Rh5Mg crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one Rh(3), two equivalent Rh(1), two equivalent Rh(2), two equivalent Rh(4), and three equivalent Rh(5) atoms to form distorted MgRh10 cuboctahedra that share corners with two equivalent Rh(1)Mg2Rh10 cuboctahedra, corners with four equivalent Mg(1)Rh10 cuboctahedra, corners with six equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with eight equivalent Rh(4)Mg2Rh10 cuboctahedra,  an edgeedge with one Rh(4)Mg2Rh10 cuboctahedra, edges with two equivalent Rh(2)Mg2Rh5 cuboctahedra, edges with four equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with two equivalent Mg(1)Rh10 cuboctahedra, faces with three equivalent Rh(1)Mg2Rh10 cuboctahedra, and faces with three equivalent Rh(4)Mg2Rh10 cuboctahedra. There are five inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to two equivalent Mg(1), one Rh(4), two equivalent Rh(1), two equivalent Rh(3), two equivalent Rh(5), and three equivalent Rh(2) atoms to form distorted RhMg2Rh10 cuboctahedra that share corners with two equivalent Mg(1)Rh10 cuboctahedra, corners with two equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with six equivalent Rh(1)Mg2Rh10 cuboctahedra, edges with four equivalent Mg(1)Rh10 cuboctahedra, edges with four equivalent Rh(4)Mg2Rh10 cuboctahedra, edges with five equivalent Rh(2)Mg2Rh5 cuboctahedra, faces with two equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with three equivalent Mg(1)Rh10 cuboctahedra, and faces with four equivalent Rh(4)Mg2Rh10 cuboctahedra. In the second Rh site, Rh(2) is bonded to two equivalent Mg(1), two equivalent Rh(4), and three equivalent Rh(1) atoms to form distorted RhMg2Rh5 cuboctahedra that share corners with two equivalent Rh(1)Mg2Rh10 cuboctahedra, corners with four equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with five equivalent Rh(4)Mg2Rh10 cuboctahedra, corners with six equivalent Mg(1)Rh10 cuboctahedra, edges with two equivalent Mg(1)Rh10 cuboctahedra, edges with three equivalent Rh(4)Mg2Rh10 cuboctahedra, edges with five equivalent Rh(1)Mg2Rh10 cuboctahedra, and faces with two equivalent Rh(2)Mg2Rh5 cuboctahedra. In the third Rh site, Rh(3) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Rh(1), and three equivalent Rh(4) atoms. In the fourth Rh site, Rh(4) is bonded to two equivalent Mg(1), one Rh(1), two equivalent Rh(2), two equivalent Rh(4), two equivalent Rh(5), and three equivalent Rh(3) atoms to form distorted RhMg2Rh10 cuboctahedra that share corners with five equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with six equivalent Rh(4)Mg2Rh10 cuboctahedra, corners with eight equivalent Mg(1)Rh10 cuboctahedra,  an edgeedge with one Mg(1)Rh10 cuboctahedra, edges with three equivalent Rh(2)Mg2Rh5 cuboctahedra, edges with four equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with two equivalent Rh(4)Mg2Rh10 cuboctahedra, faces with three equivalent Mg(1)Rh10 cuboctahedra, and faces with four equivalent Rh(1)Mg2Rh10 cuboctahedra. In the fifth Rh site, Rh(5) is bonded in a 3-coordinate geometry to three equivalent Mg(1), two equivalent Rh(1), and two equivalent Rh(4) atoms.
