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Densest Geodesic Ball Packings to S 2 × R space groups generated by screw motions

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Abstract

In this paper we study the locally optimal geodesic ball packings with equal balls to the S 2 × R space groups having rotation point groups and their generators are screw motions. We determine and visualize the densest simply transitive geodesic ball arrangements for the above space groups; moreover, we compute their optimal densities and radii. The densest packing is derived from the S 2 × R space group 3qe. I. 3 with packing density ≈0.7278. E. Molnár has shown in [9] that the Thurston geometries have an unified interpretation in the real projective 3-sphere \({\mathcal{PS}^3}\). In our work we shall use this projective model of S 2 × R geometry.

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Authors and Affiliations

  1. Department of Geometry, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, P.O. Box 91, 1521, Hungary

    Benedek Schultz & Jenő Szirmai

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  1. Benedek Schultz
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  2. Jenő Szirmai
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Correspondence to Benedek Schultz.

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Schultz, B., Szirmai, J. Densest Geodesic Ball Packings to S 2 × R space groups generated by screw motions. Mediterr. J. Math. 13, 775–788 (2016). https://doi.org/10.1007/s00009-014-0513-z

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  • DOI: https://doi.org/10.1007/s00009-014-0513-z

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