MgVRhO4 crystallizes in the monoclinic P2/m space group. Mg(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form MgO6 octahedra that share corners with four equivalent Rh(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent V(1)O6 octahedra, and faces with two equivalent Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 46°. V(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form VO6 octahedra that share corners with eight equivalent Rh(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-49°. Rh(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form distorted RhO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra, corners with eight equivalent V(1)O6 octahedra, edges with two equivalent Rh(1)O6 octahedra, and faces with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-49°. There are two inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one V(1), and two equivalent Rh(1) atoms to form distorted OMg2VRh2 square pyramids that share corners with five equivalent O(1)Mg2VRh2 square pyramids, corners with four equivalent O(2)MgV2Rh trigonal pyramids, edges with four equivalent O(1)Mg2VRh2 square pyramids, and edges with four equivalent O(2)MgV2Rh trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent V(1), and one Rh(1) atom to form distorted OMgV2Rh trigonal pyramids that share corners with four equivalent O(1)Mg2VRh2 square pyramids, corners with six equivalent O(2)MgV2Rh trigonal pyramids, edges with four equivalent O(1)Mg2VRh2 square pyramids, and  an edgeedge with one O(2)MgV2Rh trigonal pyramid.
MgVRhO4 crystallizes in the monoclinic P2/m space group. Mg(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form MgO6 octahedra that share corners with four equivalent Rh(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent V(1)O6 octahedra, and faces with two equivalent Rh(1)O6 octahedra. The corner-sharing octahedral tilt angles are 46°. Both Mg(1)-O(2) bond lengths are 1.97 Å. All Mg(1)-O(1) bond lengths are 2.11 Å. V(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form VO6 octahedra that share corners with eight equivalent Rh(1)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-49°. Both V(1)-O(1) bond lengths are 2.12 Å. All V(1)-O(2) bond lengths are 2.00 Å. Rh(1) is bonded to two equivalent O(2) and four equivalent O(1) atoms to form distorted RhO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra, corners with eight equivalent V(1)O6 octahedra, edges with two equivalent Rh(1)O6 octahedra, and faces with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-49°. Both Rh(1)-O(2) bond lengths are 2.21 Å. All Rh(1)-O(1) bond lengths are 2.15 Å. There are two inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one V(1), and two equivalent Rh(1) atoms to form distorted OMg2VRh2 square pyramids that share corners with five equivalent O(1)Mg2VRh2 square pyramids, corners with four equivalent O(2)MgV2Rh trigonal pyramids, edges with four equivalent O(1)Mg2VRh2 square pyramids, and edges with four equivalent O(2)MgV2Rh trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent V(1), and one Rh(1) atom to form distorted OMgV2Rh trigonal pyramids that share corners with four equivalent O(1)Mg2VRh2 square pyramids, corners with six equivalent O(2)MgV2Rh trigonal pyramids, edges with four equivalent O(1)Mg2VRh2 square pyramids, and  an edgeedge with one O(2)MgV2Rh trigonal pyramid.