Mg14GaSn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg10Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Ga(1); and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg10GaSn cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. In the sixth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Ga(1); and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10GaSn cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10GaSn cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg10GaSn cuboctahedra; edges with six Mg(1,1,1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three Mg(1,1,1)Mg10Sn2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six Mg(3,3)Mg10GaSn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10GaSn cuboctahedra; faces with six Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14GaSn crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.19 Å. Both Mg(1)-Sn(1) bond lengths are 3.16 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg10Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.17 Å. All Mg(2)-Mg(2) bond lengths are 3.16 Å. All Mg(2)-Mg(3,3) bond lengths are 3.16 Å. Both Mg(2)-Ga(1) bond lengths are 3.16 Å. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(1)-Mg(1) bond length. All Mg(1)-Mg(3) bond lengths are 3.19 Å. Both Mg(1)-Sn(1) bond lengths are 3.16 Å. In the fourth Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. All Mg(1)-Mg(3,3) bond lengths are 3.19 Å. Both Mg(1)-Sn(1) bond lengths are 3.16 Å. In the fifth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Ga(1); and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg10GaSn cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.16 Å. There are two shorter (3.16 Å) and two longer (3.17 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Ga(1) bond length is 3.16 Å. The Mg(3)-Sn(1) bond length is 3.19 Å. In the sixth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Ga(1); and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10GaSn cuboctahedra; edges with four Mg(1,1)Mg10Sn2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with five Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.16 Å. The Mg(3)-Ga(1) bond length is 3.16 Å. The Mg(3)-Sn(1) bond length is 3.19 Å. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg10GaSn cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg10GaSn cuboctahedra; edges with six Mg(1,1,1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three Mg(1,1,1)Mg10Sn2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10GaSn cuboctahedra. Ga(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with six Mg(3,3)Mg10GaSn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1,1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSn cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10GaSn cuboctahedra; faces with six Mg(1,1,1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.