings by translation balls in \({\widetilde{{\mathrm {SL}}_2(\mathbb{R})}}\) ⋮ Regular prism tilings in \(\widetilde{\mathbf{SL}_2\mathbf R}\) space ⋮ Kissing number in non-Euclidean spaces of constant sectional curvature

Cites Work

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• The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic \(d\)-space
• On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifolds
• The densest translation ball packing by fundamental lattices in Sol space
• The projective interpretation of the eight 3-dimensional homogeneous geometries
• The classification of \(S^2\times\mathbb{R}\) space groups
• The densest geodesic ball packing by a type of Nil lattices
• The optimal ball and horoball packings of the Coxeter tilings in the hyperbolic 3-space
• The Geometries of 3-Manifolds
• The Classification of Non-Euclidean Plane Crystallographic Groups

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