The sd-interacting boson approximation (sd-IBA) and the df-interacting boson approximation (df-IBA) can be related to each other and the states of the interacting boson approximation model can be identified with the fully symmetric states in the sdf interacting boson approximation model. A systematic study of the sdf-IBA model showed that the constructed Hamiltonian can successfully describe the strong octupole correlations in the deformed nuclei. We showed that the interacting boson approximation may account for many of these $K^{\pi} = 0^{+}$ states. It was found that the calculated energy spectra of the gadolinium isotopes agree quite well with the experimental data. The observed $B(E2)$ values were also calculated and compared with the experimental data.