NaMg14Ga crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(6); four equivalent Mg(3); four Mg(5,5); and two equivalent Ga(1) atoms to form NaMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Na(1)Mg10Ga2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. There are nine 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)Na2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaMg10Ga 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 Na(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Na2Mg8Ga2 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)NaMg10Ga cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Na(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ga(1) atoms to form distorted MgNa2Mg8Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga 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 Na(1)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; corners with four equivalent Ga(1)Na2Mg10 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(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 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)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form distorted MgNaMg10Ga cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra;  a faceface with one Na(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)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Na(1); one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with six equivalent Mg(6)NaMg11 cuboctahedra; corners with eight Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four Mg(5,5)NaMg10Ga cuboctahedra;  a faceface with one Na(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Ga(1)Na2Mg10 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. In the seventh 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)NaMg11 cuboctahedra; corners with six equivalent Mg(7)Mg11Ga cuboctahedra; corners with eight Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four Mg(5,5)NaMg10Ga cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Na(1)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. In the eighth 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 Na(1)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; corners with four equivalent Ga(1)Na2Mg10 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(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 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)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga cuboctahedra. In the ninth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form distorted MgNaMg10Ga cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra;  a faceface with one Na(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)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. Ga(1) is bonded to two equivalent Na(1); two equivalent Mg(7); four equivalent Mg(3); and four Mg(5,5) atoms to form GaNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ga(1)Na2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra.
NaMg14Ga crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(6); four equivalent Mg(3); four Mg(5,5); and two equivalent Ga(1) atoms to form NaMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Na(1)Mg10Ga2 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. Both Na(1)-Mg(6) bond lengths are 3.22 Å. There are two shorter (3.15 Å) and two longer (3.20 Å) Na(1)-Mg(3) bond lengths. All Na(1)-Mg(5,5) bond lengths are 3.19 Å. Both Na(1)-Ga(1) bond lengths are 3.20 Å. There are nine 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)Na2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(7)Mg11Ga cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.20 Å. Both Mg(1)-Mg(6) bond lengths are 3.15 Å. There are two shorter (3.17 Å) and two longer (3.18 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 Na(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight equivalent Mg(3)Na2Mg8Ga2 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)NaMg10Ga cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.21 Å. There are two shorter (3.17 Å) and two longer (3.18 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 Na(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Ga(1) atoms to form distorted MgNa2Mg8Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Ga(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga cuboctahedra. There is one shorter (3.15 Å) and one longer (3.25 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.18 Å. Both Mg(3)-Mg(6) bond lengths are 3.19 Å. Both Mg(3)-Mg(7) bond lengths are 3.15 Å. There is one shorter (3.14 Å) and one longer (3.21 Å) Mg(3)-Ga(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 Na(1)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; corners with four equivalent Ga(1)Na2Mg10 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(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 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)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga cuboctahedra. There is one shorter (3.19 Å) and one longer (3.21 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. Both Mg(4)-Mg(6) bond lengths are 3.14 Å. Both Mg(4)-Mg(7) bond lengths are 3.23 Å. In the fifth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form distorted MgNaMg10Ga cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra;  a faceface with one Na(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)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. There is one shorter (3.14 Å) and one longer (3.26 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.15 Å) and one longer (3.20 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.14 Å) and one longer (3.21 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Ga(1) bond length is 3.15 Å. In the sixth Mg site, Mg(6) is bonded to one Na(1); one Mg(1); two equivalent Mg(3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with six equivalent Mg(6)NaMg11 cuboctahedra; corners with eight Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(7)Mg11Ga cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four Mg(5,5)NaMg10Ga cuboctahedra;  a faceface with one Na(1)Mg10Ga2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Ga(1)Na2Mg10 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. The Mg(6)-Mg(4) bond length is 3.14 Å. Both Mg(6)-Mg(7) bond lengths are 3.20 Å. There is one shorter (3.15 Å) and one longer (3.20 Å) Mg(6)-Mg(5) bond length. In the seventh 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)NaMg11 cuboctahedra; corners with six equivalent Mg(7)Mg11Ga cuboctahedra; corners with eight Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with four Mg(5,5)NaMg10Ga cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Ga(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Na(1)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. The Mg(7)-Mg(4) bond length is 3.23 Å. There is one shorter (3.14 Å) and one longer (3.21 Å) Mg(7)-Mg(5) bond length. The Mg(7)-Ga(1) bond length is 3.14 Å. In the eighth 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 Na(1)Mg10Ga2 cuboctahedra; corners with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; corners with four equivalent Ga(1)Na2Mg10 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(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(5)NaMg10Ga cuboctahedra; edges with four equivalent Mg(6)NaMg11 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)Na2Mg8Ga2 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaMg10Ga cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.18 Å. In the ninth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Ga(1) atom to form distorted MgNaMg10Ga cuboctahedra that share corners with four equivalent Mg(7)Mg11Ga cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaMg10Ga cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 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)Na2Mg8Ga2 cuboctahedra; edges with two equivalent Mg(5)NaMg10Ga cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Ga(1)Na2Mg10 cuboctahedra;  a faceface with one Na(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)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; and faces with four Mg(5,5)NaMg10Ga cuboctahedra. The Mg(5)-Mg(3) bond length is 3.18 Å. The Mg(5)-Mg(4) bond length is 3.18 Å. The Mg(5)-Ga(1) bond length is 3.15 Å. Ga(1) is bonded to two equivalent Na(1); two equivalent Mg(7); four equivalent Mg(3); and four Mg(5,5) atoms to form GaNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ga(1)Na2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Na(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(7)Mg11Ga cuboctahedra; edges with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; edges with eight Mg(5,5)NaMg10Ga cuboctahedra; faces with two equivalent Na(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(7)Mg11Ga cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four equivalent Mg(3)Na2Mg8Ga2 cuboctahedra; faces with four Mg(5,5)NaMg10Ga cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra.