Ba6Lu2(WO6)3 crystallizes in the trigonal R-3m space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, 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 four equivalent Lu(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(2) and nine equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one W(2)O6 octahedra, faces with three equivalent Lu(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with three equivalent W(1)O6 octahedra, corners with three equivalent W(2)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-7°. There are two inequivalent W sites. In the first W site, W(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form WO6 octahedra that share corners with three equivalent Lu(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the second W site, W(2) is bonded to six equivalent O(1) atoms to form WO6 octahedra that share corners with six equivalent Lu(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 3°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(3), three equivalent Ba(1), one Lu(1), and one W(2) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Lu(1), and one W(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), three equivalent Ba(2), and one W(1) atom.
Ba6Lu2(WO6)3 crystallizes in the trigonal R-3m space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, 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 four equivalent Lu(1)O6 octahedra. All Ba(1)-O(2) bond lengths are 2.84 Å. There are six shorter (2.97 Å) and three longer (3.02 Å) Ba(1)-O(1) bond lengths. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(2) and nine equivalent O(3) atoms. All Ba(2)-O(2) bond lengths are 3.27 Å. There are three shorter (2.84 Å) and six longer (3.00 Å) Ba(2)-O(3) bond lengths. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one W(2)O6 octahedra, faces with three equivalent Lu(1)O6 octahedra, and faces with three equivalent W(1)O6 octahedra. All Ba(3)-O(1) bond lengths are 3.13 Å. All Ba(3)-O(3) bond lengths are 2.74 Å. All Ba(3)-O(2) bond lengths are 2.97 Å. Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with three equivalent W(1)O6 octahedra, corners with three equivalent W(2)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-7°. All Lu(1)-O(1) bond lengths are 2.27 Å. All Lu(1)-O(2) bond lengths are 2.14 Å. There are two inequivalent W sites. In the first W site, W(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form WO6 octahedra that share corners with three equivalent Lu(1)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. All W(1)-O(2) bond lengths are 2.07 Å. All W(1)-O(3) bond lengths are 1.88 Å. In the second W site, W(2) is bonded to six equivalent O(1) atoms to form WO6 octahedra that share corners with six equivalent Lu(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 3°. All W(2)-O(1) bond lengths are 1.96 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(3), three equivalent Ba(1), one Lu(1), and one W(2) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Lu(1), and one W(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), three equivalent Ba(2), and one W(1) atom.