Abstract
We construct ball packings of the universal cover of \({{\rm{SL}}_{2}({\mathbb{R}})}\) by geodesic balls and translation balls. The packings are generated by action of the prism groups \({{\mathbf{pq}}_{k}{\mathbf{o}}_{\ell}}\). We obtain volume formulae for calculations in geographical coordinates. Using these formulae we find numerically the maximal dense packings for cases \({k=1}\), \({o=2}\), \({\ell=1}\) and small values of \({p}\) and \({q}\).
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A. Vesnin was supported in part by the Laboratory of Quantum Topology, Chelyabinsk State University (contract no. 14.Z50.31.0020), the Ministry of Education and Science of the Russia (the state task number 1.1260.2014/K) and RFBR (Grant number 16-01-00414).
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Molnár, E., Szirmai, J. & Vesnin, A. Geodesic and Translation Ball Packings Generated by Prismatic Tessellations of the Universal Cover of \({{\rm {SL}}_{2}({\mathbb{R}})}\) . Results Math 71, 623–642 (2017). https://doi.org/10.1007/s00025-016-0542-y
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DOI: https://doi.org/10.1007/s00025-016-0542-y