Lu4V4O13 crystallizes in the cubic F-43m space group. Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 hexagonal pyramids that share corners with three equivalent Lu(1)O7 hexagonal pyramids, edges with three equivalent Lu(1)O7 hexagonal pyramids, and edges with six equivalent V(1)O6 octahedra. V(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form VO6 octahedra that share corners with six equivalent V(1)O6 octahedra and edges with six equivalent Lu(1)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 53-55°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form distorted OLu2V2 tetrahedra that share corners with four equivalent O(2)Lu2V2 tetrahedra, corners with eight equivalent O(1)Lu2V2 tetrahedra,  an edgeedge with one O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu2V2 tetrahedra. In the second O site, O(2) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form OLu2V2 tetrahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(1)Lu2V2 tetrahedra, corners with eight equivalent O(2)Lu2V2 tetrahedra, and edges with four equivalent O(1)Lu2V2 tetrahedra. In the third O site, O(3) is bonded to four equivalent Lu(1) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra.
Lu4V4O13 crystallizes in the cubic F-43m space group. Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 hexagonal pyramids that share corners with three equivalent Lu(1)O7 hexagonal pyramids, edges with three equivalent Lu(1)O7 hexagonal pyramids, and edges with six equivalent V(1)O6 octahedra. The Lu(1)-O(3) bond length is 2.13 Å. All Lu(1)-O(1) bond lengths are 2.38 Å. All Lu(1)-O(2) bond lengths are 2.38 Å. V(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form VO6 octahedra that share corners with six equivalent V(1)O6 octahedra and edges with six equivalent Lu(1)O7 hexagonal pyramids. The corner-sharing octahedral tilt angles range from 53-55°. All V(1)-O(1) bond lengths are 1.97 Å. All V(1)-O(2) bond lengths are 2.00 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form distorted OLu2V2 tetrahedra that share corners with four equivalent O(2)Lu2V2 tetrahedra, corners with eight equivalent O(1)Lu2V2 tetrahedra,  an edgeedge with one O(3)Lu4 tetrahedra, and edges with four equivalent O(2)Lu2V2 tetrahedra. In the second O site, O(2) is bonded to two equivalent Lu(1) and two equivalent V(1) atoms to form OLu2V2 tetrahedra that share corners with two equivalent O(3)Lu4 tetrahedra, corners with four equivalent O(1)Lu2V2 tetrahedra, corners with eight equivalent O(2)Lu2V2 tetrahedra, and edges with four equivalent O(1)Lu2V2 tetrahedra. In the third O site, O(3) is bonded to four equivalent Lu(1) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra.