Mg14GaSi crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Si2 cuboctahedra; corners with eight Mg(2,2)Mg10Ga2 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSi cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSi cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ga2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSi cuboctahedra. In the third 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 Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 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)Mg10GaSi cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 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)Mg10GaSi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ga(1); and one Si(1) atom to form distorted MgMg10GaSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg10GaSi cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ga(1); and one Si(1) atom to form distorted MgMg10GaSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10GaSi cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)Mg10GaSi cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg10GaSi cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg10Si2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. Ga(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Si2 cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSi cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ga2 cuboctahedra; faces with six Mg(3,3)Mg10GaSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSi cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10GaSi cuboctahedra; faces with six equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14GaSi crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Si2 cuboctahedra; corners with eight Mg(2,2)Mg10Ga2 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSi cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSi cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.13 Å. There are two shorter (3.11 Å) and two longer (3.13 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.13 Å. Both Mg(1)-Si(1) bond lengths are 3.12 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10GaSi cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ga2 cuboctahedra; and faces with ten Mg(3,3)Mg10GaSi cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. All Mg(2)-Mg(2,2) bond lengths are 3.12 Å. All Mg(2)-Mg(3) bond lengths are 3.14 Å. Both Mg(2)-Ga(1) bond lengths are 3.12 Å. In the third 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 Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 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)Mg10GaSi cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 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)Mg10GaSi cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. All Mg(2)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(2)-Ga(1) bond lengths are 3.12 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ga(1); and one Si(1) atom to form distorted MgMg10GaSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg10GaSi cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.12 Å. There are two shorter (3.10 Å) and two longer (3.14 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Ga(1) bond length is 3.13 Å. The Mg(3)-Si(1) bond length is 3.12 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ga(1); and one Si(1) atom to form distorted MgMg10GaSi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10GaSi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg10GaSi cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra;  a faceface with one Si(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.13 Å. The Mg(3)-Mg(2) bond length is 3.14 Å. Both Mg(3)-Mg(4) bond lengths are 3.12 Å. The Mg(3)-Ga(1) bond length is 3.13 Å. The Mg(3)-Si(1) bond length is 3.12 Å. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)Mg10GaSi cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with six Mg(3,3)Mg10GaSi cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg10Si2 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10GaSi cuboctahedra. Ga(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Si2 cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSi cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ga2 cuboctahedra; faces with six Mg(3,3)Mg10GaSi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)Mg10GaSi cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10GaSi cuboctahedra; faces with six equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.