Densest geodesic ball packings to S² × R space groups generated by screw motions

2014/05/19 by Schultz, Benedek, Szirmai, Jenő
#51M20 #52C17 #52C22 #53A35 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1405.5441

Abstract

In this paper we study the locally optimal geodesic ball packings with equal balls to the S² × 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 S² × R space group 3qe.~I.~3 with packing density ≈ 0.7278. E. Molnár has shown, that the Thurston geometries have an unified interpretation in the real projective 3-sphere PS³. In our work we shall use this projective model of S² × R geometry.

Related

• New lower bound for the optimal congruent geodesic ball packing density of screw motion groups in H² × R space
• Geodesic ball packings generated by rotations and monotonicity behavior of their densities in H² × R space
• Simply transitive geodesic ball packings to S² × R space groups generated by glide reflections
• A candidate to the densest packing with equal balls in the Thurston\n geometries
• Volumes and geodesic ball packings to the regular prism tilings in \widetildeSL₂R space