Traditional machine learning methods face significant challenges in predicting the properties of highly symmetric molecules. In this study, we developed a machine learning model based on graph neural networks (GNNs) to accurately and swiftly predict the thermodynamic and photochemical properties of fullerenols, such as C60(OH)n (n = 1 to 30). First, we established a global method for generating fullerenol isomers through isomer fingerprinting, which can generate all possible isomers or produce diverse structural types on demand. Significantly, by incorporating interpretable descriptors such as atomic labels, bond lengths, and bond angles from highly symmetric isomers, our multilayer GNN model achieved over 90% accuracy in predicting the thermodynamic stability of fullerenols. The model also performed excellently in predicting electronic properties, including the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and the energy gap. Overall, this work demonstrates a new strategy using interpretable descriptors for accurately predicting the properties of highly symmetric structures, offering theoretical chemists a valuable tool for studying these materials.