Mg14CoZn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Zn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Zn cuboctahedra. In the third Mg site, Mg(3) is bonded in a 2-coordinate geometry to two equivalent Mg(6), two equivalent Co(1), and two equivalent Zn(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(6), one Co(1), and one Zn(1) atom. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Zn(1) atom to form distorted MgMg11Zn cuboctahedra that share corners with six equivalent Mg(6)Mg11Zn cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Zn2 cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(4), two equivalent Mg(6), and one Co(1) atom. Co(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Zn(1) atoms to form distorted CoMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Zn cuboctahedra. Zn(1) is bonded in a 12-coordinate geometry to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms.
Mg14CoZn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Zn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(6) bond lengths are 3.05 Å. There are two shorter (3.08 Å) and two longer (3.19 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.26 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Zn cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.09 Å. There are two shorter (3.10 Å) and two longer (3.16 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.22 Å. In the third Mg site, Mg(3) is bonded in a 2-coordinate geometry to two equivalent Mg(6), two equivalent Co(1), and two equivalent Zn(1) atoms. Both Mg(3)-Mg(6) bond lengths are 3.02 Å. There is one shorter (2.89 Å) and one longer (3.38 Å) Mg(3)-Co(1) bond length. There is one shorter (2.94 Å) and one longer (3.33 Å) Mg(3)-Zn(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.13 Å) and one longer (3.19 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.28 Å. Both Mg(4)-Mg(6) bond lengths are 3.04 Å. Both Mg(4)-Mg(7) bond lengths are 3.11 Å. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Mg(1), one Mg(2), one Mg(4), two equivalent Mg(6), one Co(1), and one Zn(1) atom. There is one shorter (3.12 Å) and one longer (3.18 Å) Mg(5)-Mg(6) bond length. The Mg(5)-Co(1) bond length is 2.82 Å. The Mg(5)-Zn(1) bond length is 2.86 Å. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Zn(1) atom to form distorted MgMg11Zn cuboctahedra that share corners with six equivalent Mg(6)Mg11Zn cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(6)Mg11Zn cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Zn2 cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.16 Å. The Mg(6)-Zn(1) bond length is 3.03 Å. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(4), two equivalent Mg(6), and one Co(1) atom. The Mg(7)-Co(1) bond length is 2.89 Å. Co(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Zn(1) atoms to form distorted CoMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Zn cuboctahedra. Both Co(1)-Zn(1) bond lengths are 3.16 Å. Zn(1) is bonded in a 12-coordinate geometry to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms.