Carbon-based nanomaterials, including fullerenes, nanotubes, and graphene, are widely utilized in various fields for their unique properties that arise from their aromatic carbon frameworks. Among them, fullerenes are polyhedral cage molecules with the general molecular formula C 20+2n (n ≥ 0, n ̸ = 1) composed of sp 2 hybridized carbons arranged in pentagon and hexagon rings. The variation in the arrangement of these rings across the fullerene cages leads to numerous isomeric structures for each fullerene size. For example, C 60 fullerene adopts 1812 non-isomorphic structures with different distributions of the 12 pentagon and 20 hexagon rings on a spherical surface. The number of possible isomers for fullerene cages with N = 20 + 2n carbon atoms increases at a rate of O(N 9 ) , creating an extensive family of fullerenes with a vast array of isomers. The unique zero-dimensional spherical cage structures of fullerenes contribute to their remarkable physical and chemical characteristics, such as high thermal and electrical conductivity, extraordinary tensile strength, and efficient electron donation and acceptance abilities. Owing to their structural diversity that offers tunable electronic properties and reactivities, fullerenes have been extensively investigated as components in optoelectronics , solar cells , gas storage and separation , biology and medicine . Although fullerenes have significant untapped potential in various applications, fully harnessing their capabilities -especially in customizing electronic properties and functionalization for practical uses -requires a thorough understanding of the structure-property relationships across the entire spectrum of fullerene varieties.