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Mediterranean Journal of Mathematics

, Volume 13, Issue 2, pp 775–788 | Cite as

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

  • Benedek Schultz
  • Jenő Szirmai
Article
  • 45 Downloads

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.

Mathematics Subject Classification

52C17 52C22 53A35 51M20 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Geometry, Institute of MathematicsBudapest University of Technology and EconomicsBudapestHungary

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