  We treat here interaction round the face (IRF) solvable lattice models. We
study the algebraic structures underlining such models. For the three block
case, we show that the Yang Baxter equation is obeyed, if and only if, the
Birman--Murakami--Wenzl (BMW) algebra is obeyed. We prove this by an algebraic
expansion of the Yang Baxter equation (YBE). For four blocks IRF models, we
show that the BMW algebra is also obeyed, apart from the skein relation, which
is different. This indicates that the BMW algebra is a sub--algebra for all
models with three or more blocks. We find additional relations for the four
block algebra using the expansion of the YBE. The four blocks result, that is
the BMW algebra and the four blocks skein relation, is enough to define new
knot invariant, which depends on three arbitrary parameters, important in knot
theory.
