The series of magnesium compounds RE 4 RhMg (RE = Y, La-Nd, Sm, Gd-Tm, Lu) was prepared by high-frequency melting of the elements in sealed tantalum tubes. All samples were investigated by powder X-ray diffraction. The structures with RE = Sm, Gd, Dy, Ho, and Er as rare earth metal components were refined from single crystal diffractometer data: Gd 4 RhIn-type, F4̄3m, Z = 16, a = 1392.1(1) pm, wR2 = 0.060, 616 F 2 values, 19 variables for Sm 4 RhMg, a = 1380.8(2) pm, wR2 = 0.071, 530 F 2 values, 19 variables for Gd 4 RhMg, a = 1366.9(1) pm, wR2 = 0.070, 594 F2 values, 20 variables for Dy 4 RhMg, a = 1355.7(2) pm, wR2 = 0.077, 578 F 2 values, 20 variables for Ho 3.52 RhMg 1.48 , and a = 1355.4(2) pm, wR2 = 0.075, 559 F 2 values, 20 variables for Er 3.94 RhMg 1.06 .The rhodium atoms have slightly distorted trigonal prismatic rare earth coordination. Condensation of the RhRE 6 prisms leads to a three-dimensional network which leaves large voids that are filled by regular Mg 4 tetrahedra with a Mg-Mg distance of 312 pm in Sm 4 RhMg. The magnesium atoms have twelve nearest neighbors (3 Mg + 9 RE) in icosahedral coordination. In the structures with holmium and erbium, the RE1 positions which are not involved in the trigonal prismatic network exhibit RE1/Mg mixing. Shortest distances occur for Sm-Rh (286 pm) within the rigid three-dimensional network of condensed trigonal prisms.