Integrable Hamiltonians with D(D_n) symmetry from the Fateev-Zamolodchikov model

A special case of the Fateev-Zamolodchikov model is studied resulting in a solution of the Yang-Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a dihedral group. Viewing this solution as a descendant of the zero-field six-vertex model allows for the construction of functional relations and Bethe ansatz equations.