TiV15O24 is Ilmenite-like structured and crystallizes in the triclinic P1 space group. Ti(1) is bonded to one O(10), one O(2), one O(21), one O(22), one O(3), and one O(6) atom to form distorted TiO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with two equivalent V(8)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(15)O6 octahedra, and  a faceface with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-59°. There are fifteen inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(23), one O(24), one O(4), one O(5), and one O(7) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 46-60°. In the second V site, V(2) is bonded to one O(1), one O(10), one O(2), one O(21), one O(3), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent V(12)O6 octahedra, corners with two equivalent V(13)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. In the third V site, V(3) is bonded to one O(12), one O(14), one O(4), one O(7), one O(8), and one O(9) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. In the fourth V site, V(4) is bonded to one O(17), one O(24), one O(4), one O(5), one O(6), and one O(7) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra, corners with two equivalent V(15)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(14)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  a faceface with one V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. In the fifth V site, V(5) is bonded to one O(10), one O(12), one O(13), one O(17), one O(2), and one O(5) atom to form VO6 octahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and  a faceface with one V(12)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. In the sixth V site, V(6) is bonded to one O(11), one O(13), one O(15), one O(20), one O(8), and one O(9) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. In the seventh V site, V(7) is bonded to one O(11), one O(14), one O(3), one O(4), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(6)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-61°. In the eighth V site, V(8) is bonded to one O(1), one O(16), one O(19), one O(21), one O(22), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(13)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-61°. In the ninth V site, V(9) is bonded to one O(11), one O(14), one O(15), one O(20), one O(22), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent V(15)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(14)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one V(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-59°. In the tenth V site, V(10) is bonded to one O(12), one O(14), one O(16), one O(17), one O(18), and one O(19) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. In the eleventh V site, V(11) is bonded to one O(12), one O(13), one O(16), one O(18), one O(19), and one O(23) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. In the twelfth V site, V(12) is bonded to one O(10), one O(11), one O(13), one O(17), one O(18), and one O(2) atom to form VO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(11)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  a faceface with one V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. In the thirteenth V site, V(13) is bonded to one O(1), one O(16), one O(19), one O(22), one O(24), and one O(3) atom to form VO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(11)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra, and  a faceface with one V(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. In the fourteenth V site, V(14) is bonded to one O(15), one O(18), one O(20), one O(23), one O(24), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(15)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(6)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(15)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-60°. In the fifteenth V site, V(15) is bonded to one O(15), one O(20), one O(21), one O(23), one O(5), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(8)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(9)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  a faceface with one V(14)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one V(1), one V(13), one V(2), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(3)TiV3 trigonal pyramids, corners with two equivalent O(19)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(16)V4 trigonal pyramid, and  an edgeedge with one O(24)V4 trigonal pyramid. In the second O site, O(2) is bonded to one Ti(1), one V(12), one V(2), and one V(5) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(21)TiV3 trigonal pyramids, corners with two equivalent O(3)TiV3 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(17)V4 trigonal pyramid, and edges with two equivalent O(10)TiV3 trigonal pyramids. In the third O site, O(3) is bonded to one Ti(1), one V(13), one V(2), and one V(7) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(2)TiV3 trigonal pyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(10)TiV3 trigonal pyramid,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(22)TiV3 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the fourth O site, O(4) is bonded to one V(1), one V(3), one V(4), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(14)V4 trigonal pyramids, corners with two equivalent O(8)V4 trigonal pyramids,  an edgeedge with one O(24)V4 trigonal pyramid,  an edgeedge with one O(5)V4 trigonal pyramid, and edges with two equivalent O(7)V4 trigonal pyramids. In the fifth O site, O(5) is bonded to one V(1), one V(15), one V(4), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(6)TiV3 trigonal pyramids, corners with two equivalent O(7)V4 trigonal pyramids,  an edgeedge with one O(17)V4 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid,  an edgeedge with one O(24)V4 trigonal pyramid, and  an edgeedge with one O(4)V4 trigonal pyramid. In the sixth O site, O(6) is bonded to one Ti(1), one V(14), one V(15), and one V(4) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(20)V4 trigonal pyramids, corners with two equivalent O(5)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(15)V4 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid, and  an edgeedge with one O(24)V4 trigonal pyramid. In the seventh O site, O(7) is bonded to one V(1), one V(3), one V(4), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(24)V4 trigonal pyramids, corners with two equivalent O(5)V4 trigonal pyramids,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(8)V4 trigonal pyramid, and edges with two equivalent O(4)V4 trigonal pyramids. In the eighth O site, O(8) is bonded to one V(2), one V(3), one V(6), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(11)V4 trigonal pyramids, corners with two equivalent O(4)V4 trigonal pyramids,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(7)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the ninth O site, O(9) is bonded to one V(3), one V(6), one V(8), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(14)V4 trigonal pyramids, corners with two equivalent O(15)V4 trigonal pyramids,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(20)V4 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the tenth O site, O(10) is bonded to one Ti(1), one V(12), one V(2), and one V(5) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(13)V4 trigonal pyramids, corners with two equivalent O(17)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(3)TiV3 trigonal pyramid, and edges with two equivalent O(2)TiV3 trigonal pyramids. In the eleventh O site, O(11) is bonded to one V(12), one V(6), one V(7), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(15)V4 trigonal pyramids, corners with two equivalent O(8)V4 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(20)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the twelfth O site, O(12) is bonded to one V(10), one V(11), one V(3), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(16)V4 trigonal pyramids, corners with two equivalent O(17)V4 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(19)V4 trigonal pyramid. In the thirteenth O site, O(13) is bonded to one V(11), one V(12), one V(5), and one V(6) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(10)TiV3 trigonal pyramids, corners with two equivalent O(18)V4 trigonal pyramids,  an edgeedge with one O(2)TiV3 trigonal pyramid,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(12)V4 trigonal pyramid, and  an edgeedge with one O(17)V4 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one V(10), one V(3), one V(7), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(4)V4 trigonal pyramids, corners with two equivalent O(9)V4 trigonal pyramids,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(7)V4 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the fifteenth O site, O(15) is bonded to one V(14), one V(15), one V(6), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(11)V4 trigonal pyramids, corners with two equivalent O(9)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid, and edges with two equivalent O(20)V4 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one V(10), one V(11), one V(13), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(12)V4 trigonal pyramids, corners with two equivalent O(18)V4 trigonal pyramids,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid, and edges with two equivalent O(19)V4 trigonal pyramids. In the seventeenth O site, O(17) is bonded to one V(10), one V(12), one V(4), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(10)TiV3 trigonal pyramids, corners with two equivalent O(12)V4 trigonal pyramids,  an edgeedge with one O(2)TiV3 trigonal pyramid,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid. In the eighteenth O site, O(18) is bonded to one V(10), one V(11), one V(12), and one V(14) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid, corners with two equivalent O(13)V4 trigonal pyramids, corners with two equivalent O(16)V4 trigonal pyramids,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(17)V4 trigonal pyramid,  an edgeedge with one O(19)V4 