Mg14ZnSn crystallizes in the orthorhombic Amm2 space group. There are eight 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 Sn(1)Mg10Zn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Zn2Sn2 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; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Sn 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 four equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn 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 to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Zn(1), and two equivalent Sn(1) atoms to form distorted MgMg8Zn2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; and faces with eight Mg(5,5)Mg10ZnSn cuboctahedra. 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 Mg(3)Mg8Zn2Sn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(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(5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10ZnSn cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Zn(1), and one Sn(1) atom to form distorted MgMg10ZnSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with ten equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn 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 two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with four Mg(5,5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra. 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 Mg(5,5); and one Zn(1) atom to form MgMg11Zn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with six equivalent Mg(6)Mg11Zn cuboctahedra; corners with eight equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Zn2 cuboctahedra; and faces with four Mg(5,5)Mg10ZnSn cuboctahedra. In the seventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with six equivalent Mg(7)Mg11Sn cuboctahedra; corners with eight equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four Mg(5,5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10ZnSn cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Zn(1), and one Sn(1) atom to form distorted MgMg10ZnSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with ten Mg(5,5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn 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 two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form ZnMg10Sn2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Zn(1) atoms to form SnMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Zn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Zn cuboctahedra.
Mg14ZnSn crystallizes in the orthorhombic Amm2 space group. There are eight 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 Sn(1)Mg10Zn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Zn2Sn2 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; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(6) bond lengths are 3.17 Å. There are two shorter (3.14 Å) and two longer (3.16 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.18 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 four equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn 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 3.16 Å. All Mg(2)-Mg(4) bond lengths are 3.15 Å. All Mg(2)-Mg(5) bond lengths are 3.19 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Zn(1), and two equivalent Sn(1) atoms to form distorted MgMg8Zn2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; and faces with eight Mg(5,5)Mg10ZnSn cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.16 Å. Both Mg(3)-Mg(5) bond lengths are 3.18 Å. Both Mg(3)-Mg(6) bond lengths are 3.18 Å. Both Mg(3)-Mg(7) bond lengths are 3.20 Å. There is one shorter (3.14 Å) and one longer (3.16 Å) Mg(3)-Zn(1) bond length. Both Mg(3)-Sn(1) bond lengths are 3.15 Å. 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 Mg(3)Mg8Zn2Sn2 cuboctahedra; corners with four equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(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(5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10ZnSn cuboctahedra. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. Both Mg(4)-Mg(6) bond lengths are 3.19 Å. Both Mg(4)-Mg(7) bond lengths are 3.16 Å. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Zn(1), and one Sn(1) atom to form distorted MgMg10ZnSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with ten equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn 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 two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with four Mg(5,5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra. There is one shorter (3.14 Å) and one longer (3.19 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.13 Å) and one longer (3.17 Å) Mg(5)-Mg(6) bond length. Both Mg(5)-Mg(7) bond lengths are 3.15 Å. The Mg(5)-Zn(1) bond length is 3.17 Å. The Mg(5)-Sn(1) bond length is 3.18 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 Mg(5,5); and one Zn(1) atom to form MgMg11Zn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with six equivalent Mg(6)Mg11Zn cuboctahedra; corners with eight equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Zn2 cuboctahedra; and faces with four Mg(5,5)Mg10ZnSn cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.16 Å. The Mg(6)-Mg(5) bond length is 3.17 Å. The Mg(6)-Zn(1) bond length is 3.17 Å. In the seventh Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with six equivalent Mg(7)Mg11Sn cuboctahedra; corners with eight equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four Mg(5,5)Mg10ZnSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10ZnSn cuboctahedra. The Mg(7)-Mg(5) bond length is 3.15 Å. The Mg(7)-Sn(1) bond length is 3.20 Å. In the eighth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Zn(1), and one Sn(1) atom to form distorted MgMg10ZnSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Sn cuboctahedra; corners with four equivalent Mg(6)Mg11Zn cuboctahedra; corners with ten Mg(5,5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(5)Mg10ZnSn cuboctahedra; edges with two equivalent Mg(7)Mg11Sn cuboctahedra; edges with two equivalent Mg(6)Mg11Zn 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 two equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra. The Mg(5)-Mg(1) bond length is 3.18 Å. The Mg(5)-Mg(2) bond length is 3.19 Å. The Mg(5)-Mg(3) bond length is 3.18 Å. The Mg(5)-Mg(4) bond length is 3.18 Å. The Mg(5)-Zn(1) bond length is 3.17 Å. The Mg(5)-Sn(1) bond length is 3.18 Å. Zn(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form ZnMg10Sn2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Zn(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Zn cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(6)Mg11Zn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Zn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Sn cuboctahedra. Both Zn(1)-Sn(1) bond lengths are 3.16 Å. Sn(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Zn(1) atoms to form SnMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Zn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(7)Mg11Sn cuboctahedra; edges with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10ZnSn cuboctahedra; faces with two equivalent Mg(7)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg10Sn2 cuboctahedra; faces with four equivalent Mg(5)Mg10ZnSn cuboctahedra; faces with four equivalent Mg(3)Mg8Zn2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Zn cuboctahedra.