LiMg14Ga crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Li2Mg10 cuboctahedra; edges with twelve Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(1,1)Li2Mg10 cuboctahedra; faces with six Mg(3,3)LiMg10Ga cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Ga 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 Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Li2Mg10 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)LiMg10Ga cuboctahedra; faces with two equivalent Mg(1)Li2Mg10 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)LiMg10Ga cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Ga cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Ga(1) atom to form distorted MgLiMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Ga cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four Mg(3,3)LiMg10Ga cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Ga(1) atom to form distorted MgLiMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Ga cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)LiMg10Ga cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(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)LiMg10Ga cuboctahedra; edges with six Mg(1,1)Li2Mg10 cuboctahedra; edges with six Mg(3,3)LiMg10Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three Mg(1,1)Li2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga 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)Li2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(3,3)LiMg10Ga cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
LiMg14Ga crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with six Mg(1,1)Li2Mg10 cuboctahedra; edges with twelve Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(1,1)Li2Mg10 cuboctahedra; faces with six Mg(3,3)LiMg10Ga cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Li(1)-Mg(1,1) bond lengths are 3.14 Å. All Li(1)-Mg(3,3) bond lengths are 3.16 Å. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Ga cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.16 Å. There are two shorter (3.14 Å) and two longer (3.15 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.17 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 Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Li2Mg10 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)LiMg10Ga cuboctahedra; faces with two equivalent Mg(1)Li2Mg10 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)LiMg10Ga cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.17 Å. There are two shorter (3.14 Å) and two longer (3.15 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.16 Å. Both Mg(2)-Ga(1) bond lengths are 3.14 Å. In the third Mg site, Mg(1) is bonded to two equivalent Li(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Ga cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.16 Å. All Mg(1)-Mg(3) bond lengths are 3.17 Å. In the fourth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Ga(1) atom to form distorted MgLiMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Ga cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four Mg(3,3)LiMg10Ga cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.13 Å) and two longer (3.16 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Ga(1) bond length is 3.15 Å. In the fifth Mg site, Mg(3) is bonded to one Li(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Ga(1) atom to form distorted MgLiMg10Ga cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Ga cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)LiMg10Ga cuboctahedra; edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. The Mg(3)-Ga(1) bond length is 3.15 Å. In the sixth Mg site, Mg(4) is bonded to three Mg(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)LiMg10Ga cuboctahedra; edges with six Mg(1,1)Li2Mg10 cuboctahedra; edges with six Mg(3,3)LiMg10Ga cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three Mg(1,1)Li2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LiMg10Ga 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)Li2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)LiMg10Ga cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(3,3)LiMg10Ga cuboctahedra; faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.