Curvature prevalently exists in the world of carbon materials (e.g., fullerenes, buckyl bowls, carbon nanotubes, and onions), but traditional C2-addition mechanisms fail to elucidate the mechanism responsible for the formation of carbon curvature starting from a pentagonal carbon ring in currently available chemical-physical processes such as combustion. Here, we show a complete series of nascent pentagon-incorporating C5–C18 that are online produced in the flame of acetylene–cyclopentadiene–oxygen and in situ captured by C60 or trapped as polycyclic aromatic hydrocarbons for clarifying the growth of the curved subunit of C20H10. A mechanism regarding C1-substitution and C2-addition has been proposed for understanding the formation of curvature in carbon materials, as exemplified by the typical curved molecule containing a single pentagon completely surrounded by five hexagons. The present mechanism, supported by the intermediates characterized by X-ray crystallography as well as NMR, has been experimentally validated for the rational synthesis of curved molecule in the commercially useful combustion process.