Visualization of the Dirichlet-Voronoi cells in S2×R space

Abstract

The S2×R geometry can be derived by the direct product of the spherical plane S2 and the real line R. In [1] J. Z. Farkas has classified and given the complete list its space groups. In [6] the second author has studied the geodesic balls and their volumes in S2×R space, moreover he has introduced the notion of geodesic ball packing and its density and have determined the densest geodesic ball packing for generalized Coxeter space groups of S2×R.The aim of this paper to develop a method to study and visualize the Dirichlet-Voronoi cells belonging to a given ball packing. We apply our former results on the equidistant surfaces of the S2×R geometry (see [5]) to determine the D-V cells to locally optimal ball packings belonging to S2×R space groups generated by glide reflections.E. Molnar has shown in [3], that the homogeneous 3-spaces have a unified interpretation in the real projective 3-sphere, in our work we will use this projective model of S2×R geometry. We will use the Wolfram Mathematica software for...