trigonal pyramid, and  an edgeedge with one O(23)V4 trigonal pyramid. In the nineteenth O site, O(19) is bonded to one V(10), one V(11), one V(13), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(22)TiV3 trigonal pyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and edges with two equivalent O(16)V4 trigonal pyramids. In the twentieth O site, O(20) is bonded to one V(14), one V(15), one V(6), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(6)TiV3 trigonal pyramids, corners with two equivalent O(23)V4 trigonal pyramids,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(9)V4 trigonal pyramid, and edges with two equivalent O(15)V4 trigonal pyramids. In the twenty-first O site, O(21) is bonded to one Ti(1), one V(15), one V(2), and one V(8) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(2)TiV3 trigonal pyramids, corners with two equivalent O(22)TiV3 trigonal pyramids,  an edgeedge with one O(10)TiV3 trigonal pyramid,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(6)TiV3 trigonal pyramid, and  an edgeedge with one O(1)V4 trigonal pyramid. In the twenty-second O site, O(22) is bonded to one Ti(1), one V(13), one V(8), and one V(9) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid, corners with two equivalent O(21)TiV3 trigonal pyramids, corners with two equivalent O(19)V4 trigonal pyramids,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid,  an edgeedge with one O(16)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the twenty-third O site, O(23) is bonded to one V(1), one V(11), one V(14), and one V(15) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(20)V4 trigonal pyramids, corners with two equivalent O(24)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(15)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid. In the twenty-fourth O site, O(24) is bonded to one V(1), one V(13), one V(14), and one V(4) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(23)V4 trigonal pyramids, corners with two equivalent O(7)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid,  an edgeedge with one O(4)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid.
TiV15O24 is Ilmenite-like structured and crystallizes in the triclinic P1 space group. Ti(1) is bonded to one O(10), one O(2), one O(21), one O(22), one O(3), and one O(6) atom to form distorted TiO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with two equivalent V(8)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(15)O6 octahedra, and  a faceface with one V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-59°. The Ti(1)-O(10) bond length is 2.13 Å. The Ti(1)-O(2) bond length is 1.93 Å. The Ti(1)-O(21) bond length is 2.11 Å. The Ti(1)-O(22) bond length is 1.91 Å. The Ti(1)-O(3) bond length is 2.14 Å. The Ti(1)-O(6) bond length is 1.90 Å. There are fifteen inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(23), one O(24), one O(4), one O(5), and one O(7) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 46-60°. The V(1)-O(1) bond length is 2.03 Å. The V(1)-O(23) bond length is 2.00 Å. The V(1)-O(24) bond length is 2.13 Å. The V(1)-O(4) bond length is 2.13 Å. The V(1)-O(5) bond length is 2.11 Å. The V(1)-O(7) bond length is 2.06 Å. In the second V site, V(2) is bonded to one O(1), one O(10), one O(2), one O(21), one O(3), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent V(12)O6 octahedra, corners with two equivalent V(13)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. The V(2)-O(1) bond length is 2.01 Å. The V(2)-O(10) bond length is 2.11 Å. The V(2)-O(2) bond length is 2.07 Å. The V(2)-O(21) bond length is 2.08 Å. The V(2)-O(3) bond length is 2.09 Å. The V(2)-O(8) bond length is 2.01 Å. In the third V site, V(3) is bonded to one O(12), one O(14), one O(4), one O(7), one O(8), and one O(9) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. The V(3)-O(12) bond length is 2.02 Å. The V(3)-O(14) bond length is 2.12 Å. The V(3)-O(4) bond length is 2.01 Å. The V(3)-O(7) bond length is 2.12 Å. The V(3)-O(8) bond length is 2.12 Å. The V(3)-O(9) bond length is 2.03 Å. In the fourth V site, V(4) is bonded to one O(17), one O(24), one O(4), one O(5), one O(6), and one O(7) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra, corners with two equivalent V(15)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(14)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  a faceface with one V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. The V(4)-O(17) bond length is 2.03 Å. The V(4)-O(24) bond length is 2.10 Å. The V(4)-O(4) bond length is 2.10 Å. The V(4)-O(5) bond length is 2.08 Å. The V(4)-O(6) bond length is 2.07 Å. The V(4)-O(7) bond length is 2.01 Å. In the fifth V site, V(5) is bonded to one O(10), one O(12), one O(13), one O(17), one O(2), and one O(5) atom to form VO6 octahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and  a faceface with one V(12)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. The V(5)-O(10) bond length is 2.02 Å. The V(5)-O(12) bond length is 2.03 Å. The V(5)-O(13) bond length is 2.09 Å. The