High-resolution powder neutron diffraction has been used to study the crystal structure of the fullerence C₆₀ in the temperature range 5 K to 320 K. Solid C₆₀ adopts a cubic structure at all temperatures. The experimental data provide clear evidence of a continuous phase transition at ca. 90 K and confirm the existence of a first-order phase transition at 260 K. In the high-temperature face-centred-cubic phase (T > 260 K), the C₆₀ molecules are completely orientationally disordered, undergoing continuous reorientation. Below 260 K, interpretation of the diffraction data is consistent with uniaxial jump reorientation principally about a single ⟨111⟩ direction. In the lowest-temperature phase (T < 90 K), rotational motion is frozen although a small amount of static disorder still persists.