  We obtain compact orientable embedded surfaces with constant mean curvature
$0<H<\frac{1}{2}$ and arbitrary genus in $\mathbb{S}^2\times\mathbb{R}$. These
surfaces have dihedral symmetry and desingularize a pair of spheres with mean
curvature $\frac{1}{2}$ tangent along an equator. This is a particular case of
a conjugate Plateau construction of doubly periodic surfaces with constant mean
curvature in $\mathbb{S}^2\times\mathbb{R}$, $\mathbb{H}^2\times\mathbb{R}$,
and $\mathbb{R}^3$ with bounded height and enjoying the symmetries of certain
tessellations of $\mathbb{S}^2$, $\mathbb{H}^2$, and $\mathbb{R}^2$ by regular
polygons.
