The dynamics of the carbon nuclei in the C-60 molecule have been studied by Feynman path-integral (PI) quantum Monte Carlo (QMC) simulations and within a harmonic oscillator approximation, The following finite-temperature properties have been calculated : kinetic, potential, and total energy, radial and angular distribution functions (rdf, adf) as well. as parameters describing the degree of atomic de/localization. D-t measures the overall spatial atomic fluctuations, D-q the associated quantum, and D-c the classical (= thermal) contributions. PI simulations render possible the derivation of the quantum delocalization DPqPI. At T = 0 K this quantity measures the amplitude of the zero-point vibrations which correspond to the spatial uncertainty of the atoms according to the Heisenberg uncertainty principle. Comparison of results derived by quantum simulations and classical ones demonstrates the importance of quantum effects in the whole temperature range below room temperature. The possible influence of quantum fluctuations on microscopic electronic structure properties of superconducting fullerides is briefly mentioned. PI simulations as well as simple analytical results show that the spatial uncertainty of the C atoms in C-60 is comparable to the difference between the lengths of the short and long CC bonds in the icosahedral molecule. Consequences of such large zero-point motions over a large temperature interval for the microscopic interpretation of diffraction data are concisely summarized. Reliable agreement between the PI-derived rdf and the experimental curve based on neutron diffraction data is observed. The interaction between the C atoms has been modeled by the potential of Tersoff which has been developed to reproduce several properties of fullerenes such as binding energy and geometrical parameters.