Ba 2 YReO 6 is a double perovskite material where the Re 5+ (d 2 ) ions occupy a frustrated face-centered cubic lattice. Despite strong antiferromagnetic interactions between the Re ions, as indicated by a large negative Weiss constant θ = −616 K, spin freezing in Ba 2 YReO 6 only occurs at 45 K. Since no long-range order of magnetic dipoles has previously been found in either muon spin rotation or neutron diffraction experiments below this temperature, it has been assumed that the low-temperature state is a spin glass. In stark contrast with these findings, we here show that Ba 2 YReO 6 does in fact order with a strongly reduced dipole moment μ 0 = 0.29-0.42 μ B via a polarized neutron diffraction experiment on a powder sample. Using the symmetries of the two likeliest magnetic structures and the properties of the 5d 2 configuration in the presence of strong spin-orbit coupling and strong crystal fields, we use a recently derived single-ion wave function for Re 5+ to predict a large quadrupolar moment based on the experimental μ o .