The crystal structure of superconducting Na2CsC60 was studied by high-resolution powder neutron diffraction between 1.6 and 425 K. Contrary to the literature, the structure at low temperatures is primitive cubic (Pa (3) over bar), isostructural with pristine C-60. Anticlockwise rotation of the C-60 units by 98 degrees about [111] allows simultaneous optimization of C-60-C-60 and alkali-fulleride interactions. Optimal Na+-C-60(3-) coordination is achieved with each sodium ion located above one hexagon face and three hexagon-hexagon fusions of neighboring fulleride ions (coordination number 12). Reduction of the C-60 molecule lengthens the hexagon-hexagon fusions and shortens the pentagon-hexagon fusions (to similar to 1.43 angstroms). On heating, Na2CsC60 undergoes a phase transition to a face-centered-cubic Fm (3) over bar m phase, best modeled as containing quasi-spherical C-60(3-) ions. The modified structure and intermolecular potential provide an additional dimension to the behavior of superconducting fullerides and should sensitively affect their electronic and conducting properties.