Ba3MgLaIn(WO6)2 crystallizes in the trigonal R3m space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, faces with three equivalent W(2)O6 octahedra, and faces with three equivalent In(1)O6 octahedra. The corner-sharing octahedral tilt angles are 16°. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(2), three equivalent O(4), and six equivalent O(1) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(2), three equivalent O(4), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent W(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one In(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent W(2)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, and  a faceface with one W(2)O6 octahedra. La(1) is bonded in a 3-coordinate geometry to three equivalent O(3) and six equivalent O(2) atoms. There are two inequivalent W sites. In the first W site, W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent In(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. In the second W site, W(2) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form WO6 octahedra that share corners with three equivalent In(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form InO6 octahedra that share corners with three equivalent W(1)O6 octahedra, corners with three equivalent W(2)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-10°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a 2-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one W(2), and one In(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to one Ba(1), two equivalent Ba(2), one W(1), and one In(1) atom. In the third O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), one Mg(1), two equivalent La(1), and one W(1) atom. In the fourth O site, O(3) is bonded to one Ba(1), two equivalent Ba(3), one Mg(1), one La(1), and one W(2) atom to form a mixture of distorted corner and face-sharing OBa3LaMgW octahedra. The corner-sharing octahedral tilt angles range from 6-60°.
Ba3MgLaIn(WO6)2 crystallizes in the trigonal R3m space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Mg(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, faces with three equivalent W(2)O6 octahedra, and faces with three equivalent In(1)O6 octahedra. The corner-sharing octahedral tilt angles are 16°. All Ba(1)-O(1) bond lengths are 2.95 Å. All Ba(1)-O(3) bond lengths are 2.96 Å. All Ba(1)-O(4) bond lengths are 2.96 Å. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(2), three equivalent O(4), and six equivalent O(1) atoms. All Ba(2)-O(2) bond lengths are 2.69 Å. All Ba(2)-O(4) bond lengths are 3.42 Å. All Ba(2)-O(1) bond lengths are 2.99 Å. In the third Ba site, Ba(3) is bonded to three equivalent O(2), three equivalent O(4), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, corners with three equivalent W(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one In(1)O6 octahedra, faces with three equivalent Mg(1)O6 octahedra, and faces with three equivalent W(2)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. All Ba(3)-O(2) bond lengths are 3.01 Å. All Ba(3)-O(4) bond lengths are 2.99 Å. All Ba(3)-O(3) bond lengths are 2.97 Å. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one W(1)O6 octahedra, and  a faceface with one W(2)O6 octahedra. All Mg(1)-O(2) bond lengths are 2.05 Å. All Mg(1)-O(3) bond lengths are 2.08 Å. La(1) is bonded in a 3-coordinate geometry to three equivalent O(3) and six equivalent O(2) atoms. All La(1)-O(3) bond lengths are 2.42 Å. All La(1)-O(2) bond lengths are 3.10 Å. There are two inequivalent W sites. In the first W site, W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with three equivalent In(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. All W(1)-O(1) bond lengths are 1.98 Å. All W(1)-O(2) bond lengths are 2.05 Å. In the second W site, W(2) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form WO6 octahedra that share corners with three equivalent In(1)O6 octahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. All W(2)-O(3) bond lengths are 2.13 Å. All W(2)-O(4) bond lengths are 1.94 Å. In(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form InO6 octahedra that share corners with three equivalent W(1)O6 octahedra, corners with three equivalent W(2)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-10°. All In(1)-O(1) bond lengths are 2.12 Å. All In(1)-O(4) bond lengths are 2.22 Å. There are four inequivalent O sites. In the first O site, O(4) is bonded in a 2-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one W(2), and one In(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to one Ba(1), two equivalent Ba(2), one W(1), and one In(1) atom. In the third O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), one Mg(1), two equivalent La(1), and one W(1) atom. In the fourth O site, O(3) is bonded to one Ba(1), two equivalent Ba(3), one Mg(1), one La(1), and one W(2) atom to form a mixture of distorted corner and face-sharing OBa3LaMgW octahedra. The corner-sharing octahedral tilt angles range from 6-60°.