  In this paper we compute the most general nondiagonal reflection matrices of
the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter
equations. We find new one-parameter family of reflection matrices for the RSOS
model in addition to the previous result without any parameter. We also find
three classes of reflection matrices for the SOS model, which has one or two
parameters. For the hard hexagon model which can be mapped to RSOS(5) model by
folding four RSOS heights into two, the solutions can be obtained similarly
with a main difference in the boundary unitarity conditions. Due to this, the
reflection matrices can have two free parameters. We show that these extra
terms can be identified with the `decorated' solutions. We also generalize the
hard hexagon model by `folding' the RSOS heights of the general RSOS(p) model
and show that they satisfy the integrability conditions such as the Yang-
Baxter and boundary Yang-Baxter equations. These models can be solved using the
results for the RSOS models.
