Polycrystalline Li 4 MgReO 6 was prepared by means of solid-state synthesis. The crystallographic structure was determined from high-resolution powder-neutron-diffraction data. It was found that Li 4 MgReO 6 crystallizes in space group C2/m with lattice parameters, aϭ5.0978(3) Å, bϭ8.8163(5) Å, cϭ5.0815(3) Å, and ϭ109.835(2)°. This structure is an ordered variant of Li 2 SnO 3 in which Li ϩ , Mg 2ϩ , and Re 6ϩ ions occupy the Sn 4ϩ sites, which can be desribed as honeycomb layers. Due to the large differences in formal charge, the Re 6ϩ ions order on half of the Sn sites forming a distorted face-shared tetrahedral sublattice. As Re 6ϩ is an Sϭ1/2 ion this material is an attractive candidate for the study of the effects of geometric frustration on a quantum spin system. The investigation of bulk magnetic susceptibilities and magnetization studies as well as low-temperature neutron-diffraction experiments reveals a spin-glass behavior with a glass transition temperature of 12 K. Both heat-capacity and muon spin-relaxation measurements at low temperatures are consistent with a spin-glass interpretation with no long-range order detectable down to Tϭ0.5 K.