Mg3Ho7Rh2 crystallizes in the monoclinic Cm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(4) is bonded in a 13-coordinate geometry to one Mg(2), one Mg(3), one Ho(10), one Ho(2), one Ho(3), one Ho(4), one Ho(5), one Ho(6), one Ho(7), one Ho(8), one Ho(9), one Rh(1), and one Rh(2) atom. In the second Mg site, Mg(1) is bonded to one Mg(3), two equivalent Mg(2), one Ho(3), one Ho(4), one Ho(9), two equivalent Ho(10), two equivalent Ho(2), and two equivalent Ho(5) atoms to form MgHo9Mg3 cuboctahedra that share  a cornercorner with one Mg(3)Ho7Mg5 cuboctahedra, corners with two equivalent Mg(2)Ho8Mg4 cuboctahedra,  a faceface with one Mg(3)Ho7Mg5 cuboctahedra, and faces with two equivalent Mg(2)Ho8Mg4 cuboctahedra. In the third Mg site, Mg(2) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(3), one Ho(5), one Ho(6), one Ho(7), and one Ho(8) atom to form MgHo8Mg4 cuboctahedra that share  a cornercorner with one Mg(3)Ho7Mg5 cuboctahedra,  a cornercorner with one Mg(2)Ho8Mg4 cuboctahedra,  a cornercorner with one Mg(1)Ho9Mg3 cuboctahedra,  a faceface with one Mg(3)Ho7Mg5 cuboctahedra,  a faceface with one Mg(2)Ho8Mg4 cuboctahedra, and  a faceface with one Mg(1)Ho9Mg3 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Ho(1), one Ho(4), one Ho(9), two equivalent Ho(2), and two equivalent Ho(8) atoms to form MgHo7Mg5 cuboctahedra that share  a cornercorner with one Mg(1)Ho9Mg3 cuboctahedra, corners with two equivalent Mg(2)Ho8Mg4 cuboctahedra,  a faceface with one Mg(1)Ho9Mg3 cuboctahedra, and faces with two equivalent Mg(2)Ho8Mg4 cuboctahedra. There are ten inequivalent Ho sites. In the first Ho site, Ho(1) is bonded in a 3-coordinate geometry to one Mg(3), two equivalent Mg(2), one Ho(4), two equivalent Ho(5), one Rh(3), and two equivalent Rh(2) atoms. In the second Ho site, Ho(2) is bonded in a 3-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Ho(5), one Ho(6), one Rh(1), one Rh(2), and one Rh(3) atom. In the third Ho site, Ho(3) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Ho(4), one Rh(1), and two equivalent Rh(2) atoms. In the fourth Ho site, Ho(4) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(3), two equivalent Mg(4), one Ho(1), one Ho(3), two equivalent Ho(10), two equivalent Ho(5), two equivalent Ho(8), and two equivalent Rh(2) atoms. In the fifth Ho site, Ho(5) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(2), one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(4), one Ho(5), one Ho(6), one Ho(7), one Ho(8), one Ho(9), one Rh(2), and one Rh(3) atom. In the sixth Ho site, Ho(6) is bonded in a 14-coordinate geometry to two equivalent Mg(2), two equivalent Mg(4), two equivalent Ho(10), two equivalent Ho(2), two equivalent Ho(5), two equivalent Ho(8), one Rh(1), and one Rh(3) atom. In the seventh Ho site, Ho(7) is bonded in a bent 150 degrees geometry to two equivalent Mg(2), two equivalent Mg(4), two equivalent Ho(5), one Rh(1), and one Rh(3) atom. In the eighth Ho site, Ho(8) is bonded in a bent 150 degrees geometry to one Mg(2), one Mg(3), one Mg(4), one Ho(4), one Ho(5), one Ho(6), one Rh(1), and one Rh(2) atom. In the ninth Ho site, Ho(9) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(3), two equivalent Mg(4), two equivalent Ho(5), and two equivalent Rh(2) atoms. In the tenth Ho site, Ho(10) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(2), one Mg(4), one Ho(4), one Ho(5), one Ho(6), one Rh(2), and one Rh(3) atom. There are three inequivalent Rh sites. In the first Rh site, Rh(1) is bonded in a 6-coordinate geometry to two equivalent Mg(4), one Ho(3), one Ho(6), one Ho(7), two equivalent Ho(2), and two equivalent Ho(8) atoms. In the second Rh site, Rh(2) is bonded in a 6-coordinate geometry to one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(3), one Ho(4), one Ho(5), one Ho(8), and one Ho(9) atom. In the third Rh site, Rh(3) is bonded in a 6-coordinate geometry to one Ho(1), one Ho(6), one Ho(7), two equivalent Ho(10), two equivalent Ho(2), and two equivalent Ho(5) atoms.
