Mg15Cd crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Cd cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)Mg11Cd cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with four equivalent Mg(3)Mg12 cuboctahedra, and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg11Cd cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Cd cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve equivalent Mg(4)Mg11Cd cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six equivalent Mg(4)Mg11Cd cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Cd cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with six equivalent Mg(4)Mg11Cd cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Cd crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Cd cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3,3) bond lengths are 3.17 Å. All Mg(1)-Mg(4) bond lengths are 3.15 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.16 Å) and two longer (3.18 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.11 Å. Both Mg(2)-Cd(1) bond lengths are 3.17 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(3)-Mg(3,3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.15 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)Mg11Cd cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with four equivalent Mg(3)Mg12 cuboctahedra, and faces with ten equivalent Mg(4)Mg11Cd cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. All Mg(3)-Mg(4) bond lengths are 3.15 Å. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Cd cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg11Cd cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Cd cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.17 Å. All Mg(4)-Mg(4) bond lengths are 3.17 Å. The Mg(4)-Cd(1) bond length is 3.11 Å. In the sixth Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve equivalent Mg(4)Mg11Cd cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six equivalent Mg(4)Mg11Cd cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Cd cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Cd cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with six equivalent Mg(4)Mg11Cd cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.