Mg14CdSn crystallizes in the orthorhombic Amm2 space group. There are nine 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn 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 Cd(1), and two equivalent Sn(1) atoms to form distorted MgMg8Cd2Sn2 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 Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn 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)Mg8Cd2Sn2 cuboctahedra; corners with four equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Cd2 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)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); two equivalent Cd(1); and two equivalent Sn(1) atoms to form distorted MgMg8Cd2Sn2 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn cuboctahedra. In the sixth 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 Cd(1), and one Sn(1) atom to form distorted MgMg10CdSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra. In the seventh 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 Cd(1), and one Sn(1) atom to form distorted MgMg10CdSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Sn cuboctahedra; corners with eight Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10CdSn cuboctahedra. In the ninth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Cd(1) atom to form MgMg11Cd cuboctahedra that share corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10CdSn cuboctahedra. Cd(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form CdMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5); and two equivalent Cd(1) atoms to form SnMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra.
Mg14CdSn crystallizes in the orthorhombic Amm2 space group. There are nine 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.19 Å. Both Mg(1)-Mg(6) bond lengths are 3.18 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5,5) bond lengths are 3.19 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.19 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5,5) 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 Cd(1), and two equivalent Sn(1) atoms to form distorted MgMg8Cd2Sn2 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 Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.19 Å. Both Mg(3)-Mg(5) bond lengths are 3.20 Å. Both Mg(3)-Mg(6) bond lengths are 3.22 Å. Both Mg(3)-Mg(7) bond lengths are 3.21 Å. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(3)-Sn(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 Mg(3)Mg8Cd2Sn2 cuboctahedra; corners with four equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Cd2 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)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn cuboctahedra. There is one shorter (3.18 Å) and one longer (3.19 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 3.18 Å. Both Mg(4)-Mg(7) bond lengths are 3.19 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); two equivalent Cd(1); and two equivalent Sn(1) atoms to form distorted MgMg8Cd2Sn2 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Sn2 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdSn cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.19 Å. Both Mg(3)-Mg(5,5) bond lengths are 3.20 Å. Both Mg(3)-Mg(6) bond lengths are 3.22 Å. Both Mg(3)-Mg(7) bond lengths are 3.21 Å. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(3)-Sn(1) bond length. In the sixth 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 Cd(1), and one Sn(1) atom to form distorted MgMg10CdSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra. There is one shorter (3.18 Å) and one longer (3.19 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.21 Å. The Mg(5)-Sn(1) bond length is 3.21 Å. In the seventh 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 Cd(1), and one Sn(1) atom to form distorted MgMg10CdSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Sn 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)Mg8Cd2Sn2 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra. The Mg(5)-Mg(4) bond length is 3.18 Å. There is one shorter (3.18 Å) and one longer (3.19 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.21 Å. The Mg(5)-Sn(1) bond length is 3.21 Å. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Sn cuboctahedra; corners with eight Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10CdSn cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.19 Å. The Mg(6)-Sn(1) bond length is 3.21 Å. In the ninth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); four Mg(5,5); and one Cd(1) atom to form MgMg11Cd cuboctahedra that share corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CdSn cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10CdSn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10CdSn cuboctahedra. The Mg(7)-Cd(1) bond length is 3.20 Å. Cd(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form CdMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Both Cd(1)-Sn(1) bond lengths are 3.19 Å. Sn(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5); and two equivalent Cd(1) atoms to form SnMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10CdSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10CdSn cuboctahedra; faces with four Mg(3,3)Mg8Cd2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra.