The isolation and structural characterization of three new monometallic uranium metallofullerenes, U@D-2(21)-C-84, U@C-s(15)-C-86, and U@C-1(11)-C-86, allowed us to complete an interconversion map for all the characterized uranium mono-metallofullerenes. The topological analysis reveals that asymmetric fullerene cages, which may be formed by roll and wrap processes directly from graphene, are the starting points for a series of highly symmetric fullerene structures via top-down and bottom-up growth mechanisms. Moreover, some asymmetric intermediates, such as C-1(28324)-C-80, can serve as precursors to form either larger cages in consecutive growing processes or smaller cages during cascade shrinking processes. This work provides evidence for both top-down and bottom-up processes happening simultaneously during the arcing processes. This study also sheds light on the prediction of possible cage structures for minor products produced in low yields in the soot.