A neutron diffraction study on iodine heptafluoride has been performed using the high resolution powder diffractometer (HRPD) at the spallation source ISIS, England, The previously unknown structure of the low temperature phase IF7 (III) was solved. IF7 (LII) crystallizes in the orthorhombic space group Pbab (No. 54), a=852.160(4) pm, b=884.096(4) pm, c=599.089(2) pm with 4 formula units per unit cell. The IF7 molecule is found to exhibit an almost perfect pentagonal bipyramid with an axial bond length of 179.5(2) pm and an average equatorial bond length of 184.9 pm. The I(F-eq)(5) unit is slightly puckered with puckering displacements of 2.7 degrees for two of the five F-eq atoms leading to a c(2) symmetry for the molecule. Two order-disorder processes lead from the plastic phase IF7 (I) to the ordered phase IF7 (III). At the first phase transition at 150 K IF7 molecules align with respect to their F-ax-I-F-ax units. Within the second transition at 100 K they order with respect to their I(F-eq)(5) units. The latter can be grouped into two sets of five-membered rings with vertices pointing up and down the orthorhombic c axis, respectively. There is evidence suggesting a temperature dependence to this second ordering process; the amount of residual disorder is 5% at 77 K and 1.4% at 5 K.