Geodesic ball packings in \(S^{2} \times R\) space for generalized Coxeter space groups (Q717839)

The authors study the geodesic balls in \({\mathbb S}^2 \times {\mathbb R}\), compute their volume and introduce in this space the notion of geodesic ball packing and its density. It is shown that the densest packing for generalized Coxeter space groups in \({\mathbb S}^2 \times {\mathbb R}\) has the density \(0.82445423\dots\) and the kissing number \(2\). The paper is very nicely written and provides many helpful examples.