The local structure of the low-temperature ordered phase of the negative thermal expansion (NTE) material has been investigated by reverse Monte Carlo (RMC) modeling of neutron total scattering data. We obtain, for the first time, quantitative measurements of the extent to which the and polyhedra move as rigid units, and we show that these values are consistent with the predictions of rigid unit mode theory. We suggest that rigid unit modes are associated with the NTE. Our results do not support a recent interpretation of x-ray-absorption fine structure spectroscopy data in terms of a larger rigid structural component involving the Zr-O-W linkage.