The design and chemical synthesis of plasmonic nanoresonators exhibiting a strong magnetic response in the visible is a key requirement to the realization of efficient functional and self-assembled metamaterials. However, novel applications like Huygens' metasurfaces or mu-near-zero materials require stronger magnetic responses than those currently reported. Our numerical simulations demonstrate that the specific dodecahedral morphology, whereby 12 silver satellites are located on the faces of a nanosized dielectric dodecahedron, provides sufficiently large electric and magnetic dipolar and quadrupolar responses that interfere to produce so-called generalized Huygens' sources, fulfilling the generalized Kerker condition. Using a multistep colloidal engineering approach, we synthesize highly symmetric plasmonic nanoclusters with a controlled silver satellite size and show that they exhibit a strong forward scattering that may be used in various applications such as metasurfaces or perfect absorbers.