Lu3AlO6 crystallizes in the orthorhombic Cmc2_1 space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with four equivalent Lu(1)O7 pentagonal bipyramids, corners with three equivalent Al(1)O4 tetrahedra, edges with two equivalent Lu(1)O7 pentagonal bipyramids, edges with three equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Al(1)O4 tetrahedra, and  a faceface with one Lu(1)O7 pentagonal bipyramid. In the second Lu site, Lu(2) is bonded to one O(4), two equivalent O(2), and four equivalent O(1) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids,  a cornercorner with one Al(1)O4 tetrahedra, edges with two equivalent Lu(2)O7 pentagonal bipyramids, edges with six equivalent Lu(1)O7 pentagonal bipyramids, and  an edgeedge with one Al(1)O4 tetrahedra. Al(1) is bonded to one O(3), one O(4), and two equivalent O(2) atoms to form AlO4 tetrahedra that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, and edges with two equivalent Lu(1)O7 pentagonal bipyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent Lu(2) atoms to form OLu4 tetrahedra that share corners with two equivalent O(1)Lu4 tetrahedra, corners with four equivalent O(4)Lu3Al tetrahedra, corners with six equivalent O(2)Lu3Al trigonal pyramids, edges with three equivalent O(1)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Al trigonal pyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Al(1) atom to form distorted OLu3Al trigonal pyramids that share corners with two equivalent O(4)Lu3Al tetrahedra, corners with six equivalent O(1)Lu4 tetrahedra, corners with two equivalent O(2)Lu3Al trigonal pyramids,  an edgeedge with one O(4)Lu3Al tetrahedra,  an edgeedge with one O(1)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Al trigonal pyramid. In the third O site, O(3) is bonded in a distorted single-bond geometry to four equivalent Lu(1) and one Al(1) atom. In the fourth O site, O(4) is bonded to one Lu(2), two equivalent Lu(1), and one Al(1) atom to form distorted OLu3Al tetrahedra that share corners with eight equivalent O(1)Lu4 tetrahedra, corners with four equivalent O(2)Lu3Al trigonal pyramids, and edges with two equivalent O(2)Lu3Al trigonal pyramids.
Lu3AlO6 crystallizes in the orthorhombic Cmc2_1 space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with four equivalent Lu(1)O7 pentagonal bipyramids, corners with three equivalent Al(1)O4 tetrahedra, edges with two equivalent Lu(1)O7 pentagonal bipyramids, edges with three equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Al(1)O4 tetrahedra, and  a faceface with one Lu(1)O7 pentagonal bipyramid. The Lu(1)-O(4) bond length is 2.30 Å. There is one shorter (2.15 Å) and one longer (2.19 Å) Lu(1)-O(1) bond length. There is one shorter (2.21 Å) and one longer (2.34 Å) Lu(1)-O(2) bond length. Both Lu(1)-O(3) bond lengths are 2.50 Å. In the second Lu site, Lu(2) is bonded to one O(4), two equivalent O(2), and four equivalent O(1) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids,  a cornercorner with one Al(1)O4 tetrahedra, edges with two equivalent Lu(2)O7 pentagonal bipyramids, edges with six equivalent Lu(1)O7 pentagonal bipyramids, and  an edgeedge with one Al(1)O4 tetrahedra. The Lu(2)-O(4) bond length is 2.40 Å. Both Lu(2)-O(2) bond lengths are 2.37 Å. There are two shorter (2.21 Å) and two longer (2.24 Å) Lu(2)-O(1) bond lengths. Al(1) is bonded to one O(3), one O(4), and two equivalent O(2) atoms to form AlO4 tetrahedra that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with six equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, and edges with two equivalent Lu(1)O7 pentagonal bipyramids. The Al(1)-O(3) bond length is 1.79 Å. The Al(1)-O(4) bond length is 1.78 Å. Both Al(1)-O(2) bond lengths are 1.79 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent Lu(2) atoms to form OLu4 tetrahedra that share corners with two equivalent O(1)Lu4 tetrahedra, corners with four equivalent O(4)Lu3Al tetrahedra, corners with six equivalent O(2)Lu3Al trigonal pyramids, edges with three equivalent O(1)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Al trigonal pyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Al(1) atom to form distorted OLu3Al trigonal pyramids that share corners with two equivalent O(4)Lu3Al tetrahedra, corners with six equivalent O(1)Lu4 tetrahedra, corners with two equivalent O(2)Lu3Al trigonal pyramids,  an edgeedge with one O(4)Lu3Al tetrahedra,  an edgeedge with one O(1)Lu4 tetrahedra, and  an edgeedge with one O(2)Lu3Al trigonal pyramid. In the third O site, O(3) is bonded in a distorted single-bond geometry to four equivalent Lu(1) and one Al(1) atom. In the fourth O site, O(4) is bonded to one Lu(2), two equivalent Lu(1), and one Al(1) atom to form distorted OLu3Al tetrahedra that share corners with eight equivalent O(1)Lu4 tetrahedra, corners with four equivalent O(2)Lu3Al trigonal pyramids, and edges with two equivalent O(2)Lu3Al trigonal pyramids.