Mg15Ga 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) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Ga 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 Mg(4,4); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with ten Mg(4,4)Mg11Ga 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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga 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 Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 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)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga 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 Mg(4,4); and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(4,4)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga 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 Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(4,4)Mg11Ga cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six Mg(4,4)Mg11Ga cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Ga 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) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Ga 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 3.15 Å. All Mg(1)-Mg(4,4) bond lengths are 3.17 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with ten Mg(4,4)Mg11Ga 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(4,4) bond lengths are 3.09 Å. Both Mg(2)-Ga(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 Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. There are two shorter (3.14 Å) and two longer (3.16 Å) Mg(3)-Mg(3) bond lengths. All Mg(3)-Mg(4,4) bond lengths are 3.18 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 Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 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)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 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 Mg(4,4)Mg11Ga cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. There is one shorter (3.14 Å) and one longer (3.16 Å) Mg(3)-Mg(3) bond length. All Mg(3)-Mg(4) bond lengths are 3.18 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 Mg(4,4); and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(4,4)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. There are two shorter (3.14 Å) and two longer (3.17 Å) Mg(4)-Mg(4,4) bond lengths. The Mg(4)-Ga(1) bond length is 3.08 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 Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga cuboctahedra. The Mg(4)-Mg(3) bond length is 3.18 Å. Both Mg(4)-Mg(5) bond lengths are 3.15 Å. The Mg(4)-Ga(1) bond length is 3.08 Å. In the seventh Mg site, Mg(5) is bonded to three equivalent Mg(2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(4,4)Mg11Ga cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Ga cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six Mg(4,4) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(4,4)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six Mg(4,4)Mg11Ga cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.