The investigation of fundamental properties across different fullerene isomers has been the focus of numerous earlier studies. For example, Rebecca et al. investigated the relative energy distribution among the 1812 isomers of C 60 fullerene with DFT method and correlated the isomeric stability with a variety of topological indices, electronic, and geometric properties. Aside from the common isolated pentagon rule (IPR), they proposed that a small pentagon signature P 1 , a large volume, and a more spherical cage can lead to a relatively stable isomer. Zhao et al. explored the origin and characteristics of isomeric stability in four fullerene systems, C 44 , C 48 , C 52 , and C 60 , using DFT simulations. Through energy decomposition analysis, they found that electrostatic potential is the primary determinant of isomeric stability, surpassing other factors such as steric and quantum effects. They further highlighted the importance of spatial delocalization of the electron density on the stabilization of fullerene isomers. Chan and Karton studied the size dependence of a variety of electronic properties in small fullerenes from C 20 to C 50 with 812 isomeric structures, including the energy difference between the lowest-energy singlet and triplet states (i.e., S 0 and T 1 , or T 0 and S 1 ), and the related quantities of ionization potential (IP) and electron affinity (EA). They found a linear correlation between triplet-singlet energy difference and IP-EA difference, and further surveyed larger fullerenes in search of candidates with superior charge-transfer properties. Based on our comprehensive literature review, we observed that the previous research into the structure-property relationships of fullerenes has been grounded in selected datasets that represent an incomplete array of fullerene isomers, with the bulk of these studies primarily focusing on stability analysis. To the best of our knowledge, there remains a gap in literature for a comprehensive and accurate examination of the fundamental properties of all fullerene isomers from C 20 to C 60 .