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The generation in artificial composites of a magnetic response to light, comparable in magnitude with the natural electric response, may offer an invaluable control parameter for a fine steering of light at the nanoscale. In many experimental realizations, however, the magnetic response of artificial meta-atoms is too weak so that there is a need for new designs with increased magnetic polarizability. Numerical simulations show that geometrical plasmonic nanostructures based on Platonic solids are excellent candidates for the production of strong optical magnetism in visible light. Inspired by these models, we report a bottom-up approach to synthesize plasmonic nanoclusters made of 12 gold patches located at the center of the faces of a dodecahedron. The scattering of the electric and magnetic dipole induced by light is measured across the whole visible range. The ratio of the magnetic to electric response at resonance is found three times higher than its counterpart measured on disordered plasmonic clusters (“plasmonic raspberries”) of the same size. Numerical simulations confirm the experimental measurements of the magnetic response.