In this study, we have compiled the most extensive computational dataset of C 20 -C 60 fullerenes to date, incorporating a total of 5770 structures. Following our benchmark study, we calculated 12 fundamental properties with DFT-level accuracy, e.g., fullerene binding energy (E b ), HOMO-LUMO gap (E g ), and partition coefficient of solvation free energies in 1,2-dichlorobenzene (ODCB) and water phases as listed in Table , and evaluated their Pearson correlation coefficients. The weak correlations between E g and both E b and logP suggest that favorable electronic properties can be independently adjusted for particular applications without compromising the stability and solubility. To delve deeper into the structural features influencing these properties, we introduced various topological indices and geometric measures, going beyond the IPR. For the first time, we reveal that compared to pentagon-related features, atom, bond, and hexagon features demonstrate significantly superior effectiveness in capturing the intricate local structural environments of the carbon atoms on the spherical cage. The linear models fitted by those features enable precise predictions of the fullerene stability across various sizes and show robust transferability to largersize fullerenes beyond C 60 . We further offer a practical guide for researchers interested in screening fullerenes for optimal electron acceptor candidates in organic solar cells. Our study provides a deep understanding of the structure-property relationships across fullerene isomers, setting a foundation for future advancements in fullerene functionalization and applications in energy conversion and nanosciences.