Mg3Ho7Rh2 crystallizes in the monoclinic Cm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(4) is bonded in a 13-coordinate geometry to one Mg(2), one Mg(3), one Ho(10), one Ho(2), one Ho(3), one Ho(4), one Ho(5), one Ho(6), one Ho(7), one Ho(8), one Ho(9), one Rh(1), and one Rh(2) atom. The Mg(4)-Mg(2) bond length is 3.24 Å. The Mg(4)-Mg(3) bond length is 3.24 Å. The Mg(4)-Ho(10) bond length is 3.59 Å. The Mg(4)-Ho(2) bond length is 3.48 Å. The Mg(4)-Ho(3) bond length is 3.48 Å. The Mg(4)-Ho(4) bond length is 3.54 Å. The Mg(4)-Ho(5) bond length is 3.57 Å. The Mg(4)-Ho(6) bond length is 3.55 Å. The Mg(4)-Ho(7) bond length is 3.58 Å. The Mg(4)-Ho(8) bond length is 3.59 Å. The Mg(4)-Ho(9) bond length is 3.60 Å. The Mg(4)-Rh(1) bond length is 3.49 Å. The Mg(4)-Rh(2) bond length is 3.52 Å. In the second Mg site, Mg(1) is bonded to one Mg(3), two equivalent Mg(2), one Ho(3), one Ho(4), one Ho(9), two equivalent Ho(10), two equivalent Ho(2), and two equivalent Ho(5) atoms to form MgHo9Mg3 cuboctahedra that share  a cornercorner with one Mg(3)Ho7Mg5 cuboctahedra, corners with two equivalent Mg(2)Ho8Mg4 cuboctahedra,  a faceface with one Mg(3)Ho7Mg5 cuboctahedra, and faces with two equivalent Mg(2)Ho8Mg4 cuboctahedra. The Mg(1)-Mg(3) bond length is 3.11 Å. Both Mg(1)-Mg(2) bond lengths are 3.07 Å. The Mg(1)-Ho(3) bond length is 3.46 Å. The Mg(1)-Ho(4) bond length is 3.31 Å. The Mg(1)-Ho(9) bond length is 3.50 Å. Both Mg(1)-Ho(10) bond lengths are 3.48 Å. Both Mg(1)-Ho(2) bond lengths are 3.48 Å. Both Mg(1)-Ho(5) bond lengths are 3.28 Å. In the third Mg site, Mg(2) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(3), one Ho(5), one Ho(6), one Ho(7), and one Ho(8) atom to form MgHo8Mg4 cuboctahedra that share  a cornercorner with one Mg(3)Ho7Mg5 cuboctahedra,  a cornercorner with one Mg(2)Ho8Mg4 cuboctahedra,  a cornercorner with one Mg(1)Ho9Mg3 cuboctahedra,  a faceface with one Mg(3)Ho7Mg5 cuboctahedra,  a faceface with one Mg(2)Ho8Mg4 cuboctahedra, and  a faceface with one Mg(1)Ho9Mg3 cuboctahedra. The Mg(2)-Mg(2) bond length is 3.09 Å. The Mg(2)-Mg(3) bond length is 3.15 Å. The Mg(2)-Ho(1) bond length is 3.49 Å. The Mg(2)-Ho(10) bond length is 3.47 Å. The Mg(2)-Ho(2) bond length is 3.48 Å. The Mg(2)-Ho(3) bond length is 3.44 Å. The Mg(2)-Ho(5) bond length is 3.26 Å. The Mg(2)-Ho(6) bond length is 3.26 Å. The Mg(2)-Ho(7) bond length is 3.47 Å. The Mg(2)-Ho(8) bond length is 3.53 Å. In the fourth Mg site, Mg(3) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Ho(1), one Ho(4), one Ho(9), two equivalent Ho(2), and two equivalent Ho(8) atoms to form MgHo7Mg5 cuboctahedra that share  a cornercorner with one Mg(1)Ho9Mg3 cuboctahedra, corners with two equivalent Mg(2)Ho8Mg4 cuboctahedra,  a faceface with one Mg(1)Ho9Mg3 cuboctahedra, and faces with two equivalent Mg(2)Ho8Mg4 cuboctahedra. The Mg(3)-Ho(1) bond length is 3.48 Å. The Mg(3)-Ho(4) bond length is 3.22 Å. The Mg(3)-Ho(9) bond length is 3.44 Å. Both Mg(3)-Ho(2) bond lengths are 3.46 Å. Both Mg(3)-Ho(8) bond lengths are 3.50 Å. There are ten inequivalent Ho sites. In the first Ho site, Ho(1) is bonded in a 3-coordinate geometry to one Mg(3), two equivalent Mg(2), one Ho(4), two equivalent Ho(5), one Rh(3), and two equivalent Rh(2) atoms. The Ho(1)-Ho(4) bond length is 