Simply transitive geodesic ball packings to \(\mathbf{S}^2\times \mathbf{R}\) space groups generated by glide reflections

DOI10.1007/S10231-013-0324-ZzbMath1298.52022arXiv1206.0566OpenAlexW2018534007MaRDI QIDQ741306

Jenő Szirmai

Publication date: 11 September 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0566

zbMATH Keywords

Thurston geometriesgeodesic ball packingsspace groups

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) Geometries with differentiable structure (51H25)

Related Items (6)

Interior angle sums of geodesic triangles in $S^2 \times R$ and $H^2 \times R$ geometries ⋮ New horoball packing density lower bound in hyperbolic 5-space ⋮ On Menelaus' and Ceva's theorems in \textbf{Nil} geometry ⋮ New lower bound for the optimal ball packing density in hyperbolic 4-space ⋮ The least dense hyperball covering of regular prism tilings in hyperbolic \(n\)-space ⋮ Decomposition method related to saturated hyperball packings

Cites Work

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• Geodesic ball packings in \(S^{2} \times R\) space for generalized Coxeter space groups
• The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic \(d\)-space
• 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 Geometries of 3-Manifolds
• The Classification of Non-Euclidean Plane Crystallographic Groups

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