  We study the geometry and the period map of nodal complex prime Fano
threefolds with index 1 and degree 10. We show that these threefolds are
birationally isomorphic to Verra solids (hypersurfaces of bidegree $(2,2)$ in $
\P^2\times \P^2$). Using Verra's results on the period map for these solids and
on the Prym map for double \'etale covers of plane sextic curves, we prove that
the fiber of the period map for our nodal threefolds is birationally the union
of two surfaces, for which we give several descriptions. This result is the
analog in the nodal case of a result obtained in arXiv:0812.3670 for the smooth
case.