3.47 Å. Both Ho(1)-Ho(5) bond lengths are 3.48 Å. The Ho(1)-Rh(3) bond length is 2.83 Å. Both Ho(1)-Rh(2) bond lengths are 2.79 Å. In the second Ho site, Ho(2) is bonded in a 3-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), one Ho(5), one Ho(6), one Rh(1), one Rh(2), and one Rh(3) atom. The Ho(2)-Ho(5) bond length is 3.51 Å. The Ho(2)-Ho(6) bond length is 3.50 Å. The Ho(2)-Rh(1) bond length is 2.78 Å. The Ho(2)-Rh(2) bond length is 2.81 Å. The Ho(2)-Rh(3) bond length is 2.83 Å. In the third Ho site, Ho(3) is bonded in a 3-coordinate geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), one Ho(4), one Rh(1), and two equivalent Rh(2) atoms. The Ho(3)-Ho(4) bond length is 3.52 Å. The Ho(3)-Rh(1) bond length is 2.80 Å. Both Ho(3)-Rh(2) bond lengths are 2.82 Å. In the fourth Ho site, Ho(4) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(3), two equivalent Mg(4), one Ho(1), one Ho(3), two equivalent Ho(10), two equivalent Ho(5), two equivalent Ho(8), and two equivalent Rh(2) atoms. Both Ho(4)-Ho(10) bond lengths are 3.62 Å. Both Ho(4)-Ho(5) bond lengths are 3.59 Å. Both Ho(4)-Ho(8) bond lengths are 3.59 Å. Both Ho(4)-Rh(2) bond lengths are 3.46 Å. In the fifth Ho site, Ho(5) is bonded in a 14-coordinate geometry to one Mg(1), one Mg(2), one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(4), one Ho(5), one Ho(6), one Ho(7), one Ho(8), one Ho(9), one Rh(2), and one Rh(3) atom. The Ho(5)-Ho(10) bond length is 3.60 Å. The Ho(5)-Ho(5) bond length is 3.59 Å. The Ho(5)-Ho(6) bond length is 3.56 Å. The Ho(5)-Ho(7) bond length is 3.60 Å. The Ho(5)-Ho(8) bond length is 3.60 Å. The Ho(5)-Ho(9) bond length is 3.63 Å. The Ho(5)-Rh(2) bond length is 3.48 Å. The Ho(5)-Rh(3) bond length is 3.49 Å. In the sixth Ho site, Ho(6) is bonded in a 14-coordinate geometry to two equivalent Mg(2), two equivalent Mg(4), two equivalent Ho(10), two equivalent Ho(2), two equivalent Ho(5), two equivalent Ho(8), one Rh(1), and one Rh(3) atom. Both Ho(6)-Ho(10) bond lengths are 3.60 Å. Both Ho(6)-Ho(8) bond lengths are 3.62 Å. The Ho(6)-Rh(1) bond length is 3.49 Å. The Ho(6)-Rh(3) bond length is 3.47 Å. In the seventh Ho site, Ho(7) is bonded in a bent 150 degrees geometry to two equivalent Mg(2), two equivalent Mg(4), two equivalent Ho(5), one Rh(1), and one Rh(3) atom. The Ho(7)-Rh(1) bond length is 2.80 Å. The Ho(7)-Rh(3) bond length is 2.81 Å. In the eighth Ho site, Ho(8) is bonded in a bent 150 degrees geometry to one Mg(2), one Mg(3), one Mg(4), one Ho(4), one Ho(5), one Ho(6), one Rh(1), and one Rh(2) atom. The Ho(8)-Rh(1) bond length is 2.77 Å. The Ho(8)-Rh(2) bond length is 2.77 Å. In the ninth Ho site, Ho(9) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(3), two equivalent Mg(4), two equivalent Ho(5), and two equivalent Rh(2) atoms. Both Ho(9)-Rh(2) bond lengths are 2.80 Å. In the tenth Ho site, Ho(10) is bonded in a bent 150 degrees geometry to one Mg(1), one Mg(2), one Mg(4), one Ho(4), one Ho(5), one Ho(6), one Rh(2), and one Rh(3) atom. The Ho(10)-Rh(2) bond length is 2.79 Å. The Ho(10)-Rh(3) bond length is 2.78 Å. There are three inequivalent Rh sites. In the first Rh site, Rh(1) is bonded in a 6-coordinate geometry to two equivalent Mg(4), one Ho(3), one Ho(6), one Ho(7), two equivalent Ho(2), and two equivalent Ho(8) atoms. In the second Rh site, Rh(2) is bonded in a 6-coordinate geometry to one Mg(4), one Ho(1), one Ho(10), one Ho(2), one Ho(3), one Ho(4), one Ho(5), one Ho(8), and one Ho(9) atom. In the third Rh site, Rh(3) is bonded in a 6-coordinate geometry to one Ho(1), one Ho(6), one Ho(7), two equivalent Ho(10), two equivalent Ho(2), and two equivalent Ho(5) atoms.