The S2×R geometry can be derived by the direct product of the spherical plane S2 and the real line R. In  J. Z. Farkas has classified and given the complete list its space groups. In  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 ) to determine the D-V cells to locally optimal ball packings belonging to S2×R space groups generated by glide reflections.E. Molnár has shown in , 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 visualization of the arrangement of a locally optimal geodesic ball packing and its Dirichlet-Voronoi cell of a given glide reflection space group.
Farkas J. Z. The classification of S2×R space groups. Beiträge zur Algebra und Geometrie Vol. 42, 2001. pp. 235–250.
Farkas J. Z., 'The classification of S2×R space groups' (2001) 42Beiträge zur Algebra und Geometrie: 235-250.
Farkas J. Z.The classification of S2×R space groupsBeiträge zur Algebra und Geometrie200142235250)| false
Molnár E. On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifolds. Siberian Electronic Mathematical Reports, (
), Vol. 7, 2010, pp. 491–498
Molnár E., 'On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifolds' (2010) 7Siberian Electronic Mathematical Reports: 491-498.
Molnár E.On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifoldsSiberian Electronic Mathematical Reports20107491498)| false