Rh5Mg crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one Rh(3), two equivalent Rh(1), two equivalent Rh(2), two equivalent Rh(4), and three equivalent Rh(5) atoms to form distorted MgRh10 cuboctahedra that share corners with two equivalent Rh(1)Mg2Rh10 cuboctahedra, corners with four equivalent Mg(1)Rh10 cuboctahedra, corners with six equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with eight equivalent Rh(4)Mg2Rh10 cuboctahedra,  an edgeedge with one Rh(4)Mg2Rh10 cuboctahedra, edges with two equivalent Rh(2)Mg2Rh5 cuboctahedra, edges with four equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with two equivalent Mg(1)Rh10 cuboctahedra, faces with three equivalent Rh(1)Mg2Rh10 cuboctahedra, and faces with three equivalent Rh(4)Mg2Rh10 cuboctahedra. The Mg(1)-Rh(3) bond length is 2.73 Å. Both Mg(1)-Rh(1) bond lengths are 2.77 Å. Both Mg(1)-Rh(2) bond lengths are 2.71 Å. Both Mg(1)-Rh(4) bond lengths are 2.76 Å. There is one shorter (2.63 Å) and two longer (2.69 Å) Mg(1)-Rh(5) bond lengths. There are five inequivalent Rh sites. In the first Rh site, Rh(1) is bonded to two equivalent Mg(1), one Rh(4), two equivalent Rh(1), two equivalent Rh(3), two equivalent Rh(5), and three equivalent Rh(2) atoms to form distorted RhMg2Rh10 cuboctahedra that share corners with two equivalent Mg(1)Rh10 cuboctahedra, corners with two equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with six equivalent Rh(1)Mg2Rh10 cuboctahedra, edges with four equivalent Mg(1)Rh10 cuboctahedra, edges with four equivalent Rh(4)Mg2Rh10 cuboctahedra, edges with five equivalent Rh(2)Mg2Rh5 cuboctahedra, faces with two equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with three equivalent Mg(1)Rh10 cuboctahedra, and faces with four equivalent Rh(4)Mg2Rh10 cuboctahedra. The Rh(1)-Rh(4) bond length is 2.69 Å. Both Rh(1)-Rh(1) bond lengths are 2.73 Å. Both Rh(1)-Rh(3) bond lengths are 2.74 Å. Both Rh(1)-Rh(5) bond lengths are 2.68 Å. There are two shorter (2.64 Å) and one longer (2.68 Å) Rh(1)-Rh(2) bond length. In the second Rh site, Rh(2) is bonded to two equivalent Mg(1), two equivalent Rh(4), and three equivalent Rh(1) atoms to form distorted RhMg2Rh5 cuboctahedra that share corners with two equivalent Rh(1)Mg2Rh10 cuboctahedra, corners with four equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with five equivalent Rh(4)Mg2Rh10 cuboctahedra, corners with six equivalent Mg(1)Rh10 cuboctahedra, edges with two equivalent Mg(1)Rh10 cuboctahedra, edges with three equivalent Rh(4)Mg2Rh10 cuboctahedra, edges with five equivalent Rh(1)Mg2Rh10 cuboctahedra, and faces with two equivalent Rh(2)Mg2Rh5 cuboctahedra. Both Rh(2)-Rh(4) bond lengths are 2.73 Å. In the third Rh site, Rh(3) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Rh(1), and three equivalent Rh(4) atoms. There is one shorter (2.63 Å) and two longer (2.70 Å) Rh(3)-Rh(4) bond lengths. In the fourth Rh site, Rh(4) is bonded to two equivalent Mg(1), one Rh(1), two equivalent Rh(2), two equivalent Rh(4), two equivalent Rh(5), and three equivalent Rh(3) atoms to form distorted RhMg2Rh10 cuboctahedra that share corners with five equivalent Rh(2)Mg2Rh5 cuboctahedra, corners with six equivalent Rh(4)Mg2Rh10 cuboctahedra, corners with eight equivalent Mg(1)Rh10 cuboctahedra,  an edgeedge with one Mg(1)Rh10 cuboctahedra, edges with three equivalent Rh(2)Mg2Rh5 cuboctahedra, edges with four equivalent Rh(1)Mg2Rh10 cuboctahedra, faces with two equivalent Rh(4)Mg2Rh10 cuboctahedra, faces with three equivalent Mg(1)Rh10 cuboctahedra, and faces with four equivalent Rh(1)Mg2Rh10 cuboctahedra. Both Rh(4)-Rh(4) bond lengths are 2.73 Å. Both Rh(4)-Rh(5) bond lengths are 2.68 Å. In the fifth Rh site, Rh(5) is bonded in a 3-coordinate geometry to three equivalent Mg(1), two equivalent Rh(1), and two equivalent Rh(4) atoms.