Although fullerenes were discovered nearly three decades ago, the mechanism of their formation remains a mystery. Many versions of the classic 'bottom-up' formation mechanism have been advanced, starting with C2 units that build up to form chains and rings of carbon atoms and ultimately form those well-known isolated fullerenes (for example, I(h)-C60). In recent years, evidence from laboratory and interstellar observations has emerged to suggest a 'top-down' mechanism, whereby small isolated fullerenes are formed via shrinkage of giant fullerenes generated from graphene sheets. Here, we present molecular structural evidence for this top-down mechanism based on metal carbide metallofullerenes M2C2@C1(51383)-C84 (M = Y, Gd). We propose that the unique asymmetric C1(51383)-C84 cage with destabilizing fused pentagons is a preserved 'missing link' in the top-down mechanism, and in well-established rearrangement steps can form many well-known, high-symmetry fullerene structures that account for the majority of solvent-extractable metallofullerenes.