  For hexagonal nets, descriptive of {111} fcc surfaces, we derive from
combinatoric arguments a simple, low-temperature formula for the orientation
dependence of the surface step line tension and stiffness, as well as the
leading correction, based on the Ising model with nearest-neighbor (NN)
interactions. Our formula agrees well with experimental data for both Ag and
Cu{111} surfaces, indicating that NN-interactions alone can account for the
data in these cases (in contrast to results for Cu{001}). Experimentally
significant corollaries of the low-temperature derivation show that the step
line tension cannot be extracted from the stiffness and that with plausible
assumptions the low-temperature stiffness should have 6-fold symmetry, in
contrast to the 3-fold symmetry of the crystal shape. We examine Zia's exact
implicit solution in detail, using numerical methods for general orientations
and deriving many analytic results including explicit solutions in the two
high-symmetry directions. From these exact results we rederive our simple
result and explore subtle behavior near close-packed directions. To account for
the 3-fold symmetry in a lattice gas model, we invoke a novel
orientation-dependent trio interaction and examine its consequences.
