Mg14CdAl crystallizes in the orthorhombic Amm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)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 Mg(4,4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Al cuboctahedra. In the third 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 Al(1) atoms to form distorted MgMg8Al2Cd2 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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. In the fourth 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. In the fifth 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six Mg(4,4)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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd 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 Al(1) atom to form distorted MgMg10AlCd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with ten equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(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)Mg10Al2 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Al2Cd2 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 Al(1) atom to form distorted MgMg10AlCd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(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)Mg10Al2 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5); and one Al(1) atom to form MgMg11Al cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Al cuboctahedra; corners with eight Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10AlCd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Al2 cuboctahedra; and faces with four Mg(5,5)Mg10AlCd cuboctahedra. In the ninth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with four Mg(5,5)Mg10AlCd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10AlCd cuboctahedra. In the tenth 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six Mg(4,4)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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. Cd(1) is bonded to two equivalent Mg(7); four equivalent Mg(3); four Mg(5,5); and two equivalent Al(1) atoms to form CdMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Al2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Al(1) is bonded to two equivalent Mg(6); four equivalent Mg(3); four Mg(5,5); and two equivalent Cd(1) atoms to form AlMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Al(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra.
Mg14CdAl crystallizes in the orthorhombic Amm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.17 Å. Both Mg(1)-Mg(6) bond lengths are 3.17 Å. There are two shorter (3.14 Å) and two longer (3.15 Å) Mg(1)-Mg(4,4,4) 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 Mg(4,4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.16 Å. There are two shorter (3.13 Å) and two longer (3.16 Å) Mg(2)-Mg(4,4,4) bond lengths. All Mg(2)-Mg(5,5) bond lengths are 3.20 Å. In the third 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 Al(1) atoms to form distorted MgMg8Al2Cd2 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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. There is one shorter (3.17 Å) and one longer (3.18 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5,5) bond lengths are 3.15 Å. Both Mg(3)-Mg(6) bond lengths are 3.17 Å. Both Mg(3)-Mg(7) bond lengths are 3.18 Å. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(3)-Cd(1) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Al(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 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. There is one shorter (3.17 Å) and one longer (3.18 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.20 Å. Both Mg(4)-Mg(6) bond lengths are 3.19 Å. Both Mg(4)-Mg(7) bond lengths are 3.17 Å. In the fifth 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six Mg(4,4)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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. There is one shorter (3.17 Å) and one longer (3.18 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5,5) bond lengths are 3.20 Å. Both Mg(4)-Mg(6) bond lengths are 3.19 Å. Both Mg(4)-Mg(7) bond lengths are 3.17 Å. 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 Al(1) atom to form distorted MgMg10AlCd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with ten equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(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)Mg10Al2 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra. There is one shorter (3.15 Å) and one longer (3.19 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.15 Å. The Mg(5)-Al(1) bond length is 3.14 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 Al(1) atom to form distorted MgMg10AlCd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with ten Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with two equivalent Al(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)Mg10Al2 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with four equivalent Mg(5)Mg10AlCd cuboctahedra; faces with four Mg(4,4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra. There is one shorter (3.15 Å) and one longer (3.19 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Cd(1) bond length is 3.15 Å. The Mg(5)-Al(1) bond length is 3.14 Å. In the eighth Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5); and one Al(1) atom to form MgMg11Al cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Al cuboctahedra; corners with eight Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10AlCd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Al2 cuboctahedra; and faces with four Mg(5,5)Mg10AlCd cuboctahedra. The Mg(6)-Mg(4) bond length is 3.19 Å. Both Mg(6)-Mg(7) bond lengths are 3.17 Å. The Mg(6)-Al(1) bond length is 3.14 Å. In the ninth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10AlCd cuboctahedra; edges with two equivalent Mg(6)Mg11Al cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with four Mg(5,5)Mg10AlCd cuboctahedra; edges with four Mg(4,4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10AlCd cuboctahedra. The Mg(7)-Mg(4) bond length is 3.17 Å. The Mg(7)-Cd(1) bond length is 3.17 Å. In the tenth 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)Mg8Al2Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Al2 cuboctahedra; corners with four equivalent Al(1)Mg10Cd2 cuboctahedra; corners with six Mg(4,4)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)Mg10AlCd cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(7)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)Mg8Al2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10AlCd cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.20 Å. Cd(1) is bonded to two equivalent Mg(7); four equivalent Mg(3); four Mg(5,5); and two equivalent Al(1) atoms to form CdMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Al2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg10Cd2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Both Cd(1)-Al(1) bond lengths are 3.17 Å. Al(1) is bonded to two equivalent Mg(6); four equivalent Mg(3); four Mg(5,5); and two equivalent Cd(1) atoms to form AlMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Al(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(6)Mg11Al cuboctahedra; edges with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10AlCd cuboctahedra; faces with two equivalent Mg(6)Mg11Al cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Al2 cuboctahedra; faces with four Mg(5,5)Mg10AlCd cuboctahedra; faces with four equivalent Mg(3)Mg8Al2Cd2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra.