Buckminsterfullerene (C(60)) was recently confirmed as the largest molecule identified in space. However, it remains unclear how and where this molecule is formed. It is generally believed that C(60) is formed from the buildup of small carbonaceous compounds in the hot and dense envelopes of evolved stars. Analyzing infrared observations, obtained by Spitzer and Herschel, we found that C(60) is efficiently formed in the tenuous and cold environment of an interstellar cloud illuminated by strong ultraviolet (UV) radiation fields. This implies that another formation pathway, efficient at low densities, must exist. Based on recent laboratory and theoretical studies, we argue that polycyclic aromatic hydrocarbons are converted into graphene, and subsequently C(60), under UV irradiation from massive stars. This shows that alternative--top-down--routes are key to understanding the organic inventory in space.