Octacalcium phosphate (OCP, Ca8(PO4)4(HPO4)2.5H2O) is a notable calcium phosphate due to its biocompatibility, making it a widely studied material for bone substitution. It is known to be a precursor of bone mineral, but its role in biomineralisation remains unclear. While the structure of OCP has been the subject of thorough investigations (including using Rietveld refinements of X-ray diffraction data, and NMR crystallography studies), important questions regarding the symmetry and H-bonding network in the material remain. In this study, it is shown that OCP undergoes a lowering of symmetry below 200 K, evidenced by 1H, 17O, 31P and 43Ca solid state NMR experiments. Using ab-initio molecular dynamics (MD) simulations and Gauge Including Projected Augmented Wave (GIPAW) DFT calculations of NMR parameters, the presence of rapid motions of the water molecules in the crystal cell at room temperature is proved. This information leads to an improved description of the OCP structure at both low and ambient temperatures, and helps explain long-standing issues of symmetry. Remaining challenges related to the understanding of the structure of OCP are then discussed.