Even after significant advances in the structural characterization of quasicrystals-phases whose diffraction patterns combine the sharp peaks normally associated with lattice periodicity and rotational symmetries antithetical to such periodicity this new form of long-range order remains enigmatic. Here, we present DFT-chemical pressure calculations on the Tsai-type quasicrystal approximant CaCd6, which reveal how its icosahedral clusters can be traced to simple CaCu5-type (hP6) intermetallics. The results indicate that the Tsai-type clusters emerge from an atomic-size-driven transformation from planar arrangements to spherical clusters, recalling the relationship between graphene and C-60.