  A mean field theory is developed for the calculation of the surface free
energy of the staggered BCSOS, (or six vertex) model as function of the surface
orientation and of temperature. The model approximately describes surfaces of
crystals with nearest neighbor attractions and next nearest neighbor
repulsions. The mean field free energy is calculated by expressing the model in
terms of interacting directed walks on a lattice. The resulting equilibrium
shape is very rich with facet boundaries and boundaries between reconstructed
and unreconstructed regions which can be either sharp (first order) or smooth
(continuous). In addition there are tricritical points where a smooth boundary
changes into a sharp one and triple points where three sharp boundaries meet.
Finally our numerical results strongly suggest the existence of conical points,
at which tangent planes of a finite range of orientations all intersect each
other. The thermal evolution of the equilibrium shape in this model shows
strong similarity to that seen experimentally for ionic crystals.
