The familiarity of water ice means we often overlook its non-trivial character illustrated, for example, by the many snowflake morphologies resulting from disordered combinations of covalent and hydrogen bonds between hydrogen and oxygen atoms in water ice’s most common phase (Ih) that keep the H_2 O molecular character. Using neutron diffraction on the flat-cone diffractometer E2 at BER-II, Helmholtz-Zentrum Berlin, we probe the atomic scale configuration in the Ih phase of water ice to test theories that describe this “disordered” state as exhibiting a form of topological order characterized by an emergent gauge field. We find excellent agreement between low-temperature experiment and analytical theory, which even allows us to estimate the density of defects charged under this emergent gauge field. The development of quantitative models of water ice paves the way for further studies to develop a comprehensive atomic-scale understanding of this most commonplace of solids. The merged untransformed datasets from the flat-cone diffractometer E2 at the neutron source BER II is given in the Nexus/HDF5 file format. The calculated reciprocal space and the simulation are stored as HDF5 files.