  We consider a 3-dimensional lattice model of a network-forming fluid, which
has been recently investigated by Girardi and coworkers by means of Monte Carlo
simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of
describing water anomalies. We develop an approximate semi-analytical
calculation, based on a cluster-variation technique, which turns out to
reproduce almost quantitatively different thermodynamic properties and phase
transitions determined by the Monte Carlo method. Nevertheless, our calculation
points out the existence of two different phases characterized by long-range
orientational order, and of critical transitions between them and to a
high-temperature orientationally-disordered phase. Also, the existence of such
critical lines allows us to explain certain ``kinks'' in the isotherms and
isobars determined by the Monte Carlo analysis. The picture of the phase
diagram becomes much more complex and richer, though unfortunately less
suitable to describe real water.
