Lattice-like translation ball packings in Nil space
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Publication:2915409
DOI10.5486/PMD.2012.5117zbMath1274.52030MaRDI QIDQ2915409
Publication date: 17 September 2012
Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)
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)
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Densest geodesic ball packings to \({\mathbf S^2 \times \mathbf R}\) space groups generated by screw motions ⋮ Non-periodic geodesic ball packings generated by infinite regular prism tilings in \(\widetilde{\mathbf{SL}_2\mathbf{R}}\) space ⋮ 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 ⋮ Translation-like isoptic surfaces and angle sums of translation triangles in \(\mathbf{Nil}\) geometry ⋮ Isoptic surfaces of segments in \(\mathbf{S}^2 \times \mathbf{R}\) and \(\mathbf{H}^2 \times \mathbf{R}\) geometries ⋮ On Menelaus' and Ceva's theorems in \textbf{Nil} geometry ⋮ On lattice coverings of Nil space by congruent geodesic balls ⋮ A candidate for the densest packing with equal balls in Thurston geometries ⋮ Nil geodesic triangles and their interior angle sums ⋮ Packings by translation balls in \({\widetilde{{\mathrm {SL}}_2(\mathbb{R})}}\) ⋮ Regular prism tilings in \(\widetilde{\mathbf{SL}_2\mathbf R}\) space
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