Mg15W crystallizes in the hexagonal P-6m2 space group. There are five 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 equivalent Mg(2)Mg10W2 cuboctahedra, edges with six equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent W(1)Mg12 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 equivalent Mg(2), four equivalent Mg(4), and two equivalent W(1) atoms to form distorted MgMg10W2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10W2 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent W(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10W2 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent W(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Mg10W2 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 W(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10W2 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, faces with two equivalent Mg(2)Mg10W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Mg12 cuboctahedra. In the fourth Mg site, Mg(4) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and one W(1) atom. In the fifth Mg site, Mg(5) is bonded to three equivalent Mg(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, edges with six equivalent Mg(2)Mg10W2 cuboctahedra, edges with six equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10W2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg12 cuboctahedra, and faces with three equivalent W(1)Mg12 cuboctahedra. W(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form WMg12 cuboctahedra that share corners with six equivalent W(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)Mg12 cuboctahedra, edges with six equivalent Mg(2)Mg10W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10W2 cuboctahedra, and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15W crystallizes in the hexagonal P-6m2 space group. There are five 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 equivalent Mg(2)Mg10W2 cuboctahedra, edges with six equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent W(1)Mg12 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 3.15 Å. All Mg(1)-Mg(4) bond lengths are 3.14 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 W(1) atoms to form distorted MgMg10W2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10W2 cuboctahedra, corners with eight equivalent Mg(3)Mg12 cuboctahedra, edges with two equivalent W(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10W2 cuboctahedra, edges with four equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with two equivalent W(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Mg10W2 cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.12 Å. All Mg(2)-Mg(2) bond lengths are 3.15 Å. All Mg(2)-Mg(4) bond lengths are 3.05 Å. Both Mg(2)-W(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 equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent W(1)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg12 cuboctahedra, corners with eight equivalent Mg(2)Mg10W2 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, faces with two equivalent Mg(2)Mg10W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Mg12 cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.09 Å. There are two shorter (3.13 Å) and two longer (3.17 Å) Mg(3)-Mg(3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.19 Å. In the fourth Mg site, Mg(4) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), and one W(1) atom. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. The Mg(4)-W(1) bond length is 2.99 Å. In the fifth Mg site, Mg(5) is bonded to three equivalent Mg(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, edges with six equivalent Mg(2)Mg10W2 cuboctahedra, edges with six equivalent Mg(3)Mg12 cuboctahedra, faces with two equivalent Mg(5)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10W2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg12 cuboctahedra, and faces with three equivalent W(1)Mg12 cuboctahedra. W(1) is bonded to six equivalent Mg(2) and six equivalent Mg(4) atoms to form WMg12 cuboctahedra that share corners with six equivalent W(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)Mg12 cuboctahedra, edges with six equivalent Mg(2)Mg10W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10W2 cuboctahedra, and faces with six equivalent Mg(5)Mg12 cuboctahedra.