MgCu2(RhS2)4 crystallizes in the trigonal R-3m space group. Mg(1) is bonded to two equivalent Cu(1) and six equivalent S(1) atoms to form distorted MgCu2S6 hexagonal bipyramids that share corners with six equivalent Rh(2)S6 octahedra, corners with six equivalent S(1)MgCuRh3 square pyramids, corners with two equivalent S(2)CuRh3 trigonal pyramids, and edges with six equivalent Rh(1)S6 octahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to two equivalent S(2) and four equivalent S(1) atoms to form RhS6 octahedra that share edges with two equivalent Mg(1)Cu2S6 hexagonal bipyramids, edges with two equivalent Rh(2)S6 octahedra, and edges with four equivalent Rh(1)S6 octahedra. In the second Rh site, Rh(2) is bonded to six equivalent S(1) atoms to form RhS6 octahedra that share corners with six equivalent Mg(1)Cu2S6 hexagonal bipyramids and edges with six equivalent Rh(1)S6 octahedra. Cu(1) is bonded in a 5-coordinate geometry to one Mg(1), one S(2), and three equivalent S(1) atoms. There are two inequivalent S sites. In the first S site, S(1) is bonded to one Mg(1), one Rh(2), two equivalent Rh(1), and one Cu(1) atom to form SMgCuRh3 square pyramids that share  a cornercorner with one Mg(1)Cu2S6 hexagonal bipyramid, corners with six equivalent S(1)MgCuRh3 square pyramids, corners with three equivalent S(2)CuRh3 trigonal pyramids, edges with six equivalent S(1)MgCuRh3 square pyramids, and  an edgeedge with one S(2)CuRh3 trigonal pyramid. In the second S site, S(2) is bonded to three equivalent Rh(1) and one Cu(1) atom to form distorted SCuRh3 trigonal pyramids that share  a cornercorner with one Mg(1)Cu2S6 hexagonal bipyramid, corners with nine equivalent S(1)MgCuRh3 square pyramids, corners with three equivalent S(2)CuRh3 trigonal pyramids, and edges with three equivalent S(1)MgCuRh3 square pyramids.
MgCu2(RhS2)4 crystallizes in the trigonal R-3m space group. Mg(1) is bonded to two equivalent Cu(1) and six equivalent S(1) atoms to form distorted MgCu2S6 hexagonal bipyramids that share corners with six equivalent Rh(2)S6 octahedra, corners with six equivalent S(1)MgCuRh3 square pyramids, corners with two equivalent S(2)CuRh3 trigonal pyramids, and edges with six equivalent Rh(1)S6 octahedra. The corner-sharing octahedral tilt angles are 7°. Both Mg(1)-Cu(1) bond lengths are 2.51 Å. All Mg(1)-S(1) bond lengths are 2.62 Å. There are two inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to two equivalent S(2) and four equivalent S(1) atoms to form RhS6 octahedra that share edges with two equivalent Mg(1)Cu2S6 hexagonal bipyramids, edges with two equivalent Rh(2)S6 octahedra, and edges with four equivalent Rh(1)S6 octahedra. Both Rh(1)-S(2) bond lengths are 2.37 Å. All Rh(1)-S(1) bond lengths are 2.41 Å. In the second Rh site, Rh(2) is bonded to six equivalent S(1) atoms to form RhS6 octahedra that share corners with six equivalent Mg(1)Cu2S6 hexagonal bipyramids and edges with six equivalent Rh(1)S6 octahedra. All Rh(2)-S(1) bond lengths are 2.41 Å. Cu(1) is bonded in a 5-coordinate geometry to one Mg(1), one S(2), and three equivalent S(1) atoms. The Cu(1)-S(2) bond length is 2.22 Å. All Cu(1)-S(1) bond lengths are 2.45 Å. There are two inequivalent S sites. In the first S site, S(1) is bonded to one Mg(1), one Rh(2), two equivalent Rh(1), and one Cu(1) atom to form SMgCuRh3 square pyramids that share  a cornercorner with one Mg(1)Cu2S6 hexagonal bipyramid, corners with six equivalent S(1)MgCuRh3 square pyramids, corners with three equivalent S(2)CuRh3 trigonal pyramids, edges with six equivalent S(1)MgCuRh3 square pyramids, and  an edgeedge with one S(2)CuRh3 trigonal pyramid. In the second S site, S(2) is bonded to three equivalent Rh(1) and one Cu(1) atom to form distorted SCuRh3 trigonal pyramids that share  a cornercorner with one Mg(1)Cu2S6 hexagonal bipyramid, corners with nine equivalent S(1)MgCuRh3 square pyramids, corners with three equivalent S(2)CuRh3 trigonal pyramids, and edges with three equivalent S(1)MgCuRh3 square pyramids.