The discovery of the C \(_{60}\) fullerene opened new horizons to design carbon nanostructures with targeted electronic structure as well as transport and optical properties. For example, endohedral \(^{12}\) C \(_{60}\) molecules were proposed as candidates for functional quantum architectures to store and manipulate encased atomic and molecular qubits. Recent advances in cryogenic buffer-gas cooling and frequency-comb spectroscopy have enabled rovibrational quantum-state-resolved measurements of gas-phase \(^{12}\) C \(_{60}\) , revealing rotational fine structure reflecting its high icosahedral symmetry. Here, we present a perturbative quantum description of the \(^{12}\) C \(_{60}\) molecule interacting with a buffer gas of \(^{40}\) Ar atoms at temperatures of order 150 K, including a detailed analysis of their electronic structure, their interaction anisotropies, and the collision-induced rotational quenching of \(^{12}\) C \(_{60}\) in its vibrational and electronic ground state. The role of the icosahedral symmetry on the collisional dynamics is emphasized leading to a complex dependence on the \(^{12}\) C \(_{60}\) rotational quantum number. Finally, we compute the isotropic and anisotropic static and dynamic dipole polarizability of \(^{12}\) C \(_{60}\) in its absolute ground state in order to evaluate the long-range, van der Waals interaction between \(^{12}\) C \(_{60}\) and \(^{40}\) Ar.
