Mg15Zn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) 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)Mg10Zn2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Zn cuboctahedra; faces with six Mg(3,3,3)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 Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Zn 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. In the fourth 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. In the fifth 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. In the sixth 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 Zn(1) atom to form distorted MgMg11Zn cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Zn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg11Zn cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Zn cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); 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)Mg11Zn cuboctahedra; edges with six equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with six equivalent Mg(4)Mg11Zn cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Zn cuboctahedra. Zn(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with six equivalent Mg(4)Mg11Zn cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Zn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3,3) 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)Mg10Zn2 cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Zn cuboctahedra; faces with six Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3,3,3) bond lengths are 3.15 Å. All Mg(1)-Mg(4) bond lengths are 3.16 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 Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Zn cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.12 Å. There are two shorter (3.13 Å) and two longer (3.18 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.06 Å. Both Mg(2)-Zn(1) bond lengths are 3.15 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.10 Å. There are two shorter (3.14 Å) and two longer (3.17 Å) Mg(3)-Mg(3,3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.17 Å. In the fourth 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.10 Å. There is one shorter (3.14 Å) and one longer (3.17 Å) Mg(3)-Mg(3) bond length. All Mg(3)-Mg(4) bond lengths are 3.17 Å. In the fifth 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 Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra; faces with two equivalent Mg(2)Mg10Zn2 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)Mg11Zn cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.10 Å. All Mg(3)-Mg(4) bond lengths are 3.17 Å. In the sixth 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 Zn(1) atom to form distorted MgMg11Zn cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Zn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg11Zn cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with five Mg(3,3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Zn cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. There are two shorter (3.13 Å) and two longer (3.18 Å) Mg(4)-Mg(4) bond lengths. The Mg(4)-Zn(1) bond length is 3.05 Å. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3,3); 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)Mg11Zn cuboctahedra; edges with six equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with six equivalent Mg(4)Mg11Zn cuboctahedra; edges with six Mg(3,3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3,3)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Zn cuboctahedra. Zn(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Zn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra; faces with six equivalent Mg(4)Mg11Zn cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.