Mg14CuCd crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Cu2 cuboctahedra; corners with eight Mg(2,2)Mg10Cd2 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cu(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cu(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cu(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Cu(1); and one Cd(1) atom to form distorted MgMg10CdCu cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10CdCu cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four Mg(3,3)Mg10CdCu cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra;  a faceface with one Cu(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Cd2 cuboctahedra; faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Cu(1); and one Cd(1) atom to form distorted MgMg10CdCu cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10CdCu cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(3)Mg10CdCu cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra;  a faceface with one Cu(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Cd2 cuboctahedra; faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10CdCu cuboctahedra; edges with six Mg(2,2)Mg10Cd2 cuboctahedra; edges with six Mg(3,3)Mg10CdCu cuboctahedra; edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with three equivalent Cu(1)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. Cu(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form CuMg12 cuboctahedra that share corners with six equivalent Cu(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Cd2 cuboctahedra; edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with twelve Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10CdCu cuboctahedra; faces with six equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cd(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with six Mg(2,2)Mg10Cd2 cuboctahedra; edges with twelve Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Cu(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Cd2 cuboctahedra; faces with six Mg(3,3)Mg10CdCu cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14CuCd crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Cu2 cuboctahedra; corners with eight Mg(2,2)Mg10Cd2 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cu(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.11 Å. There are two shorter (3.11 Å) and two longer (3.17 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.09 Å. Both Mg(1)-Cu(1) bond lengths are 3.14 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cu(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.11 Å. There are two shorter (3.13 Å) and two longer (3.14 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.18 Å. Both Mg(2)-Cd(1) bond lengths are 3.14 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cu(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)Mg10CdCu cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.11 Å. All Mg(2)-Mg(3,3) bond lengths are 3.18 Å. Both Mg(2)-Cd(1) bond lengths are 3.14 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Cu(1); and one Cd(1) atom to form distorted MgMg10CdCu cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10CdCu cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four Mg(3,3)Mg10CdCu cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra;  a faceface with one Cu(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Cd2 cuboctahedra; faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.08 Å) and two longer (3.20 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Cu(1) bond length is 3.05 Å. The Mg(3)-Cd(1) bond length is 3.15 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Cu(1); and one Cd(1) atom to form distorted MgMg10CdCu cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10CdCu cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cu(1)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(3)Mg10CdCu cuboctahedra; edges with four equivalent Mg(1)Mg10Cu2 cuboctahedra;  a faceface with one Cu(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Cd2 cuboctahedra; faces with five equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.09 Å. The Mg(3)-Mg(2) bond length is 3.18 Å. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. The Mg(3)-Cu(1) bond length is 3.05 Å. The Mg(3)-Cd(1) bond length is 3.15 Å. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10CdCu cuboctahedra; edges with six Mg(2,2)Mg10Cd2 cuboctahedra; edges with six Mg(3,3)Mg10CdCu cuboctahedra; edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg10Cu2 cuboctahedra; faces with three equivalent Cu(1)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10CdCu cuboctahedra. Cu(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form CuMg12 cuboctahedra that share corners with six equivalent Cu(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Cd2 cuboctahedra; edges with six equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with twelve Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10CdCu cuboctahedra; faces with six equivalent Mg(1)Mg10Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cd(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Cu2 cuboctahedra; edges with six Mg(2,2)Mg10Cd2 cuboctahedra; edges with twelve Mg(3,3)Mg10CdCu cuboctahedra; faces with two equivalent Cu(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Cd2 cuboctahedra; faces with six Mg(3,3)Mg10CdCu cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.