Mg14GaAl 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(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(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 equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al 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 Al(1) atoms to form distorted MgMg8Al2Ga2 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)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10AlGa 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)Mg8Al2Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(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)Mg10AlGa cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga 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)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10AlGa cuboctahedra. In the fifth 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 Al(1) atom to form distorted MgMg10AlGa cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra, corners with four equivalent Mg(7)Mg11Ga cuboctahedra, corners with ten equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(7)Mg11Ga 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)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(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)Mg10Al2 cuboctahedra,  a faceface with one Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Al(1) atom to form MgMg11Al cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra, corners with six equivalent Mg(6)Mg11Al cuboctahedra, corners with eight equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(7)Mg11Ga cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, faces with three equivalent Ga(1)Mg10Al2 cuboctahedra, and faces with four equivalent Mg(5)Mg10AlGa cuboctahedra. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra, corners with six equivalent Mg(7)Mg11Ga cuboctahedra, corners with eight equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Al(1)Mg10Ga2 cuboctahedra, and faces with four equivalent Mg(5)Mg10AlGa cuboctahedra. Ga(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Al(1) atoms to form GaMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Al(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form AlMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ga cuboctahedra.
Mg14GaAl 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(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.11 Å. Both Mg(1)-Mg(6) bond lengths are 3.15 Å. There are two shorter (3.13 Å) and two longer (3.15 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.18 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.14 Å. There are two shorter (3.13 Å) and two longer (3.16 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.18 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 Al(1) atoms to form distorted MgMg8Al2Ga2 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)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10AlGa cuboctahedra. There is one shorter (3.10 Å) and one longer (3.13 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.13 Å. Both Mg(3)-Mg(6) bond lengths are 3.16 Å. Both Mg(3)-Mg(7) bond lengths are 3.17 Å. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(3)-Ga(1) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Al(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)Mg8Al2Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(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)Mg10AlGa cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga 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)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(5)Mg10AlGa cuboctahedra. Both Mg(4)-Mg(4) bond lengths are 3.11 Å. Both Mg(4)-Mg(5) bond lengths are 3.20 Å. Both Mg(4)-Mg(6) bond lengths are 3.16 Å. Both Mg(4)-Mg(7) bond lengths are 3.15 Å. In the fifth 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 Al(1) atom to form distorted MgMg10AlGa cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra, corners with four equivalent Mg(7)Mg11Ga cuboctahedra, corners with ten equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(7)Mg11Ga 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)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(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)Mg10Al2 cuboctahedra,  a faceface with one Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra. Both Mg(5)-Mg(5) bond lengths are 3.11 Å. There is one shorter (3.12 Å) and one longer (3.17 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.12 Å) and one longer (3.17 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Ga(1) bond length is 3.12 Å. The Mg(5)-Al(1) bond length is 3.12 Å. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Al(1) atom to form MgMg11Al cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra, corners with six equivalent Mg(6)Mg11Al cuboctahedra, corners with eight equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(7)Mg11Ga cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, faces with three equivalent Ga(1)Mg10Al2 cuboctahedra, and faces with four equivalent Mg(5)Mg10AlGa cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.11 Å. The Mg(6)-Al(1) bond length is 3.14 Å. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ga(1) atom to form distorted MgMg11Ga cuboctahedra that share corners with four equivalent Mg(6)Mg11Al cuboctahedra, corners with six equivalent Mg(7)Mg11Ga cuboctahedra, corners with eight equivalent Mg(5)Mg10AlGa cuboctahedra, edges with two equivalent Mg(6)Mg11Al cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(5)Mg10AlGa cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Al(1)Mg10Ga2 cuboctahedra, and faces with four equivalent Mg(5)Mg10AlGa cuboctahedra. The Mg(7)-Ga(1) bond length is 3.16 Å. Ga(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Al(1) atoms to form GaMg10Al2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ga cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(7)Mg11Ga cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(6)Mg11Al cuboctahedra. Both Ga(1)-Al(1) bond lengths are 3.11 Å. Al(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form AlMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(6)Mg11Al cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(5)Mg10AlGa cuboctahedra, faces with two equivalent Mg(6)Mg11Al cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(5)Mg10AlGa cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ga cuboctahedra.