V(5)-O(17) bond length is 2.11 Å. The V(5)-O(2) bond length is 2.18 Å. The V(5)-O(5) bond length is 1.98 Å. In the sixth V site, V(6) is bonded to one O(11), one O(13), one O(15), one O(20), one O(8), and one O(9) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. The V(6)-O(11) bond length is 2.11 Å. The V(6)-O(13) bond length is 2.03 Å. The V(6)-O(15) bond length is 2.01 Å. The V(6)-O(20) bond length is 2.10 Å. The V(6)-O(8) bond length is 2.02 Å. The V(6)-O(9) bond length is 2.13 Å. In the seventh V site, V(7) is bonded to one O(11), one O(14), one O(3), one O(4), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(6)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-61°. The V(7)-O(11) bond length is 2.02 Å. The V(7)-O(14) bond length is 2.11 Å. The V(7)-O(3) bond length is 2.02 Å. The V(7)-O(4) bond length is 2.02 Å. The V(7)-O(7) bond length is 2.10 Å. The V(7)-O(8) bond length is 2.12 Å. In the eighth V site, V(8) is bonded to one O(1), one O(16), one O(19), one O(21), one O(22), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(15)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(13)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-61°. The V(8)-O(1) bond length is 2.12 Å. The V(8)-O(16) bond length is 2.10 Å. The V(8)-O(19) bond length is 2.02 Å. The V(8)-O(21) bond length is 2.00 Å. The V(8)-O(22) bond length is 2.18 Å. The V(8)-O(9) bond length is 2.01 Å. In the ninth V site, V(9) is bonded to one O(11), one O(14), one O(15), one O(20), one O(22), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(6)O6 octahedra, corners with two equivalent V(15)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(14)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one V(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-59°. The V(9)-O(11) bond length is 2.11 Å. The V(9)-O(14) bond length is 2.01 Å. The V(9)-O(15) bond length is 1.99 Å. The V(9)-O(20) bond length is 2.07 Å. The V(9)-O(22) bond length is 2.10 Å. The V(9)-O(9) bond length is 2.11 Å. In the tenth V site, V(10) is bonded to one O(12), one O(14), one O(16), one O(17), one O(18), and one O(19) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. The V(10)-O(12) bond length is 2.11 Å. The V(10)-O(14) bond length is 2.02 Å. The V(10)-O(16) bond length is 2.03 Å. The V(10)-O(17) bond length is 2.02 Å. The V(10)-O(18) bond length is 2.11 Å. The V(10)-O(19) bond length is 2.10 Å. In the eleventh V site, V(11) is bonded to one O(12), one O(13), one O(16), one O(18), one O(19), and one O(23) atom to form a mixture of corner, edge, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. The V(11)-O(12) bond length is 2.11 Å. The V(11)-O(13) bond length is 2.04 Å. The V(11)-O(16) bond length is 2.02 Å. The V(11)-O(18) bond length is 2.10 Å. The V(11)-O(19) bond length is 2.14 Å. The V(11)-O(23) bond length is 2.00 Å. In the twelfth V site, V(12) is bonded to one O(10), one O(11), one O(13), one O(17), one O(18), and one O(2) atom to form VO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(11)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  a faceface with one V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. The V(12)-O(10) bond length is 2.03 Å. The V(12)-O(11) bond length is 2.00 Å. The V(12)-O(13) bond length is 2.11 Å. The V(12)-O(17) bond length is 2.10 Å. The V(12)-O(18) bond length is 2.02 Å. The V(12)-O(2) bond length is 2.15 Å. In the thirteenth V site, V(13) is bonded to one O(1), one O(16), one O(19), one O(22), one O(24), and one O(3) atom to form VO6 octahedra that share  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(11)O6 octahedra, corners with two equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra, and  a faceface with one V(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-61°. The V(13)-O(1) bond length is 2.11 Å. The V(13)-O(16) bond length is 2.12 Å. The V(13)-O(19) bond length is 2.00 Å. The V(13)-O(22) bond length is 2.15 Å. The V(13)-O(24) bond length is 2.01 Å. The V(13)-O(3) bond length is 2.03 Å. In the fourteenth V site, V(14) is bonded to one O(15), one O(18), one O(20), one O(23), one O(24), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(15)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(6)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one V(15)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-60°. The V(14)-O(15) bond length is 2.10 Å. The V(14)-O(18) bond length is 2.03 Å. The V(14)-O(20) bond length is 2.02 Å. The V(14)-O(23) bond length is 2.10 Å. The V(14)-O(24) bond length is 2.03 Å. The V(14)-O(6) bond length is 2.18 Å. In the fifteenth V site, V(15) is bonded to one O(15), one O(20), one O(21), one O(23), one O(5), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(14)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(8)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(9)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  a faceface with one V(14)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-61°. The V(15)-O(15) bond length is 2.13 Å. The V(15)-O(20) bond length is 2.07 Å. The V(15)-O(21) bond length is 2.07 Å. The V(15)-O(23) bond length is 2.13 Å. The V(15)-O(5) bond length is 2.06 Å. The V(15)-O(6) bond length is 2.15 Å. