If the microscopic background of the IBA-2 model is used, a correspondence can be established between the IBA-1 and the IBA-2 model spaces. Since the space of the IBA-1 model can be regarded as a subspace of the IBA-2 model there is a unique way to "project" the operators of the IBA-2 model onto those of the IBA-1 model. This projection can be carried out by using the F-spin formalism. In the IBA-2 model, the lowest states are, indeed, fully symmetric, and in the calculations with the help of this projection, we explore the energy levels, the electric quadrupole transition probabilities B(E2;I-2 -> I-f), and the gamma-ray E2/M1 mixing ratios for selected transitions of Gd-152 similar to 156. For the first time, this projection is shown to be applicable to some heavier isotopes, and the results obtained for the Gd-152 similar to 156 isotopes are reasonably in good agreement with the previous experimental values.
