MgLu6WO12 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share  a faceface with one W(1)O6 octahedra. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share  a faceface with one Mg(1)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one W(1) atom to form distorted OLu3W trigonal pyramids that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with six equivalent O(4)Lu4 tetrahedra, corners with four equivalent O(1)Lu3W trigonal pyramids, and edges with two equivalent O(3)Lu4Mg square pyramids. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), two equivalent Lu(1), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), two equivalent Lu(1), and two equivalent Lu(2) atoms to form distorted OLu4Mg square pyramids that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with two equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W trigonal pyramids, edges with two equivalent O(3)Lu4Mg square pyramids, edges with three equivalent O(4)Lu4 tetrahedra, and edges with two equivalent O(1)Lu3W trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Lu(1) and two equivalent Lu(2) atoms to form OLu4 tetrahedra that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with four equivalent O(4)Lu4 tetrahedra, corners with six equivalent O(1)Lu3W trigonal pyramids, and edges with three equivalent O(3)Lu4Mg square pyramids.
MgLu6WO12 crystallizes in the trigonal R3 space group. Mg(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form MgO6 octahedra that share  a faceface with one W(1)O6 octahedra. All Mg(1)-O(2) bond lengths are 2.11 Å. All Mg(1)-O(3) bond lengths are 2.12 Å. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. The Lu(1)-O(1) bond length is 2.52 Å. There is one shorter (2.15 Å) and one longer (2.35 Å) Lu(1)-O(2) bond length. There is one shorter (2.21 Å) and one longer (2.43 Å) Lu(1)-O(3) bond length. There is one shorter (2.17 Å) and one longer (2.28 Å) Lu(1)-O(4) bond length. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms. There is one shorter (2.25 Å) and one longer (2.27 Å) Lu(2)-O(1) bond length. Both Lu(2)-O(3) bond lengths are 2.33 Å. There is one shorter (2.20 Å) and one longer (2.22 Å) Lu(2)-O(4) bond length. W(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form WO6 octahedra that share  a faceface with one Mg(1)O6 octahedra. All W(1)-O(1) bond lengths are 2.07 Å. All W(1)-O(2) bond lengths are 2.12 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one W(1) atom to form distorted OLu3W trigonal pyramids that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with six equivalent O(4)Lu4 tetrahedra, corners with four equivalent O(1)Lu3W trigonal pyramids, and edges with two equivalent O(3)Lu4Mg square pyramids. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), two equivalent Lu(1), and one W(1) atom. In the third O site, O(3) is bonded to one Mg(1), two equivalent Lu(1), and two equivalent Lu(2) atoms to form distorted OLu4Mg square pyramids that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with two equivalent O(4)Lu4 tetrahedra, corners with two equivalent O(1)Lu3W trigonal pyramids, edges with two equivalent O(3)Lu4Mg square pyramids, edges with three equivalent O(4)Lu4 tetrahedra, and edges with two equivalent O(1)Lu3W trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Lu(1) and two equivalent Lu(2) atoms to form OLu4 tetrahedra that share corners with two equivalent O(3)Lu4Mg square pyramids, corners with four equivalent O(4)Lu4 tetrahedra, corners with six equivalent O(1)Lu3W trigonal pyramids, and edges with three equivalent O(3)Lu4Mg square pyramids.