Self-assembly of twelve pentatopic tectons, which have complementary edges or can be linked using either digonal or trigonal connectors, represents the optimal synthetic strategy to achieve spherical objects, such as chemical capsids. This process requires conditions that secure uninterrupted equilibria of binding and self-correction en route to the global energy minimum. Here we report the synthesis of a highly soluble, deca-heterosubstituted corannulene that bears five terpyridine ligands. Spontaneous self-assembly of twelve such tectons with 30 cadmium(II) cations produces a giant icosahedral capsid as a thermodynamically stable single product in high yield. Nuclear magnetic resonance (NMR) methods, mass spectrometry analyses, small-angle X-ray scattering, transmission electron microscopy, and atomic force microscopy indicate that this spherical capsid has an external diameter of nearly 6 nm and shell thickness of 1 nm, in agreement with molecular modeling. NMR and liquid chromatography evidences imply that chiral self-sorting complexation generates a racemic mixture of homochiral capsids.