  Using notation inherited from the six-vertex model, we construct diagrams
that represent the action of the factorizing $F$-matrices associated to the
finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize
the tensor $R^{\sigma}_{1... n}$ corresponding with elements of the permutation
group. We consider in particular the diagram for the tensor $R^{\sigma_c}_{1...
n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic
construction of the local spin operators $S_i^{\pm}$ and $S_i^{z}$ in terms of
the monodromy matrix operators.
