The crystal structure of sulphur hexafluoride in its low temperature phase has been solved from neutron powder diffraction measurements. At both 23 K and 85 K the structure is triclinic, space groupP1, withZ= 3. It is in good agreement with the structure predicted previously by molecular dynamics simulations. No evidence was found for the existence of an hexagonal phase. The phase transition is interpreted in terms of two separate lattice distortions from the cubic, high temperature phase which couple to different stages of orientational ordering. The mechanism driving the transition is the resolution of orientational frustration as the temperature is reduced. The present results confirm the validity of the simple intermolecular force model employed in the simulations for SF6and they have been used to improve the parameters of this model.