A construction of solutions to reflection equations for interaction-round-a-face models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency 1. Among such models are the Andrews - Baxter - Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions