The material structure described by Li2CoTi3O8 is Spinel-derived structured and crystallizes in the triclinic P1 space group. There are eight inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(27), one O(30), and one O(31) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Ti(9)O6 octahedra, and corners with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the second Li site, Li(2) is bonded to one O(2), one O(28), one O(29), and one O(32) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra, corners with two equivalent Ti(10)O6 octahedra, and corners with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the third Li site, Li(3) is bonded to one O(21), one O(24), one O(25), and one O(3) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(9)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, and corners with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the fourth Li site, Li(4) is bonded to one O(22), one O(23), one O(26), and one O(4) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(10)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, and corners with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the fifth Li site, Li(5) is bonded in a distorted rectangular see-saw-like geometry to one O(13), one O(18), one O(19), and one O(8) atom. In the sixth Li site, Li(6) is bonded in a distorted rectangular see-saw-like geometry to one O(14), one O(17), one O(20), and one O(7) atom. In the seventh Li site, Li(7) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(11), one O(16), and one O(5) atom. In the eighth Li site, Li(8) is bonded in a distorted rectangular see-saw-like geometry to one O(12), one O(15), one O(6), and one O(9) atom. There are twelve inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(14), one O(17), one O(21), one O(23), and one O(6) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Ti site, Ti(2) is bonded to one O(13), one O(18), one O(2), one O(22), one O(24), and one O(5) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the third Ti site, Ti(3) is bonded to one O(1), one O(13), one O(19), one O(21), one O(25), and one O(5) atom to form TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the fourth Ti site, Ti(4) is bonded to one O(14), one O(2), one O(20), one O(22), one O(26), and one O(6) atom to form TiO6 octahedra that share corners with two equivalent Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and  an edgeedge with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the fifth Ti site, Ti(5) is bonded to one O(1), one O(17), one O(20), one O(23), one O(25), and one O(6) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the sixth Ti site, Ti(6) is bonded to one O(18), one O(19), one O(2), one O(24), one O(26), and one O(5) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the seventh Ti site, Ti(7) is bonded to one O(10), one O(11), one O(27), one O(29), one O(3), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(11)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the eighth Ti site, Ti(8) is bonded to one O(12), one O(28), one O(30), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(12)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the ninth Ti site, Ti(9) is bonded to one O(15), one O(27), one O(3), one O(31), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent Co(3)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra,  an edgeedge with one Ti(8)O6 octahedra, and  an edgeedge with one Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the tenth Ti site, Ti(10) is bonded to one O(10), one O(16), one O(28), one O(32), one O(4), and one O(8) atom to form TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra,  an edgeedge with one Ti(8)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the eleventh Ti site, Ti(11) is bonded to one O(11), one O(16), one O(29), one O(3), one O(31), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the twelfth Ti site, Ti(12) is bonded to one O(12), one O(15), one O(30), one O(32), one O(4), and one O(7) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(8)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(10), one O(12), one O(16), one O(22), one O(24), and one O(26) atom to form CoO6 octahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra, corners with two equivalent Ti(10)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and  an edgeedge with one Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the second Co site, Co(2) is bonded to one O(13), one O(17), one O(19), one O(27), one O(29), and one O(31) atom to form CoO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and  an edgeedge with one Ti(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the third Co site, Co(3) is bonded to one O(11), one O(15), one O(21), one O(23), one O(25), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra, corners with two equivalent Ti(9)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and  an edgeedge with one Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the fourth Co site, Co(4) is bonded to one O(14), one O(18), one O(20), one O(28), one O(30), and one O(32) atom to form CoO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra, and  an edgeedge with one Ti(8)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are thirty-two inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(1), one Ti(3), and one Ti(5) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra, corners with two equivalent O(6)LiTi3 tetrahedra,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(23)LiTi2Co tetrahedra, and  an edgeedge with one O(25)LiTi2Co tetrahedra. In the second O site, O(2) is bonded to one Li(2), one Ti(2), one Ti(4), and one Ti(6) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra, corners with two equivalent O(5)LiTi3 tetrahedra,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(24)LiTi2Co tetrahedra, and  an edgeedge with one O(26)LiTi2Co tetrahedra. In the third O site, O(3) is bonded to one Li(3), one Ti(11), one Ti(7), and one Ti(9) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra, corners with two equivalent O(8)LiTi3 tetrahedra,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(29)LiTi2Co tetrahedra, and  an edgeedge with one O(31)LiTi2Co tetrahedra. In the fourth O site, O(4) is bonded to one Li(4), one Ti(10), one Ti(12), and one Ti(8) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra, corners with two equivalent O(7)LiTi3 tetrahedra,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(30)LiTi2Co tetrahedra, and  an edgeedge with one O(32)LiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(7), one Ti(2), one Ti(3), and one Ti(6) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(24)LiTi2Co tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid, and corners with two equivalent O(2)LiTi3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(8), one Ti(1), one Ti(4), and one Ti(5) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(23)LiTi2Co tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid, and corners with two equivalent O(1)LiTi3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Li(6), one Ti(12), one Ti(8), and one Ti(9) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(30)LiTi2Co tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid, and corners with two equivalent O(4)LiTi3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Li(5), one Ti(10), one Ti(11), and one Ti(7) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(29)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid, and corners with two equivalent O(3)LiTi3 trigonal pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(8), one Ti(9), and one Co(3) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(7), one Ti(10), one Ti(7), and one Co(1) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(7), one Ti(11), one Ti(7), and one Co(3) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(12), one Ti(8), and one Co(1) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(2), one Ti(3), and one Co(2) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(6), one Ti(1), one Ti(4), and one Co(4) atom. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(12), one Ti(9), and one Co(3) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Li(7), one Ti(10), one Ti(11), and one Co(1) atom. In the seventeenth O site, O(17) is bonded in a distorted rectangular see-saw-like geometry to one Li(6), one Ti(1), one Ti(5), and one Co(2) atom. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(2), one Ti(6), and one Co(4) atom. In the nineteenth O site, O(19) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(3), one Ti(6), and one Co(2) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Li(6), one Ti(4), one Ti(5), and one Co(4) atom. In the twenty-first O site, O(21) is bonded to one Li(3), one Ti(1), one Ti(3), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(23)LiTi2Co tetrahedra,  an edgeedge with one O(25)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-second O site, O(22) is bonded to one Li(4), one Ti(2), one Ti(4), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(24)LiTi2Co tetrahedra,  an edgeedge with one O(26)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-third O site, O(23) is bonded to one Li(4), one Ti(1), one Ti(5), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(25)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-fourth O site, O(24) is bonded to one Li(3), one Ti(2), one Ti(6), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra, corners with two equivalent O(5)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(26)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-fifth O site, O(25) is bonded to one Li(3), one Ti(3), one Ti(5), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(23)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-sixth O site, O(26) is bonded to one Li(4), one Ti(4), one Ti(6), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(24)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-seventh O site, O(27) is bonded to one Li(1), one Ti(7), one Ti(9), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(29)LiTi2Co tetrahedra,  an edgeedge with one O(31)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the twenty-eighth O site, O(28) is bonded to one Li(2), one Ti(10), one Ti(8), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(30)LiTi2Co tetrahedra,  an edgeedge with one O(32)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. In the twenty-ninth O site, O(29) is bonded to one Li(2), one Ti(11), one Ti(7), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(31)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the thirtieth O site, O(30) is bonded to one Li(1), one Ti(12), one Ti(8), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra, corners with two equivalent O(7)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(32)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. In the thirty-first O site, O(31) is bonded to one Li(1), one Ti(11), one Ti(9), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(29)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the thirty-second O site, O(32) is bonded to one Li(2), one Ti(10), one Ti(12), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(30)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. is represented by the CIF file [CIF]
data_Li2Ti3CoO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.945
_cell_length_b   5.945
_cell_length_c   9.770
_cell_angle_alpha   90.016
_cell_angle_beta   90.000
_cell_angle_gamma   60.005
_symmetry_Int_Tables_number   1
_cell_volume   299.051
_cell_formula_units_Z   2
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
  Co  Co0  1  0.335  0.333  0.506  1.0
  Co  Co1  1  0.669  0.665  0.006  1.0
  Li  Li2  1  0.333  0.333  0.110  1.0
  Li  Li3  1  0.667  0.667  0.610  1.0
  Li  Li4  1  1.000  1.000  0.001  1.0
  Li  Li5  1  0.000  0.000  0.501  1.0
  O  O6  1  0.333  0.334  0.895  1.0
  O  O7  1  0.667  0.667  0.395  1.0
  O  O8  1  1.000  0.000  0.685  1.0
  O  O9  1  1.000  0.000  0.185  1.0
  O  O10  1  0.158  0.684  0.393  1.0
  O  O11  1  0.684  0.158  0.393  1.0
  O  O12  1  0.842  0.842  0.893  1.0
  O  O13  1  0.158  0.158  0.393  1.0
  O  O14  1  0.316  0.842  0.893  1.0
  O  O15  1  0.842  0.317  0.893  1.0
  O  O16  1  0.482  0.483  0.672  1.0
  O  O17  1  0.035  0.483  0.672  1.0
  O  O18  1  0.482  0.035  0.672  1.0
  O  O19  1  0.517  0.965  0.172  1.0
  O  O20  1  0.965  0.517  0.172  1.0
  O  O21  1  0.517  0.517  0.172  1.0
  Ti  Ti22  1  0.168  0.663  0.784  1.0
  Ti  Ti23  1  0.662  0.169  0.784  1.0
  Ti  Ti24  1  0.169  0.169  0.785  1.0
  Ti  Ti25  1  0.831  0.831  0.285  1.0
  Ti  Ti26  1  0.337  0.832  0.285  1.0
  Ti  Ti27  1  0.831  0.338  0.284  1.0
[/CIF]
.
The material structure described by Li2CoTi3O8 is Spinel-derived structured and crystallizes in the triclinic P1 space group. There are eight inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(27), one O(30), and one O(31) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Ti(9)O6 octahedra, and corners with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the second Li site, Li(2) is bonded to one O(2), one O(28), one O(29), and one O(32) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra, corners with two equivalent Ti(10)O6 octahedra, and corners with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the third Li site, Li(3) is bonded to one O(21), one O(24), one O(25), and one O(3) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(9)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, and corners with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the fourth Li site, Li(4) is bonded to one O(22), one O(23), one O(26), and one O(4) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(10)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, and corners with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the fifth Li site, Li(5) is bonded in a distorted rectangular see-saw-like geometry to one O(13), one O(18), one O(19), and one O(8) atom. In the sixth Li site, Li(6) is bonded in a distorted rectangular see-saw-like geometry to one O(14), one O(17), one O(20), and one O(7) atom. In the seventh Li site, Li(7) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(11), one O(16), and one O(5) atom. In the eighth Li site, Li(8) is bonded in a distorted rectangular see-saw-like geometry to one O(12), one O(15), one O(6), and one O(9) atom. There are twelve inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(14), one O(17), one O(21), one O(23), and one O(6) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Ti site, Ti(2) is bonded to one O(13), one O(18), one O(2), one O(22), one O(24), and one O(5) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the third Ti site, Ti(3) is bonded to one O(1), one O(13), one O(19), one O(21), one O(25), and one O(5) atom to form TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the fourth Ti site, Ti(4) is bonded to one O(14), one O(2), one O(20), one O(22), one O(26), and one O(6) atom to form TiO6 octahedra that share corners with two equivalent Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and  an edgeedge with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the fifth Ti site, Ti(5) is bonded to one O(1), one O(17), one O(20), one O(23), one O(25), and one O(6) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the sixth Ti site, Ti(6) is bonded to one O(18), one O(19), one O(2), one O(24), one O(26), and one O(5) atom to form TiO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the seventh Ti site, Ti(7) is bonded to one O(10), one O(11), one O(27), one O(29), one O(3), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(11)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the eighth Ti site, Ti(8) is bonded to one O(12), one O(28), one O(30), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(12)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the ninth Ti site, Ti(9) is bonded to one O(15), one O(27), one O(3), one O(31), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent Co(3)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra,  an edgeedge with one Ti(8)O6 octahedra, and  an edgeedge with one Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the tenth Ti site, Ti(10) is bonded to one O(10), one O(16), one O(28), one O(32), one O(4), and one O(8) atom to form TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra,  an edgeedge with one Ti(8)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the eleventh Ti site, Ti(11) is bonded to one O(11), one O(16), one O(29), one O(3), one O(31), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the twelfth Ti site, Ti(12) is bonded to one O(12), one O(15), one O(30), one O(32), one O(4), and one O(7) atom to form TiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(9)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(8)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(10), one O(12), one O(16), one O(22), one O(24), and one O(26) atom to form CoO6 octahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra, corners with two equivalent Ti(10)O6 octahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and  an edgeedge with one Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the second Co site, Co(2) is bonded to one O(13), one O(17), one O(19), one O(27), one O(29), and one O(31) atom to form CoO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(11)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and  an edgeedge with one Ti(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the third Co site, Co(3) is bonded to one O(11), one O(15), one O(21), one O(23), one O(25), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Ti(11)O6 octahedra,  a cornercorner with one Ti(12)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  a cornercorner with one Ti(8)O6 octahedra, corners with two equivalent Ti(9)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and  an edgeedge with one Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the fourth Co site, Co(4) is bonded to one O(14), one O(18), one O(20), one O(28), one O(30), and one O(32) atom to form CoO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(10)O6 octahedra,  an edgeedge with one Ti(12)O6 octahedra, and  an edgeedge with one Ti(8)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are thirty-two inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(1), one Ti(3), and one Ti(5) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra, corners with two equivalent O(6)LiTi3 tetrahedra,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(23)LiTi2Co tetrahedra, and  an edgeedge with one O(25)LiTi2Co tetrahedra. In the second O site, O(2) is bonded to one Li(2), one Ti(2), one Ti(4), and one Ti(6) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra, corners with two equivalent O(5)LiTi3 tetrahedra,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(24)LiTi2Co tetrahedra, and  an edgeedge with one O(26)LiTi2Co tetrahedra. In the third O site, O(3) is bonded to one Li(3), one Ti(11), one Ti(7), and one Ti(9) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra, corners with two equivalent O(8)LiTi3 tetrahedra,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(29)LiTi2Co tetrahedra, and  an edgeedge with one O(31)LiTi2Co tetrahedra. In the fourth O site, O(4) is bonded to one Li(4), one Ti(10), one Ti(12), and one Ti(8) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra, corners with two equivalent O(7)LiTi3 tetrahedra,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(30)LiTi2Co tetrahedra, and  an edgeedge with one O(32)LiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(7), one Ti(2), one Ti(3), and one Ti(6) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(24)LiTi2Co tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid, and corners with two equivalent O(2)LiTi3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(8), one Ti(1), one Ti(4), and one Ti(5) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(23)LiTi2Co tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid, and corners with two equivalent O(1)LiTi3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Li(6), one Ti(12), one Ti(8), and one Ti(9) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(30)LiTi2Co tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid, and corners with two equivalent O(4)LiTi3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Li(5), one Ti(10), one Ti(11), and one Ti(7) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(29)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid, and corners with two equivalent O(3)LiTi3 trigonal pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(8), one Ti(9), and one Co(3) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(7), one Ti(10), one Ti(7), and one Co(1) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(7), one Ti(11), one Ti(7), and one Co(3) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(12), one Ti(8), and one Co(1) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(2), one Ti(3), and one Co(2) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(6), one Ti(1), one Ti(4), and one Co(4) atom. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Li(8), one Ti(12), one Ti(9), and one Co(3) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Li(7), one Ti(10), one Ti(11), and one Co(1) atom. In the seventeenth O site, O(17) is bonded in a distorted rectangular see-saw-like geometry to one Li(6), one Ti(1), one Ti(5), and one Co(2) atom. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(2), one Ti(6), and one Co(4) atom. In the nineteenth O site, O(19) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(3), one Ti(6), and one Co(2) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Li(6), one Ti(4), one Ti(5), and one Co(4) atom. In the twenty-first O site, O(21) is bonded to one Li(3), one Ti(1), one Ti(3), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(23)LiTi2Co tetrahedra,  an edgeedge with one O(25)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-second O site, O(22) is bonded to one Li(4), one Ti(2), one Ti(4), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(24)LiTi2Co tetrahedra,  an edgeedge with one O(26)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-third O site, O(23) is bonded