Rhenium heptafluoride, ReF7, is one of only two stable binary compounds MX(7) with a heptacoordinated metal atom M and halide atom X. Its low-temperature crystal structure, as determined by high-resolution powder neutron diffraction, reveals the molecular structure, which has been the subject of speculation and debate for many years. Here it is shown within experimental error that at 1.5 kelvin the lowest energy configuration of ReF7 has symmetry C-s(m) and is a distorted pentagonal bipyramid. The deviation of the two axial Re-F bonds from collinear and the puckering of the ring of equatorial fluorine atoms are similar to what has been postulated as one of the conformations of the pseudorotational motion observed at higher temperatures.