  We examine the last unexplored regime of the asymmetric six-vertex model: the
low-temperature phase of the so-called ferroelectric model. The original
publication of the exact solution, by Sutherland, Yang, and Yang, and various
derivations and reviews published afterwards, do not contain many details about
this regime. We study the exact solution for this model, by numerical and
analytical methods. In particular, we examine the behavior of the model in the
vicinity of an unusual coexistence point that we call the ``conical'' point.
This point corresponds to additional singularities in the free energy that were
not discussed in the original solution. We show analytically that in this point
many polarizations coexist, and that unusual scaling properties hold in its
vicinity.
