The material described by 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. is represented by the CIF file [CIF]
data_TiV15O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.559
_cell_length_b   9.149
_cell_length_c   9.160
_cell_angle_alpha   68.368
_cell_angle_beta   84.899
_cell_angle_gamma   84.848
_symmetry_Int_Tables_number   1
_cell_volume   430.569
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.294  0.072  0.071  1.0
  V  V1  1  0.799  0.578  0.073  1.0
  V  V2  1  0.699  0.179  0.173  1.0
  V  V3  1  0.701  0.425  0.427  1.0
  V  V4  1  0.197  0.672  0.178  1.0
  V  V5  1  0.799  0.824  0.324  1.0
  V  V6  1  0.801  0.074  0.574  1.0
  V  V7  1  0.299  0.325  0.325  1.0
  V  V8  1  0.797  0.324  0.825  1.0
  V  V9  1  0.203  0.172  0.673  1.0
  V  V10  1  0.298  0.573  0.576  1.0
  V  V11  1  0.701  0.675  0.676  1.0
  V  V12  1  0.204  0.925  0.425  1.0
  V  V13  1  0.203  0.427  0.927  1.0
  V  V14  1  0.303  0.827  0.823  1.0
  V  V15  1  0.699  0.925  0.925  1.0
  O  O16  1  0.848  0.377  0.026  1.0
  O  O17  1  0.010  0.031  0.214  1.0
  O  O18  1  0.345  0.274  0.127  1.0
  O  O19  1  0.997  0.471  0.278  1.0
  O  O20  1  0.851  0.776  0.129  1.0
  O  O21  1  0.339  0.882  0.032  1.0
  O  O22  1  0.496  0.527  0.225  1.0
  O  O23  1  0.654  0.222  0.374  1.0
  O  O24  1  0.850  0.277  0.627  1.0
  O  O25  1  0.502  0.974  0.273  1.0
  O  O26  1  0.153  0.124  0.470  1.0
  O  O27  1  0.651  0.624  0.475  1.0
  O  O28  1  0.849  0.875  0.523  1.0
  O  O29  1  0.347  0.373  0.529  1.0
  O  O30  1  0.501  0.030  0.720  1.0
  O  O31  1  0.998  0.525  0.724  1.0
  O  O32  1  0.153  0.723  0.376  1.0
  O  O33  1  0.349  0.776  0.625  1.0
  O  O34  1  0.496  0.471  0.779  1.0
  O  O35  1  0.005  0.975  0.774  1.0
  O  O36  1  0.647  0.129  0.974  1.0
  O  O37  1  0.158  0.216  0.884  1.0
  O  O38  1  0.650  0.720  0.875  1.0
  O  O39  1  0.156  0.627  0.973  1.0
[/CIF]
.
The material described by 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. is represented by the CIF file [CIF]
data_TiV15O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.559
_cell_length_b   9.149
_cell_length_c   9.160
_cell_angle_alpha   68.368
_cell_angle_beta   84.899
_cell_angle_gamma   84.848
_symmetry_Int_Tables_number   1
_cell_volume   430.569
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.294  0.072  0.071  1.0
  V  V1  1  0.799  0.578  0.073  1.0
  V  V2  1  0.699  0.179  0.173  1.0
  V  V3  1  0.701  0.425  0.427  1.0
  V  V4  1  0.197  0.672  0.178  1.0
  V  V5  1  0.799  0.824  0.324  1.0
  V  V6  1  0.801  0.074  0.574  1.0
  V  V7  1  0.299  0.325  0.325  1.0
  V  V8  1  0.797  0.324  0.825  1.0
  V  V9  1  0.203  0.172  0.673  1.0
  V  V10  1  0.298  0.573  0.576  1.0
  V  V11  1  0.701  0.675  0.676  1.0
  V  V12  1  0.204  0.925  0.425  1.0
  V  V13  1  0.203  0.427  0.927  1.0
  V  V14  1  0.303  0.827  0.823  1.0
  V  V15  1  0.699  0.925  0.925  1.0
  O  O16  1  0.848  0.377  0.026  1.0
  O  O17  1  0.010  0.031  0.214  1.0
  O  O18  1  0.345  0.274  0.127  1.0
  O  O19  1  0.997  0.471  0.278  1.0
  O  O20  1  0.851  0.776  0.129  1.0
  O  O21  1  0.339  0.882  0.032  1.0
  O  O22  1  0.496  0.527  0.225  1.0
  O  O23  1  0.654  0.222  0.374  1.0
  O  O24  1  0.850  0.277  0.627  1.0
  O  O25  1  0.502  0.974  0.273  1.0
  O  O26  1  0.153  0.124  0.470  1.0
  O  O27  1  0.651  0.624  0.475  1.0
  O  O28  1  0.849  0.875  0.523  1.0
  O  O29  1  0.347  0.373  0.529  1.0
  O  O30  1  0.501  0.030  0.720  1.0
  O  O31  1  0.998  0.525  0.724  1.0
  O  O32  1  0.153  0.723  0.376  1.0
  O  O33  1  0.349  0.776  0.625  1.0
  O  O34  1  0.496  0.471  0.779  1.0
  O  O35  1  0.005  0.975  0.774  1.0
  O  O36  1  0.647  0.129  0.974  1.0
  O  O37  1  0.158  0.216  0.884  1.0
  O  O38  1  0.650  0.720  0.875  1.0
  O  O39  1  0.156  0.627  0.973  1.0
[/CIF]
.