to one Li(4), one Ti(1), one Ti(5), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(26)LiTi2Co tetrahedra, corners with two equivalent O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(25)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-fourth O site, O(24) is bonded to one Li(3), one Ti(2), one Ti(6), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(25)LiTi2Co tetrahedra, corners with two equivalent O(5)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(26)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-fifth O site, O(25) is bonded to one Li(3), one Ti(3), one Ti(5), and one Co(3) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(21)LiTi2Co tetrahedra,  a cornercorner with one O(24)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(21)LiTi2Co tetrahedra,  an edgeedge with one O(23)LiTi2Co tetrahedra, and  an edgeedge with one O(1)LiTi3 trigonal pyramid. In the twenty-sixth O site, O(26) is bonded to one Li(4), one Ti(4), one Ti(6), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(22)LiTi2Co tetrahedra,  a cornercorner with one O(23)LiTi2Co tetrahedra,  a cornercorner with one O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 tetrahedra,  a cornercorner with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(22)LiTi2Co tetrahedra,  an edgeedge with one O(24)LiTi2Co tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the twenty-seventh O site, O(27) is bonded to one Li(1), one Ti(7), one Ti(9), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(29)LiTi2Co tetrahedra,  an edgeedge with one O(31)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the twenty-eighth O site, O(28) is bonded to one Li(2), one Ti(10), one Ti(8), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(30)LiTi2Co tetrahedra,  an edgeedge with one O(32)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. In the twenty-ninth O site, O(29) is bonded to one Li(2), one Ti(11), one Ti(7), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(32)LiTi2Co tetrahedra, corners with two equivalent O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(31)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the thirtieth O site, O(30) is bonded to one Li(1), one Ti(12), one Ti(8), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(31)LiTi2Co tetrahedra, corners with two equivalent O(7)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(32)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. In the thirty-first O site, O(31) is bonded to one Li(1), one Ti(11), one Ti(9), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(27)LiTi2Co tetrahedra,  a cornercorner with one O(30)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  an edgeedge with one O(27)LiTi2Co tetrahedra,  an edgeedge with one O(29)LiTi2Co tetrahedra, and  an edgeedge with one O(3)LiTi3 trigonal pyramid. In the thirty-second O site, O(32) is bonded to one Li(2), one Ti(10), one Ti(12), and one Co(4) atom to form distorted OLiTi2Co tetrahedra that share  a cornercorner with one O(28)LiTi2Co tetrahedra,  a cornercorner with one O(29)LiTi2Co tetrahedra,  a cornercorner with one O(7)LiTi3 tetrahedra,  a cornercorner with one O(8)LiTi3 tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(28)LiTi2Co tetrahedra,  an edgeedge with one O(30)LiTi2Co tetrahedra, and  an edgeedge with one O(4)LiTi3 trigonal pyramid. is represented by the CIF file [CIF]
data_Li2Ti3CoO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.945
_cell_length_b   5.945
_cell_length_c   9.770
_cell_angle_alpha   90.016
_cell_angle_beta   90.000
_cell_angle_gamma   60.005
_symmetry_Int_Tables_number   1
_cell_volume   299.051
_cell_formula_units_Z   2
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
  Co  Co0  1  0.335  0.333  0.506  1.0
  Co  Co1  1  0.669  0.665  0.006  1.0
  Li  Li2  1  0.333  0.333  0.110  1.0
  Li  Li3  1  0.667  0.667  0.610  1.0
  Li  Li4  1  1.000  1.000  0.001  1.0
  Li  Li5  1  0.000  0.000  0.501  1.0
  O  O6  1  0.333  0.334  0.895  1.0
  O  O7  1  0.667  0.667  0.395  1.0
  O  O8  1  1.000  0.000  0.685  1.0
  O  O9  1  1.000  0.000  0.185  1.0
  O  O10  1  0.158  0.684  0.393  1.0
  O  O11  1  0.684  0.158  0.393  1.0
  O  O12  1  0.842  0.842  0.893  1.0
  O  O13  1  0.158  0.158  0.393  1.0
  O  O14  1  0.316  0.842  0.893  1.0
  O  O15  1  0.842  0.317  0.893  1.0
  O  O16  1  0.482  0.483  0.672  1.0
  O  O17  1  0.035  0.483  0.672  1.0
  O  O18  1  0.482  0.035  0.672  1.0
  O  O19  1  0.517  0.965  0.172  1.0
  O  O20  1  0.965  0.517  0.172  1.0
  O  O21  1  0.517  0.517  0.172  1.0
  Ti  Ti22  1  0.168  0.663  0.784  1.0
  Ti  Ti23  1  0.662  0.169  0.784  1.0
  Ti  Ti24  1  0.169  0.169  0.785  1.0
  Ti  Ti25  1  0.831  0.831  0.285  1.0
  Ti  Ti26  1  0.337  0.832  0.285  1.0
  Ti  Ti27  1  0.831  0.338  0.284  1.0
[/CIF]
.