In the search for efficient building blocks for nonlinear metamaterials, plasmonic nanoparticles have received considerable attention. Their quadratic nonlinear optical properties result from a complex interplay between the nature of the bulk material, the object shape, surface defects and retardation effects. This versatility can be used to tailor the properties of the resulting material. However, despite extensive investigation, separating and controlling these contributions is still a challenge. In this report, we control the morphology ofexplore the second harmonic scattering response from colloidal gold nanoparticles with tetrahedral symmetry and explore their second harmonic scattering response. The material itself is centrosymmetric but not the shape, conferring to the first hyperpolarizability an almost purely octupolar symmetry. Gradually reshaping the nanoparticles into spheres (and thus decreasing their asymmetry) reduces their nonlinear response, showing that it is is controlled by the morphology.