Mg6GaSn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg8Ga2Sn2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2,2); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Sn2 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2,2); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Sn(1)Mg10Ga2 cuboctahedra. In the seventh Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Sn(1) atoms to form GaMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Sn2 cuboctahedra. Sn(1) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Ga(1) atoms to form SnMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with six equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra.
Mg6GaSn crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.19 Å. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There is one shorter (3.12 Å) and one longer (3.13 Å) Mg(1)-Ga(1) bond length. Both Mg(1)-Sn(1) bond lengths are 3.13 Å. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(2,2)Mg8Ga2Sn2 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.16 Å. Both Mg(1)-Mg(3) bond lengths are 3.17 Å. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There is one shorter (3.12 Å) and one longer (3.13 Å) Mg(1)-Ga(1) bond length. Both Mg(1)-Sn(1) bond lengths are 3.13 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. There is one shorter (3.15 Å) and one longer (3.24 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.11 Å) and one longer (3.14 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.15 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Ga(1) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.19 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.14 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.15 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Ga(1) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.19 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2,2); and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Sn2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.19 Å. The Mg(3)-Mg(2) bond length is 3.14 Å. Both Mg(3)-Sn(1) bond lengths are 3.16 Å. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2,2); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Sn(1)Mg10Ga2 cuboctahedra. The Mg(4)-Mg(2) bond length is 3.15 Å. Both Mg(4)-Ga(1) bond lengths are 3.14 Å. In the seventh Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Sn(1) atoms to form distorted MgMg8Ga2Sn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Sn2 cuboctahedra; edges with four equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.16 Å. There is one shorter (3.15 Å) and one longer (3.24 Å) Mg(2)-Mg(2) bond length. Both Mg(2)-Ga(1) bond lengths are 3.16 Å. Both Mg(2)-Sn(1) bond lengths are 3.19 Å. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Sn(1) atoms to form GaMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Sn(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Sn2 cuboctahedra. Both Ga(1)-Sn(1) bond lengths are 3.19 Å. Sn(1) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Ga(1) atoms to form SnMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Sn2 cuboctahedra; corners with six equivalent Sn(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with two equivalent Ga(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra; edges with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; edges with eight Mg(2,2,2)Mg8Ga2Sn2 cuboctahedra; faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra; faces with two equivalent Ga(1)Mg10Sn2 cuboctahedra; faces with two equivalent Sn(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Sn2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra.