Mg14CdBi crystallizes in the orthorhombic Amm2 space group. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cd 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi 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)Mg8Cd2Bi2 cuboctahedra; corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(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 Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(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)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi 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 Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four Mg(5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 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 Cd(1), and one Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 cuboctahedra. In the ninth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with six equivalent Mg(6)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with four Mg(5,5,5)Mg10CdBi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Bi2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CdBi cuboctahedra. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5,5); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with six equivalent Mg(7)Mg11Bi cuboctahedra; corners with eight Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5,5)Mg10CdBi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Bi2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CdBi cuboctahedra. In the eleventh 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. In the twelfth 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdBi cuboctahedra. In the thirteenth 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 Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 cuboctahedra. Cd(1) is bonded to two equivalent Mg(6); four Mg(3,3,3,3); four Mg(5,5,5); and two equivalent Bi(1) atoms to form CdMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Bi(1) is bonded to two equivalent Mg(7); four Mg(3,3,3,3); four Mg(5,5,5); and two equivalent Cd(1) atoms to form BiMg10Cd2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Bi(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cd cuboctahedra.
Mg14CdBi crystallizes in the orthorhombic Amm2 space group. There are thirteen inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.27 Å. Both Mg(1)-Mg(6) bond lengths are 3.18 Å. There are two shorter (3.18 Å) and two longer (3.20 Å) Mg(1)-Mg(4,4) bond lengths. All Mg(1)-Mg(5,5,5) bond lengths are 3.17 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cd cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.16 Å. There are two shorter (3.19 Å) and two longer (3.20 Å) Mg(2)-Mg(4,4) bond lengths. All Mg(2)-Mg(5,5,5) bond lengths are 3.20 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. There is one shorter (3.26 Å) and one longer (3.28 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.22 Å. Both Mg(3)-Mg(6) bond lengths are 3.22 Å. Both Mg(3)-Mg(7) bond lengths are 3.26 Å. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(3)-Bi(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)Mg8Cd2Bi2 cuboctahedra; corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(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 Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. There is one shorter (3.26 Å) and one longer (3.28 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. Both Mg(4)-Mg(6) bond lengths are 3.21 Å. Both Mg(4)-Mg(7) bond lengths are 3.15 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. There is one shorter (3.26 Å) and one longer (3.28 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.22 Å. Both Mg(3)-Mg(6) bond lengths are 3.22 Å. Both Mg(3)-Mg(7) bond lengths are 3.26 Å. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(3)-Bi(1) bond length. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); two Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; corners with four equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(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)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. Both Mg(4)-Mg(5,5) bond lengths are 3.15 Å. Both Mg(4)-Mg(6) bond lengths are 3.21 Å. Both Mg(4)-Mg(7) bond lengths are 3.15 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 Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four Mg(5,5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 cuboctahedra. There is one shorter (3.21 Å) and one longer (3.33 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.24 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.24 Å. The Mg(5)-Bi(1) bond length is 3.26 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 Cd(1), and one Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 cuboctahedra. There is one shorter (3.21 Å) and one longer (3.33 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.15 Å) and one longer (3.24 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.24 Å. The Mg(5)-Bi(1) bond length is 3.26 Å. In the ninth Mg site, Mg(6) is bonded to one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5,5); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with six equivalent Mg(6)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with four Mg(5,5,5)Mg10CdBi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Bi2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CdBi cuboctahedra. The Mg(6)-Mg(3) bond length is 3.22 Å. Both Mg(6)-Mg(7) bond lengths are 3.27 Å. The Mg(6)-Mg(5) bond length is 3.20 Å. The Mg(6)-Cd(1) bond length is 3.18 Å. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5,5); and one Bi(1) atom to form distorted MgMg11Bi cuboctahedra that share corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with six equivalent Mg(7)Mg11Bi cuboctahedra; corners with eight Mg(5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5,5)Mg10CdBi cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Mg8Cd2Bi2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Bi2 cuboctahedra; and faces with four Mg(5,5,5)Mg10CdBi cuboctahedra. The Mg(7)-Mg(3) bond length is 3.26 Å. The Mg(7)-Mg(5) bond length is 3.15 Å. The Mg(7)-Bi(1) bond length is 3.25 Å. In the eleventh 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5,5)Mg10CdBi cuboctahedra. Both Mg(3)-Mg(5,5) bond lengths are 3.22 Å. Both Mg(3)-Mg(6) bond lengths are 3.22 Å. Both Mg(3)-Mg(7) bond lengths are 3.26 Å. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(3)-Bi(1) bond length. In the twelfth 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 Bi(1) atoms to form distorted MgMg8Cd2Bi2 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CdBi cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cd2Bi2 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CdBi cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.22 Å. There is one shorter (3.17 Å) and one longer (3.22 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.19 Å) and one longer (3.20 Å) Mg(3)-Bi(1) bond length. In the thirteenth 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 Bi(1) atom to form distorted MgMg10CdBi cuboctahedra that share corners with four equivalent Mg(7)Mg11Bi cuboctahedra; corners with four equivalent Mg(6)Mg11Cd cuboctahedra; corners with ten Mg(5,5,5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(5)Mg10CdBi cuboctahedra; edges with two equivalent Mg(7)Mg11Bi cuboctahedra; edges with two equivalent Mg(6)Mg11Cd 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)Mg8Cd2Bi2 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(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)Mg10Bi2 cuboctahedra;  a faceface with one Bi(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10CdBi cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3,3)Mg8Cd2Bi2 cuboctahedra. The Mg(5)-Mg(4) bond length is 3.15 Å. The Mg(5)-Cd(1) bond length is 3.24 Å. The Mg(5)-Bi(1) bond length is 3.26 Å. Cd(1) is bonded to two equivalent Mg(6); four Mg(3,3,3,3); four Mg(5,5,5); and two equivalent Bi(1) atoms to form CdMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Bi2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cd cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(6)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Bi cuboctahedra. Both Cd(1)-Bi(1) bond lengths are 3.27 Å. Bi(1) is bonded to two equivalent Mg(7); four Mg(3,3,3,3); four Mg(5,5,5); and two equivalent Cd(1) atoms to form BiMg10Cd2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Bi(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(7)Mg11Bi cuboctahedra; edges with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; edges with eight Mg(5,5,5)Mg10CdBi cuboctahedra; faces with two equivalent Mg(7)Mg11Bi cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Bi2 cuboctahedra; faces with four Mg(5,5,5)Mg10CdBi cuboctahedra; faces with four Mg(3,3,3,3)Mg8Cd2Bi2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cd cuboctahedra.