Na5Lu(WO4)4 crystallizes in the tetragonal I4_1/a space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded to four equivalent O(2) atoms to form distorted NaO4 tetrahedra that share corners with eight equivalent Na(2)O6 pentagonal pyramids and corners with four equivalent W(1)O4 tetrahedra. In the second Na site, Na(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted NaO6 pentagonal pyramids that share corners with two equivalent Na(1)O4 tetrahedra, corners with six equivalent W(1)O4 tetrahedra, and edges with two equivalent Na(2)O6 pentagonal pyramids. Lu(1) is bonded in a 8-coordinate geometry to four equivalent O(3) and four equivalent O(4) atoms. W(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form WO4 tetrahedra that share corners with six equivalent Na(2)O6 pentagonal pyramids and  a cornercorner with one Na(1)O4 tetrahedra. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted trigonal planar geometry to one Na(2), one Lu(1), and one W(1) atom. In the second O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(2) and one W(1) atom. In the third O site, O(2) is bonded to one Na(1), two equivalent Na(2), and one W(1) atom to form distorted corner-sharing ONa3W tetrahedra. In the fourth O site, O(3) is bonded in a distorted trigonal planar geometry to one Na(2), one Lu(1), and one W(1) atom.
Na5Lu(WO4)4 crystallizes in the tetragonal I4_1/a space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded to four equivalent O(2) atoms to form distorted NaO4 tetrahedra that share corners with eight equivalent Na(2)O6 pentagonal pyramids and corners with four equivalent W(1)O4 tetrahedra. All Na(1)-O(2) bond lengths are 2.43 Å. In the second Na site, Na(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted NaO6 pentagonal pyramids that share corners with two equivalent Na(1)O4 tetrahedra, corners with six equivalent W(1)O4 tetrahedra, and edges with two equivalent Na(2)O6 pentagonal pyramids. The Na(2)-O(3) bond length is 2.44 Å. The Na(2)-O(4) bond length is 2.38 Å. There is one shorter (2.33 Å) and one longer (2.46 Å) Na(2)-O(1) bond length. There is one shorter (2.40 Å) and one longer (2.53 Å) Na(2)-O(2) bond length. Lu(1) is bonded in a 8-coordinate geometry to four equivalent O(3) and four equivalent O(4) atoms. All Lu(1)-O(3) bond lengths are 2.33 Å. All Lu(1)-O(4) bond lengths are 2.34 Å. W(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form WO4 tetrahedra that share corners with six equivalent Na(2)O6 pentagonal pyramids and  a cornercorner with one Na(1)O4 tetrahedra. The W(1)-O(1) bond length is 1.80 Å. The W(1)-O(2) bond length is 1.81 Å. The W(1)-O(3) bond length is 1.83 Å. The W(1)-O(4) bond length is 1.86 Å. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted trigonal planar geometry to one Na(2), one Lu(1), and one W(1) atom. In the second O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(2) and one W(1) atom. In the third O site, O(2) is bonded to one Na(1), two equivalent Na(2), and one W(1) atom to form distorted corner-sharing ONa3W tetrahedra. In the fourth O site, O(3) is bonded in a distorted trigonal planar geometry to one Na(2), one Lu(1), and one W(1) atom.