BaV13O18 crystallizes in the trigonal R-3 space group. Ba(1) is bonded to six equivalent O(2) and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent V(2)O6 octahedra, corners with eighteen equivalent V(1)O6 octahedra, faces with two equivalent V(3)O6 octahedra, and faces with six equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-50°. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(2), two equivalent O(3), and three equivalent O(1) atoms to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(2)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with three equivalent V(1)O6 octahedra, and edges with five equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-9°. In the second V site, V(2) is bonded to one O(3), two equivalent O(1), and three equivalent O(2) atoms to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(2)O6 octahedra, edges with three equivalent V(2)O6 octahedra, edges with five equivalent V(1)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-13°. In the third V site, V(3) is bonded to six equivalent O(3) atoms to form VO6 octahedra that share corners with six equivalent V(2)O6 octahedra, edges with six equivalent V(1)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent V(2) and three equivalent V(1) atoms to form a mixture of edge and corner-sharing OV5 square pyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), and three equivalent V(2) atoms. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(2), one V(3), and two equivalent V(1) atoms.
BaV13O18 crystallizes in the trigonal R-3 space group. Ba(1) is bonded to six equivalent O(2) and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with six equivalent V(2)O6 octahedra, corners with eighteen equivalent V(1)O6 octahedra, faces with two equivalent V(3)O6 octahedra, and faces with six equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-50°. All Ba(1)-O(2) bond lengths are 3.14 Å. All Ba(1)-O(3) bond lengths are 3.24 Å. There are three inequivalent V sites. In the first V site, V(1) is bonded to one O(2), two equivalent O(3), and three equivalent O(1) atoms to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(2)O6 octahedra, corners with two equivalent V(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with three equivalent V(1)O6 octahedra, and edges with five equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-9°. The V(1)-O(2) bond length is 2.03 Å. There is one shorter (2.02 Å) and one longer (2.04 Å) V(1)-O(3) bond length. There are a spread of V(1)-O(1) bond distances ranging from 2.09-2.17 Å. In the second V site, V(2) is bonded to one O(3), two equivalent O(1), and three equivalent O(2) atoms to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(2)O6 octahedra, edges with three equivalent V(2)O6 octahedra, edges with five equivalent V(1)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-13°. The V(2)-O(3) bond length is 2.12 Å. There is one shorter (2.12 Å) and one longer (2.24 Å) V(2)-O(1) bond length. There are a spread of V(2)-O(2) bond distances ranging from 2.07-2.14 Å. In the third V site, V(3) is bonded to six equivalent O(3) atoms to form VO6 octahedra that share corners with six equivalent V(2)O6 octahedra, edges with six equivalent V(1)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. All V(3)-O(3) bond lengths are 2.14 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent V(2) and three equivalent V(1) atoms to form a mixture of edge and corner-sharing OV5 square pyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), and three equivalent V(2) atoms. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(2), one V(3), and two equivalent V(1) atoms.