In contrast to E b , E g displays no correlation with all the geometric measures collected in this study, yielding R 2 values below 0.1 (Table and Figure ). Importantly, this low correlation is independent of the cage size of fullerenes (see Table and Figure ). Additionally, we calculated the R 2 values for logP. As shown in Table and Figure , across the entire C 20 -C 60 fullerene database, both V and A exhibit strong correlations with logP values of fullerenes, yielding R 2 values of 0.977 and 0.995, respectively. Given that the V and A of a fullerene cage depend on its size, these findings align with our earlier discussion that logP strongly correlates with fullerene cage size. Interestingly, the R 2 values of both V versus logP and A versus logP for 1812 C 60 isomers significantly decrease to 0.32, and 0.064 as presented in Table and Figure , suggesting that V and A are inadequate to differentiate the solubility of fullerenes with identical size. κ and A/V ratio also exhibit high correlates with logP values, resulting in R 2 values of 0.919 and 0.85 for C 20 -C 60 , respectively (see Figure )). The observed similarity in the distributions of logP when plotted against κ and the A/V ratio suggests a strong correlation between A/V and κ. In fact, A/V = 3κ for a perfect sphere.