  The $S^2 \times R$ geometry can be derived by the direct product of the
spherical plane $\bS^2$ and the real line $\bR$. J. Z. Farkas has classified
and given the complete list of the space groups of $S^2 \times R$. The $S^2
\times R$ manifolds were classified by E. Moln\'ar and J. Z. Farkas by
similarity and diffeomorphism. In Szirmai we have studied the geodesic balls
and their volumes in $S^2 \times R$ space, moreover we have introduced the
notion of geodesic ball packing and its density and have determined the densest
geodesic ball packing for generalized Coxeter space groups of $S^2 \times R$.
  In this paper we study the locally optimal ball packings to the $S^2 \times
R$ space groups having Coxeter point groups and at least one of the generators
is a glide reflection. We determine the densest simply transitive geodesic ball
arrangements for the above space groups, moreover we compute their optimal
densities and radii.
  The density of the densest packing is $\approx 0.80407553$, may be surprising
enough in comparison with the Euclidean result $\frac{\pi}{\sqrt{18}} \approx
0.74048$. E. Moln\'ar has shown, that the homogeneous 3-spaces have a unified
interpretation in the real projective 3-sphere $\mathcal{PS}^3(\bV^4,\BV_4,
\mathbb{R})$. In our work we shall use this projective model of $S^2 \times R$
geometry.

Metric Geometry;Group Theory