Mg15Al 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)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Al 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 Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Al2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Al2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Al2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Al 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 Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra; faces with two equivalent Mg(2)Mg10Al2 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)Mg11Al 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 Al(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 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)Mg11Al 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 Al(1) atom to form distorted MgMg11Al cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Al cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg11Al cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Al2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Al 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)Mg11Al cuboctahedra; edges with six equivalent Mg(2)Mg10Al2 cuboctahedra; edges with six equivalent Mg(4)Mg11Al cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Al2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Al cuboctahedra. Al(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Al2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Al2 cuboctahedra; faces with six equivalent Mg(4)Mg11Al cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Al 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)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg11Al 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 3.16 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 Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Al2 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Al2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Al2 cuboctahedra; and faces with ten equivalent Mg(4)Mg11Al cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.14 Å) and two longer (3.17 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.11 Å. Both Mg(2)-Al(1) bond lengths are 3.16 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 Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra; faces with two equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.15 Å) and two longer (3.16 Å) Mg(3)-Mg(3,3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.16 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 Al(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 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)Mg11Al cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. All Mg(3)-Mg(4) bond lengths are 3.16 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 Al(1) atom to form distorted MgMg11Al cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen equivalent Mg(4)Mg11Al cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg11Al cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Al2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Al cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.16 Å. There are two shorter (3.13 Å) and two longer (3.18 Å) Mg(4)-Mg(4) bond lengths. The Mg(4)-Al(1) bond length is 3.10 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)Mg11Al cuboctahedra; edges with six equivalent Mg(2)Mg10Al2 cuboctahedra; edges with six equivalent Mg(4)Mg11Al cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Al2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six equivalent Mg(4)Mg11Al cuboctahedra. Al(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Al2 cuboctahedra; edges with twelve equivalent Mg(4)Mg11Al cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Al2 cuboctahedra; faces with six equivalent Mg(4)Mg11Al cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.