Fullerenes (C60, C70) detected in planetary nebulae and carbonaceous chondrites have been implicated to play a key role in the astrochemical evolution of the interstellar medium. However, the formation mechanism of even their simplest molecular building block-the corannulene molecule (C20H10)-has remained elusive. Here we demonstrate via a combined molecular beams and ab initio investigation that corannulene can be synthesized in the gas phase through the reactions of 7-fluoranthenyl (C16H9˙) and benzo[ghi]fluoranthen-5-yl (C18H9˙) radicals with acetylene (C2H2) mimicking conditions in carbon-rich circumstellar envelopes. This reaction sequence reveals a reaction class in which a polycyclic aromatic hydrocarbon (PAH) radical undergoes ring expansion while simultaneously forming an out-of-plane carbon backbone central to 3D nanostructures such as buckybowls and buckyballs. These fundamental reaction mechanisms are critical in facilitating an intimate understanding of the origin and evolution of the molecular universe and, in particular, of carbon in our galaxy.