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one V(1), one V(13), one V(2), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(3)TiV3 trigonal pyramids, corners with two equivalent O(19)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(16)V4 trigonal pyramid, and  an edgeedge with one O(24)V4 trigonal pyramid. In the second O site, O(2) is bonded to one Ti(1), one V(12), one V(2), and one V(5) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(21)TiV3 trigonal pyramids, corners with two equivalent O(3)TiV3 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(17)V4 trigonal pyramid, and edges with two equivalent O(10)TiV3 trigonal pyramids. In the third O site, O(3) is bonded to one Ti(1), one V(13), one V(2), and one V(7) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(2)TiV3 trigonal pyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(10)TiV3 trigonal pyramid,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(22)TiV3 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the fourth O site, O(4) is bonded to one V(1), one V(3), one V(4), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(14)V4 trigonal pyramids, corners with two equivalent O(8)V4 trigonal pyramids,  an edgeedge with one O(24)V4 trigonal pyramid,  an edgeedge with one O(5)V4 trigonal pyramid, and edges with two equivalent O(7)V4 trigonal pyramids. In the fifth O site, O(5) is bonded to one V(1), one V(15), one V(4), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(6)TiV3 trigonal pyramids, corners with two equivalent O(7)V4 trigonal pyramids,  an edgeedge with one O(17)V4 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid,  an edgeedge with one O(24)V4 trigonal pyramid, and  an edgeedge with one O(4)V4 trigonal pyramid. In the sixth O site, O(6) is bonded to one Ti(1), one V(14), one V(15), and one V(4) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(20)V4 trigonal pyramids, corners with two equivalent O(5)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(15)V4 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid, and  an edgeedge with one O(24)V4 trigonal pyramid. In the seventh O site, O(7) is bonded to one V(1), one V(3), one V(4), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(24)V4 trigonal pyramids, corners with two equivalent O(5)V4 trigonal pyramids,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(8)V4 trigonal pyramid, and edges with two equivalent O(4)V4 trigonal pyramids. In the eighth O site, O(8) is bonded to one V(2), one V(3), one V(6), and one V(7) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(11)V4 trigonal pyramids, corners with two equivalent O(4)V4 trigonal pyramids,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(7)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the ninth O site, O(9) is bonded to one V(3), one V(6), one V(8), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(14)V4 trigonal pyramids, corners with two equivalent O(15)V4 trigonal pyramids,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(20)V4 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the tenth O site, O(10) is bonded to one Ti(1), one V(12), one V(2), and one V(5) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(13)V4 trigonal pyramids, corners with two equivalent O(17)V4 trigonal pyramids,  an edgeedge with one O(21)TiV3 trigonal pyramid,  an edgeedge with one O(3)TiV3 trigonal pyramid, and edges with two equivalent O(2)TiV3 trigonal pyramids. In the eleventh O site, O(11) is bonded to one V(12), one V(6), one V(7), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(15)V4 trigonal pyramids, corners with two equivalent O(8)V4 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(20)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the twelfth O site, O(12) is bonded to one V(10), one V(11), one V(3), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(16)V4 trigonal pyramids, corners with two equivalent O(17)V4 trigonal pyramids,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(14)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(19)V4 trigonal pyramid. In the thirteenth O site, O(13) is bonded to one V(11), one V(12), one V(5), and one V(6) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(10)TiV3 trigonal pyramids, corners with two equivalent O(18)V4 trigonal pyramids,  an edgeedge with one O(2)TiV3 trigonal pyramid,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(12)V4 trigonal pyramid, and  an edgeedge with one O(17)V4 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one V(10), one V(3), one V(7), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(4)V4 trigonal pyramids, corners with two equivalent O(9)V4 trigonal pyramids,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(7)V4 trigonal pyramid, and  an edgeedge with one O(8)V4 trigonal pyramid. In the fifteenth O site, O(15) is bonded to one V(14), one V(15), one