Mg14GaSn crystallizes in the orthorhombic Amm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. In the sixth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ga(1), and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra. In the seventh Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with six equivalent Mg(6)Mg11Sn cuboctahedra; corners with eight Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four Mg(5,5)Mg10GaSn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10GaSn cuboctahedra. In the eighth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with six equivalent Mg(7)Mg11Ga cuboctahedra; corners with eight Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10GaSn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with four Mg(5,5)Mg10GaSn cuboctahedra. In the ninth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. In the tenth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ga(1), and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form distorted GaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5); and two equivalent Ga(1) atoms to form distorted SnMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra.
Mg14GaSn crystallizes in the orthorhombic Amm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.26 Å. Both Mg(1)-Mg(6) bond lengths are 3.12 Å. There are two shorter (3.14 Å) and two longer (3.15 Å) Mg(1)-Mg(4,4) bond lengths. All Mg(1)-Mg(5,5) bond lengths are 3.20 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.14 Å. There are two shorter (3.14 Å) and two longer (3.15 Å) Mg(2)-Mg(4,4) bond lengths. All Mg(2)-Mg(5,5) bond lengths are 3.17 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.26 Å. Both Mg(3)-Mg(5) bond lengths are 3.15 Å. Both Mg(3)-Mg(6) bond lengths are 3.21 Å. Both Mg(3)-Mg(7) bond lengths are 3.18 Å. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(3)-Ga(1) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Sn(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. Both Mg(4)-Mg(4) bond lengths are 3.26 Å. Both Mg(4)-Mg(5) bond lengths are 3.16 Å. Both Mg(4)-Mg(6) bond lengths are 3.15 Å. Both Mg(4)-Mg(7) bond lengths are 3.19 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with six Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. Both Mg(3)-Mg(3) bond lengths are 3.26 Å. Both Mg(3)-Mg(5) bond lengths are 3.15 Å. Both Mg(3)-Mg(6) bond lengths are 3.21 Å. Both Mg(3)-Mg(7) bond lengths are 3.18 Å. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(3)-Ga(1) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Sn(1) bond length. In the sixth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ga(1), and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra. There is one shorter (3.21 Å) and one longer (3.31 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Ga(1) bond length is 3.17 Å. The Mg(5)-Sn(1) bond length is 3.19 Å. In the seventh Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom to form distorted MgMg11Sn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with six equivalent Mg(6)Mg11Sn cuboctahedra; corners with eight Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four Mg(5,5)Mg10GaSn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg10Sn2 cuboctahedra; and faces with four Mg(5,5)Mg10GaSn cuboctahedra. The Mg(6)-Mg(4) bond length is 3.15 Å. Both Mg(6)-Mg(7) bond lengths are 3.26 Å. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(6)-Mg(5) bond length. The Mg(6)-Sn(1) bond length is 3.17 Å. In the eighth Mg site, Mg(7) is bonded to one Mg(2); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with six equivalent Mg(7)Mg11Ga cuboctahedra; corners with eight Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four Mg(5,5)Mg10GaSn cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg10Ga2 cuboctahedra; and faces with four Mg(5,5)Mg10GaSn cuboctahedra. The Mg(7)-Mg(4) bond length is 3.19 Å. There is one shorter (3.11 Å) and one longer (3.18 Å) Mg(7)-Mg(5) bond length. The Mg(7)-Ga(1) bond length is 3.12 Å. In the ninth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg10GaSn cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(5,5)Mg10GaSn cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.16 Å. In the tenth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ga(1), and one Sn(1) atom to form distorted MgMg10GaSn cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)Mg11Sn cuboctahedra; corners with ten Mg(5,5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(5)Mg10GaSn cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(6)Mg11Sn cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(3)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg10Sn2 cuboctahedra;  a faceface with one Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; and faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra. The Mg(5)-Mg(3) bond length is 3.15 Å. The Mg(5)-Ga(1) bond length is 3.17 Å. The Mg(5)-Sn(1) bond length is 3.19 Å. Ga(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form distorted GaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(6)Mg11Sn cuboctahedra. Both Ga(1)-Sn(1) bond lengths are 3.26 Å. Sn(1) is bonded to two equivalent Mg(6); four Mg(3,3); four Mg(5,5); and two equivalent Ga(1) atoms to form distorted SnMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(6)Mg11Sn cuboctahedra; edges with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(5,5)Mg10GaSn cuboctahedra; faces with two equivalent Mg(6)Mg11Sn cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(5,5)Mg10GaSn cuboctahedra; faces with four Mg(3,3)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra.