The crystal structure described by LiTi4O8 crystallizes in the triclinic P1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded in a rectangular see-saw-like geometry to one O(15), one O(16), one O(8), and one O(9) atom. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(10), one O(12), one O(13), and one O(18) atom. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(11), one O(12), one O(14), and one O(19) atom. There are twelve inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(20), one O(21), one O(24), one O(4), and one O(6) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the second Ti site, Ti(2) is bonded to one O(1), one O(17), one O(23), one O(24), one O(4), and one O(8) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the third Ti site, Ti(3) is bonded to one O(1), one O(18), one O(22), one O(23), one O(3), and one O(7) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the fourth Ti site, Ti(4) is bonded to one O(19), one O(2), one O(21), one O(22), one O(3), and one O(5) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the fifth Ti site, Ti(5) is bonded to one O(1), one O(10), one O(13), one O(5), one O(7), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the sixth Ti site, Ti(6) is bonded to one O(10), one O(12), one O(14), one O(3), one O(5), and one O(6) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 48-49°. In the seventh Ti site, Ti(7) is bonded to one O(11), one O(12), one O(15), one O(2), one O(6), and one O(8) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 48-50°. In the eighth Ti site, Ti(8) is bonded to one O(11), one O(16), one O(4), one O(7), one O(8), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. In the ninth Ti site, Ti(9) is bonded to one O(13), one O(16), one O(17), one O(20), one O(23), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the tenth Ti site, Ti(10) is bonded to one O(10), one O(13), one O(14), one O(17), one O(18), and one O(22) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-51°. In the eleventh Ti site, Ti(11) is bonded to one O(12), one O(14), one O(15), one O(18), one O(19), and one O(21) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the twelfth Ti site, Ti(12) is bonded to one O(11), one O(15), one O(16), one O(19), one O(20), and one O(24) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(5) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(4), and one Ti(7) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Ti(3), one Ti(4), and one Ti(6) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Ti(8) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(4), one Ti(5), and one Ti(6) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(6), and one Ti(7) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Ti(3), one Ti(5), and one Ti(8) atom. In the eighth O site, O(8) is bonded to one Li(1), one Ti(2), one Ti(7), and one Ti(8) atom to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(12)Li2Ti3 square pyramid and corners with two equivalent O(9)LiTi3 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(5), one Ti(8), and one Ti(9) atom to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(10), one Ti(5), and one Ti(6) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(12), one Ti(7), and one Ti(8) atom. In the twelfth O site, O(12) is bonded to one Li(2), one Li(3), one Ti(11), one Ti(6), and one Ti(7) atom to form a mixture of edge and corner-sharing OLi2Ti3 square pyramids. In the thirteenth O site, O(13) is bonded to one Li(2), one Ti(10), one Ti(5), and one Ti(9) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(12)Li2Ti3 square pyramid,  a cornercorner with one O(14)LiTi3 tetrahedra, corners with two equivalent O(18)LiTi3 trigonal pyramids, and  an edgeedge with one O(9)LiTi3 tetrahedra. In the fourteenth O site, O(14) is bonded to one Li(3), one Ti(10), one Ti(11), and one Ti(6) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(12)Li2Ti3 square pyramid,  a cornercorner with one O(13)LiTi3 tetrahedra, corners with two equivalent O(19)LiTi3 trigonal pyramids,  an edgeedge with one O(12)Li2Ti3 square pyramid, and  an edgeedge with one O(18)LiTi3 trigonal pyramid. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(11), one Ti(12), and one Ti(7) atom. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(12), one Ti(8), and one Ti(9) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal planar geometry to one Ti(10), one Ti(2), and one Ti(9) atom. In the eighteenth O site, O(18) is bonded to one Li(2), one Ti(10), one Ti(11), and one Ti(3) atom to form OLiTi3 trigonal pyramids that share corners with two equivalent O(13)LiTi3 tetrahedra,  a cornercorner with one O(19)LiTi3 trigonal pyramid,  an edgeedge with one O(12)Li2Ti3 square pyramid, and  an edgeedge with one O(14)LiTi3 tetrahedra. In the nineteenth O site, O(19) is bonded to one Li(3), one Ti(11), one Ti(12), and one Ti(4) atom to form OLiTi3 trigonal pyramids that share corners with two equivalent O(14)LiTi3 tetrahedra,  a cornercorner with one O(18)LiTi3 trigonal pyramid, and  an edgeedge with one O(12)Li2Ti3 square pyramid. In the twentieth O site, O(20) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(12), and one Ti(9) atom. In the twenty-first O site, O(21) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(11), and one Ti(4) atom. In the twenty-second O site, O(22) is bonded in a distorted T-shaped geometry to one Ti(10), one Ti(3), and one Ti(4) atom. In the twenty-third O site, O(23) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(9) atom. In the twenty-fourth O site, O(24) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(12), and one Ti(2) atom. is represented by the CIF file [CIF]
data_LiTi4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.801
_cell_length_b   7.250
_cell_length_c   10.187
_cell_angle_alpha   78.712
_cell_angle_beta   88.527
_cell_angle_gamma   85.843
_symmetry_Int_Tables_number   1
_cell_volume   419.038
_cell_formula_units_Z   3
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
  Li  Li0  1  0.994  0.427  0.931  1.0
  Li  Li1  1  0.251  0.573  0.316  1.0
  Li  Li2  1  0.509  0.572  0.573  1.0
  Ti  Ti3  1  0.749  0.003  0.751  1.0
  Ti  Ti4  1  0.001  0.989  0.004  1.0
  Ti  Ti5  1  0.254  0.011  0.247  1.0
  Ti  Ti6  1  0.497  0.006  0.496  1.0
  Ti  Ti7  1  0.733  0.311  0.208  1.0
  Ti  Ti8  1  0.972  0.306  0.460  1.0
  Ti  Ti9  1  0.225  0.305  0.704  1.0
  Ti  Ti10  1  0.482  0.309  0.951  1.0
  Ti  Ti11  1  0.518  0.689  0.041  1.0
  Ti  Ti12  1  0.774  0.696  0.291  1.0
  Ti  Ti13  1  0.012  0.691  0.552  1.0
  Ti  Ti14  1  0.278  0.696  0.794  1.0
  O  O15  1  0.974  0.138  0.151  1.0
  O  O16  1  0.472  0.134  0.654  1.0
  O  O17  1  0.221  0.136  0.404  1.0
  O  O18  1  0.727  0.137  0.903  1.0
  O  O19  1  0.710  0.190  0.397  1.0
  O  O20  1  0.960  0.188  0.648  1.0
  O  O21  1  0.466  0.191  0.147  1.0
  O  O22  1  0.202  0.201  0.900  1.0
  O  O23  1  0.714  0.457  0.018  1.0
  O  O24  1  0.971  0.459  0.271  1.0
  O  O25  1  0.468  0.459  0.764  1.0
  O  O26  1  0.225  0.461  0.516  1.0
  O  O27  1  0.536  0.543  0.232  1.0
  O  O28  1  0.785  0.543  0.484  1.0
  O  O29  1  0.031  0.541  0.735  1.0
  O  O30  1  0.278  0.541  0.979  1.0
  O  O31  1  0.785  0.810  0.102  1.0
  O  O32  1  0.046  0.799  0.352  1.0
  O  O33  1  0.297  0.800  0.600  1.0
  O  O34  1  0.540  0.811  0.853  1.0
  O  O35  1  0.773  0.864  0.597  1.0
  O  O36  1  0.524  0.859  0.350  1.0
  O  O37  1  0.276  0.861  0.100  1.0
  O  O38  1  0.026  0.866  0.845  1.0
[/CIF]
.
The crystal structure described by LiTi4O8 crystallizes in the triclinic P1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded in a rectangular see-saw-like geometry to one O(15), one O(16), one O(8), and one O(9) atom. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(10), one O(12), one O(13), and one O(18) atom. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(11), one O(12), one O(14), and one O(19) atom. There are twelve inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(20), one O(21), one O(24), one O(4), and one O(6) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the second Ti site, Ti(2) is bonded to one O(1), one O(17), one O(23), one O(24), one O(4), and one O(8) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the third Ti site, Ti(3) is bonded to one O(1), one O(18), one O(22), one O(23), one O(3), and one O(7) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the fourth Ti site, Ti(4) is bonded to one O(19), one O(2), one O(21), one O(22), one O(3), and one O(5) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the fifth Ti site, Ti(5) is bonded to one O(1), one O(10), one O(13), one O(5), one O(7), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the sixth Ti site, Ti(6) is bonded to one O(10), one O(12), one O(14), one O(3), one O(5), and one O(6) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 48-49°. In the seventh Ti site, Ti(7) is bonded to one O(11), one O(12), one O(15), one O(2), one O(6), and one O(8) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 48-50°. In the eighth Ti site, Ti(8) is bonded to one O(11), one O(16), one O(4), one O(7), one O(8), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. In the ninth Ti site, Ti(9) is bonded to one O(13), one O(16), one O(17), one O(20), one O(23), and one O(9) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. In the tenth Ti site, Ti(10) is bonded to one O(10), one O(13), one O(14), one O(17), one O(18), and one O(22) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-51°. In the eleventh Ti site, Ti(11) is bonded to one O(12), one O(14), one O(15), one O(18), one O(19), and one O(21) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-50°. In the twelfth Ti site, Ti(12) is bonded to one O(11), one O(15), one O(16), one O(19), one O(20), and one O(24) atom to form a mixture of edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 46-51°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(5) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(4), and one Ti(7) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Ti(3), one Ti(4), and one Ti(6) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Ti(8) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(4), one Ti(5), and one Ti(6) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(6), and one Ti(7) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Ti(3), one Ti(5), and one Ti(8) atom. In the eighth O site, O(8) is bonded to one Li(1), one Ti(2), one Ti(7), and one Ti(8) atom to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(12)Li2Ti3 square pyramid and corners with two equivalent O(9)LiTi3 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(5), one Ti(8), and one Ti(9) atom to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(10), one Ti(5), and one Ti(6) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(12), one Ti(7), and one Ti(8) atom. In the twelfth O site, O(12) is bonded to one Li(2), one Li(3), one Ti(11), one Ti(6), and one Ti(7) atom to form a mixture of edge and corner-sharing OLi2Ti3 square pyramids. In the thirteenth O site, O(13) is bonded to one Li(2), one Ti(10), one Ti(5), and one Ti(9) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(12)Li2Ti3 square pyramid,  a cornercorner with one O(14)LiTi3 tetrahedra, corners with two equivalent O(18)LiTi3 trigonal pyramids, and  an edgeedge with one O(9)LiTi3 tetrahedra. In the fourteenth O site, O(14) is bonded to one Li(3), one Ti(10), one Ti(11), and one Ti(6) atom to form distorted OLiTi3 tetrahedra that share  a cornercorner with one O(12)Li2Ti3 square pyramid,  a cornercorner with one O(13)LiTi3 tetrahedra, corners with two equivalent O(19)LiTi3 trigonal pyramids,  an edgeedge with one O(12)Li2Ti3 square pyramid, and  an edgeedge with one O(18)LiTi3 trigonal pyramid. In the fifteenth O site, O(15) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(11), one Ti(12), and one Ti(7) atom. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(12), one Ti(8), and one Ti(9) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal planar geometry to one Ti(10), one Ti(2), and one Ti(9) atom. In the eighteenth O site, O(18) is bonded to one Li(2), one Ti(10), one Ti(11), and one Ti(3) atom to form OLiTi3 trigonal pyramids that share corners with two equivalent O(13)LiTi3 tetrahedra,  a cornercorner with one O(19)LiTi3 trigonal pyramid,  an edgeedge with one O(12)Li2Ti3 square pyramid, and  an edgeedge with one O(14)LiTi3 tetrahedra. In the nineteenth O site, O(19) is bonded to one Li(3), one Ti(11), one Ti(12), and one Ti(4) atom to form OLiTi3 trigonal pyramids that share corners with two equivalent O(14)LiTi3 tetrahedra,  a cornercorner with one O(18)LiTi3 trigonal pyramid, and  an edgeedge with one O(12)Li2Ti3 square pyramid. In the twentieth O site, O(20) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(12), and one Ti(9) atom. In the twenty-first O site, O(21) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(11), and one Ti(4) atom. In the twenty-second O site, O(22) is bonded in a distorted T-shaped geometry to one Ti(10), one Ti(3), and one Ti(4) atom. In the twenty-third O site, O(23) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Ti(9) atom. In the twenty-fourth O site, O(24) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(12), and one Ti(2) atom. is represented by the CIF file [CIF]
data_LiTi4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.801
_cell_length_b   7.250
_cell_length_c   10.187
_cell_angle_alpha   78.712
_cell_angle_beta   88.527
_cell_angle_gamma   85.843
_symmetry_Int_Tables_number   1
_cell_volume   419.038
_cell_formula_units_Z   3
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
  Li  Li0  1  0.994  0.427  0.931  1.0
  Li  Li1  1  0.251  0.573  0.316  1.0
  Li  Li2  1  0.509  0.572  0.573  1.0
  Ti  Ti3  1  0.749  0.003  0.751  1.0
  Ti  Ti4  1  0.001  0.989  0.004  1.0
  Ti  Ti5  1  0.254  0.011  0.247  1.0
  Ti  Ti6  1  0.497  0.006  0.496  1.0
  Ti  Ti7  1  0.733  0.311  0.208  1.0
  Ti  Ti8  1  0.972  0.306  0.460  1.0
  Ti  Ti9  1  0.225  0.305  0.704  1.0
  Ti  Ti10  1  0.482  0.309  0.951  1.0
  Ti  Ti11  1  0.518  0.689  0.041  1.0
  Ti  Ti12  1  0.774  0.696  0.291  1.0
  Ti  Ti13  1  0.012  0.691  0.552  1.0
  Ti  Ti14  1  0.278  0.696  0.794  1.0
  O  O15  1  0.974  0.138  0.151  1.0
  O  O16  1  0.472  0.134  0.654  1.0
  O  O17  1  0.221  0.136  0.404  1.0
  O  O18  1  0.727  0.137  0.903  1.0
  O  O19  1  0.710  0.190  0.397  1.0
  O  O20  1  0.960  0.188  0.648  1.0
  O  O21  1  0.466  0.191  0.147  1.0
  O  O22  1  0.202  0.201  0.900  1.0
  O  O23  1  0.714  0.457  0.018  1.0
  O  O24  1  0.971  0.459  0.271  1.0
  O  O25  1  0.468  0.459  0.764  1.0
  O  O26  1  0.225  0.461  0.516  1.0
  O  O27  1  0.536  0.543  0.232  1.0
  O  O28  1  0.785  0.543  0.484  1.0
  O  O29  1  0.031  0.541  0.735  1.0
  O  O30  1  0.278  0.541  0.979  1.0
  O  O31  1  0.785  0.810  0.102  1.0
  O  O32  1  0.046  0.799  0.352  1.0
  O  O33  1  0.297  0.800  0.600  1.0
  O  O34  1  0.540  0.811  0.853  1.0
  O  O35  1  0.773  0.864  0.597  1.0
  O  O36  1  0.524  0.859  0.350  1.0
  O  O37  1  0.276  0.861  0.100  1.0
  O  O38  1  0.026  0.866  0.845  1.0
[/CIF]
.