Mg14CrCd 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 Mg(4,4); and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four Mg(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); and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr 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 Cr(1), and two equivalent Cd(1) atoms to form distorted MgMg8Cr2Cd2 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(5)Mg10CrCd cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5)Mg10CrCd 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)Mg8Cr2Cd2 cuboctahedra; corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Cr2 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)Mg10CrCd cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CrCd cuboctahedra. In the fifth 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)Mg8Cr2Cd2 cuboctahedra, corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Cr2 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)Mg10CrCd cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(6)Mg11Cr cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10CrCd 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 Cr(1), and one Cd(1) atom to form distorted MgMg10CrCd cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra. In the seventh 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 Cr(1) atom to form distorted MgMg11Cr cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Cr cuboctahedra; corners with eight Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CrCd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Cr2 cuboctahedra; and faces with four Mg(5,5)Mg10CrCd cuboctahedra. In the eighth 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)Mg11Cr cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5)Mg10CrCd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10CrCd cuboctahedra. In the ninth 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 Cr(1), and one Cd(1) atom to form distorted MgMg10CrCd cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cd(1) atoms to form CrMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Cd(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cr(1) atoms to form CdMg10Cr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Cr2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra.
Mg14CrCd 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 Mg(4,4); and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(6) bond lengths are 3.15 Å. All Mg(1)-Mg(4,4) bond lengths are 3.16 Å. All Mg(1)-Mg(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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.14 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(2)-Mg(4,4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.18 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 Cr(1), and two equivalent Cd(1) atoms to form distorted MgMg8Cr2Cd2 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(5)Mg10CrCd cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; and faces with eight Mg(5,5)Mg10CrCd cuboctahedra. There is one shorter (3.14 Å) and one longer (3.19 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.12 Å. Both Mg(3)-Mg(6) bond lengths are 3.13 Å. Both Mg(3)-Mg(7) bond lengths are 3.16 Å. There is one shorter (3.15 Å) and one longer (3.18 Å) Mg(3)-Cr(1) bond length. There is one shorter (3.15 Å) and one longer (3.17 Å) Mg(3)-Cd(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)Mg8Cr2Cd2 cuboctahedra; corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Cr2 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)Mg10CrCd cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; and faces with eight Mg(5,5)Mg10CrCd 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 3.19 Å. Both Mg(4)-Mg(6) bond lengths are 3.17 Å. Both Mg(4)-Mg(7) bond lengths are 3.15 Å. In the fifth 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)Mg8Cr2Cd2 cuboctahedra, corners with four equivalent Cr(1)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Cr2 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)Mg10CrCd cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(6)Mg11Cr cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10CrCd 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 3.19 Å. Both Mg(4)-Mg(6) bond lengths are 3.17 Å. Both Mg(4)-Mg(7) bond lengths are 3.15 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 Cr(1), and one Cd(1) atom to form distorted MgMg10CrCd cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra. There is one shorter (3.13 Å) and one longer (3.20 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.12 Å) and one longer (3.20 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)-Cr(1) bond length is 3.10 Å. The Mg(5)-Cd(1) bond length is 3.12 Å. In the seventh 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 Cr(1) atom to form distorted MgMg11Cr cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with six equivalent Mg(6)Mg11Cr cuboctahedra; corners with eight Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with four Mg(5,5)Mg10CrCd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg10Cr2 cuboctahedra; and faces with four Mg(5,5)Mg10CrCd cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.16 Å. The Mg(6)-Mg(5) bond length is 3.20 Å. The Mg(6)-Cr(1) bond length is 3.11 Å. In the eighth 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)Mg11Cr cuboctahedra; corners with six equivalent Mg(7)Mg11Cd cuboctahedra; corners with eight Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four Mg(5,5)Mg10CrCd cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg10Cd2 cuboctahedra; and faces with four Mg(5,5)Mg10CrCd cuboctahedra. The Mg(7)-Mg(5) bond length is 3.17 Å. The Mg(7)-Cd(1) bond length is 3.15 Å. In the ninth 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 Cr(1), and one Cd(1) atom to form distorted MgMg10CrCd cuboctahedra that share corners with four equivalent Mg(7)Mg11Cd cuboctahedra; corners with four equivalent Mg(6)Mg11Cr cuboctahedra; corners with ten Mg(5,5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(5)Mg10CrCd cuboctahedra; edges with two equivalent Mg(7)Mg11Cd cuboctahedra; edges with two equivalent Mg(6)Mg11Cr 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)Mg8Cr2Cd2 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg10Cd2 cuboctahedra;  a faceface with one Cd(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with four Mg(5,5)Mg10CrCd cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra. The Mg(5)-Mg(1) bond length is 3.17 Å. The Mg(5)-Mg(2) bond length is 3.18 Å. The Mg(5)-Mg(3) bond length is 3.12 Å. The Mg(5)-Mg(4) bond length is 3.19 Å. The Mg(5)-Cr(1) bond length is 3.10 Å. The Mg(5)-Cd(1) bond length is 3.12 Å. Cr(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cd(1) atoms to form CrMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Cr(1)Mg10Cd2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(6)Mg11Cr cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(6)Mg11Cr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg10Cr2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Both Cr(1)-Cd(1) bond lengths are 3.16 Å. Cd(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cr(1) atoms to form CdMg10Cr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Cd(1)Mg10Cr2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(7)Mg11Cd cuboctahedra; edges with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; edges with eight Mg(5,5)Mg10CrCd cuboctahedra; faces with two equivalent Mg(7)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg10Cd2 cuboctahedra; faces with four equivalent Mg(5)Mg10CrCd cuboctahedra; faces with four equivalent Mg(3)Mg8Cr2Cd2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Cr cuboctahedra.