V(6), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(11)V4 trigonal pyramids, corners with two equivalent O(9)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(23)V4 trigonal pyramid, and edges with two equivalent O(20)V4 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one V(10), one V(11), one V(13), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(12)V4 trigonal pyramids, corners with two equivalent O(18)V4 trigonal pyramids,  an edgeedge with one O(22)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid, and edges with two equivalent O(19)V4 trigonal pyramids. In the seventeenth O site, O(17) is bonded to one V(10), one V(12), one V(4), and one V(5) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(10)TiV3 trigonal pyramids, corners with two equivalent O(12)V4 trigonal pyramids,  an edgeedge with one O(2)TiV3 trigonal pyramid,  an edgeedge with one O(13)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid. In the eighteenth O site, O(18) is bonded to one V(10), one V(11), one V(12), and one V(14) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid, corners with two equivalent O(13)V4 trigonal pyramids, corners with two equivalent O(16)V4 trigonal pyramids,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(17)V4 trigonal pyramid,  an edgeedge with one O(19)V4 trigonal pyramid, and  an edgeedge with one O(23)V4 trigonal pyramid. In the nineteenth O site, O(19) is bonded to one V(10), one V(11), one V(13), and one V(8) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(22)TiV3 trigonal pyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(12)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and edges with two equivalent O(16)V4 trigonal pyramids. In the twentieth O site, O(20) is bonded to one V(14), one V(15), one V(6), and one V(9) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid, corners with two equivalent O(6)TiV3 trigonal pyramids, corners with two equivalent O(23)V4 trigonal pyramids,  an edgeedge with one O(11)V4 trigonal pyramid,  an edgeedge with one O(9)V4 trigonal pyramid, and edges with two equivalent O(15)V4 trigonal pyramids. In the twenty-first O site, O(21) is bonded to one Ti(1), one V(15), one V(2), and one V(8) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(23)V4 trigonal pyramid,  a cornercorner with one O(5)V4 trigonal pyramid,  a cornercorner with one O(8)V4 trigonal pyramid,  a cornercorner with one O(9)V4 trigonal pyramid, corners with two equivalent O(2)TiV3 trigonal pyramids, corners with two equivalent O(22)TiV3 trigonal pyramids,  an edgeedge with one O(10)TiV3 trigonal pyramid,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(6)TiV3 trigonal pyramid, and  an edgeedge with one O(1)V4 trigonal pyramid. In the twenty-second O site, O(22) is bonded to one Ti(1), one V(13), one V(8), and one V(9) atom to form distorted OTiV3 trigonal pyramids that share  a cornercorner with one O(10)TiV3 trigonal pyramid,  a cornercorner with one O(2)TiV3 trigonal pyramid,  a cornercorner with one O(6)TiV3 trigonal pyramid,  a cornercorner with one O(11)V4 trigonal pyramid,  a cornercorner with one O(14)V4 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid,  a cornercorner with one O(24)V4 trigonal pyramid, corners with two equivalent O(21)TiV3 trigonal pyramids, corners with two equivalent O(19)V4 trigonal pyramids,  an edgeedge with one O(3)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid,  an edgeedge with one O(16)V4 trigonal pyramid, and  an edgeedge with one O(9)V4 trigonal pyramid. In the twenty-third O site, O(23) is bonded to one V(1), one V(11), one V(14), and one V(15) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(21)TiV3 trigonal pyramid,  a cornercorner with one O(1)V4 trigonal pyramid,  a cornercorner with one O(12)V4 trigonal pyramid,  a cornercorner with one O(13)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(4)V4 trigonal pyramid,  a cornercorner with one O(7)V4 trigonal pyramid, corners with two equivalent O(20)V4 trigonal pyramids, corners with two equivalent O(24)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(15)V4 trigonal pyramid,  an edgeedge with one O(18)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid. In the twenty-fourth O site, O(24) is bonded to one V(1), one V(13), one V(14), and one V(4) atom to form distorted OV4 trigonal pyramids that share  a cornercorner with one O(22)TiV3 trigonal pyramid,  a cornercorner with one O(3)TiV3 trigonal pyramid,  a cornercorner with one O(15)V4 trigonal pyramid,  a cornercorner with one O(16)V4 trigonal pyramid,  a cornercorner with one O(17)V4 trigonal pyramid,  a cornercorner with one O(18)V4 trigonal pyramid,  a cornercorner with one O(19)V4 trigonal pyramid,  a cornercorner with one O(20)V4 trigonal pyramid, corners with two equivalent O(23)V4 trigonal pyramids, corners with two equivalent O(7)V4 trigonal pyramids,  an edgeedge with one O(6)TiV3 trigonal pyramid,  an edgeedge with one O(1)V4 trigonal pyramid,  an edgeedge with one O(4)V4 trigonal pyramid, and  an edgeedge with one O(5)V4 trigonal pyramid.