In the framework of the sdg-interacting boson model (sdg-IBM1), we study the nuclear structure of Os isotopes. Recent calculations of E2 and E4 transitions in the Os isotopes that can not be clarified in the sd-boson models need this extension. We illustrate how gamma-unstable and triaxial shapes arise from special Hamiltonian sdg- model choices and explore ways to restrict the number of free parameters through conditions of consistency and coherence. Os nuclei, a satisfactory explanation of E2 and E4 properties is obtained, which also predicts complex shape transitions in these isotopes.In summary, a coherent overview of the E2 and E4 properties in the Os using a restricted set of parameters, isotopes were obtained. The problems with the transitions of quadrupole moments, yrast E2 and E4, which cannot be clarified in the sd-models, have been resolved satisfactorily. The complex shape transitions that could be checked with the new 4 -detector systems "Euroball" and "Gamma-Sphere" are an important prediction of the current calculations.