Mg15Sn 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 equivalent Mg(3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Sn cuboctahedra; faces with six equivalent Mg(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 Mg(2,2); four equivalent Mg(4); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Sn2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Sn cuboctahedra. In the third 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 Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Mg10Sn2 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)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg10Sn2 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)Mg11Sn cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)Mg11Sn cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Sn2 cuboctahedra, and faces with ten equivalent Mg(4)Mg11Sn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg11Sn cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Sn2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Sn cuboctahedra. In the sixth Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(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)Mg11Sn cuboctahedra; edges with six Mg(2,2)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(4)Mg11Sn cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Sn cuboctahedra. Sn(1) is bonded to six Mg(2,2) and six equivalent Mg(4) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Sn2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Sn2 cuboctahedra; faces with six equivalent Mg(4)Mg11Sn cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Sn 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 equivalent Mg(3) and six equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Sn cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3) bond lengths are 3.17 Å. All Mg(1)-Mg(4) bond lengths are 3.17 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four equivalent Mg(4); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Sn2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Sn cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.16 Å. There are two shorter (3.16 Å) and two longer (3.18 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.16 Å. Both Mg(2)-Sn(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 equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Mg10Sn2 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)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg10Sn2 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)Mg11Sn cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.16 Å. All Mg(3)-Mg(3) bond lengths are 3.17 Å. All Mg(3)-Mg(4) bond lengths are 3.16 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, edges with eight equivalent Mg(4)Mg11Sn cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Sn2 cuboctahedra, and faces with ten equivalent Mg(4)Mg11Sn cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.16 Å. All Mg(2)-Mg(4) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.17 Å. In the fifth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg11Sn cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Sn2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Sn cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.17 Å. There are two shorter (3.16 Å) and two longer (3.18 Å) Mg(4)-Mg(4) bond lengths. The Mg(4)-Sn(1) bond length is 3.17 Å. In the sixth Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(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)Mg11Sn cuboctahedra; edges with six Mg(2,2)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(4)Mg11Sn cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Sn cuboctahedra. Sn(1) is bonded to six Mg(2,2) and six equivalent Mg(4) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Sn2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Sn2 cuboctahedra; faces with six equivalent Mg(4)Mg11Sn cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.