The structure described by Li4Ti5Co3O16 is Hausmannite-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-67°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent 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 range from 57-66°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-66°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Ti(4)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. In the second Ti site, Ti(2) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-54°. In the third Ti site, Ti(3) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), one Ti(3), and one Co(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(3), and two equivalent Ti(2) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Co(1) atom to form corner-sharing OLiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Co(2) atoms to form OLiTiCo2 tetrahedra that share corners with two equivalent O(12)LiTiCo2 tetrahedra and corners with four equivalent O(9)LiTi2Co trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Co(1) atom to form a mixture of distorted edge and corner-sharing OLiTi2Co tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Ti(4), and one Co(2) atom to form distorted OLiTi2Co trigonal pyramids that share  a cornercorner with one O(12)LiTiCo2 tetrahedra, corners with two equivalent O(5)LiTiCo2 tetrahedra,  a cornercorner with one O(9)LiTi2Co trigonal pyramid,  an edgeedge with one O(12)LiTiCo2 tetrahedra, and  an edgeedge with one O(9)LiTi2Co trigonal pyramid. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Co(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Co(2) atoms to form OLiTiCo2 tetrahedra that share corners with two equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(9)LiTi2Co trigonal pyramids, and edges with two equivalent O(9)LiTi2Co trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti5Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.805
_cell_length_b   5.805
_cell_length_c   9.515
_cell_angle_alpha   89.683
_cell_angle_beta   89.683
_cell_angle_gamma   60.578
_symmetry_Int_Tables_number   1
_cell_volume   279.246
_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
  Li  Li0  1  0.334  0.334  0.108  1.0
  Li  Li1  1  0.011  0.011  0.008  1.0
  Li  Li2  1  0.004  0.004  0.505  1.0
  Li  Li3  1  0.665  0.665  0.598  1.0
  Ti  Ti4  1  0.825  0.825  0.273  1.0
  Ti  Ti5  1  0.651  0.161  0.779  1.0
  Ti  Ti6  1  0.333  0.333  0.496  1.0
  Ti  Ti7  1  0.161  0.651  0.779  1.0
  Ti  Ti8  1  0.654  0.654  0.006  1.0
  Co  Co9  1  0.173  0.173  0.791  1.0
  Co  Co10  1  0.829  0.344  0.288  1.0
  Co  Co11  1  0.344  0.829  0.288  1.0
  O  O12  1  0.666  0.175  0.403  1.0
  O  O13  1  0.484  0.484  0.665  1.0
  O  O14  1  0.339  0.339  0.898  1.0
  O  O15  1  0.003  0.003  0.695  1.0
  O  O16  1  0.004  0.004  0.197  1.0
  O  O17  1  0.175  0.666  0.403  1.0
  O  O18  1  0.499  0.036  0.651  1.0
  O  O19  1  0.036  0.499  0.651  1.0
  O  O20  1  0.833  0.833  0.904  1.0
  O  O21  1  0.168  0.168  0.399  1.0
  O  O22  1  0.965  0.517  0.163  1.0
  O  O23  1  0.517  0.965  0.163  1.0
  O  O24  1  0.666  0.666  0.393  1.0
  O  O25  1  0.820  0.340  0.909  1.0
  O  O26  1  0.522  0.522  0.170  1.0
  O  O27  1  0.340  0.820  0.909  1.0
[/CIF]
.
The structure described by Li4Ti5Co3O16 is Hausmannite-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-67°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent 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 range from 57-66°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-66°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Ti(4)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. In the second Ti site, Ti(2) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-54°. In the third Ti site, Ti(3) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), one Ti(3), and one Co(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(3), and two equivalent Ti(2) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Co(1) atom to form corner-sharing OLiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Co(2) atoms to form OLiTiCo2 tetrahedra that share corners with two equivalent O(12)LiTiCo2 tetrahedra and corners with four equivalent O(9)LiTi2Co trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Co(1) atom to form a mixture of distorted edge and corner-sharing OLiTi2Co tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Ti(4), and one Co(2) atom to form distorted OLiTi2Co trigonal pyramids that share  a cornercorner with one O(12)LiTiCo2 tetrahedra, corners with two equivalent O(5)LiTiCo2 tetrahedra,  a cornercorner with one O(9)LiTi2Co trigonal pyramid,  an edgeedge with one O(12)LiTiCo2 tetrahedra, and  an edgeedge with one O(9)LiTi2Co trigonal pyramid. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Co(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Co(2) atoms to form OLiTiCo2 tetrahedra that share corners with two equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(9)LiTi2Co trigonal pyramids, and edges with two equivalent O(9)LiTi2Co trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti5Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.805
_cell_length_b   5.805
_cell_length_c   9.515
_cell_angle_alpha   89.683
_cell_angle_beta   89.683
_cell_angle_gamma   60.578
_symmetry_Int_Tables_number   1
_cell_volume   279.246
_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
  Li  Li0  1  0.334  0.334  0.108  1.0
  Li  Li1  1  0.011  0.011  0.008  1.0
  Li  Li2  1  0.004  0.004  0.505  1.0
  Li  Li3  1  0.665  0.665  0.598  1.0
  Ti  Ti4  1  0.825  0.825  0.273  1.0
  Ti  Ti5  1  0.651  0.161  0.779  1.0
  Ti  Ti6  1  0.333  0.333  0.496  1.0
  Ti  Ti7  1  0.161  0.651  0.779  1.0
  Ti  Ti8  1  0.654  0.654  0.006  1.0
  Co  Co9  1  0.173  0.173  0.791  1.0
  Co  Co10  1  0.829  0.344  0.288  1.0
  Co  Co11  1  0.344  0.829  0.288  1.0
  O  O12  1  0.666  0.175  0.403  1.0
  O  O13  1  0.484  0.484  0.665  1.0
  O  O14  1  0.339  0.339  0.898  1.0
  O  O15  1  0.003  0.003  0.695  1.0
  O  O16  1  0.004  0.004  0.197  1.0
  O  O17  1  0.175  0.666  0.403  1.0
  O  O18  1  0.499  0.036  0.651  1.0
  O  O19  1  0.036  0.499  0.651  1.0
  O  O20  1  0.833  0.833  0.904  1.0
  O  O21  1  0.168  0.168  0.399  1.0
  O  O22  1  0.965  0.517  0.163  1.0
  O  O23  1  0.517  0.965  0.163  1.0
  O  O24  1  0.666  0.666  0.393  1.0
  O  O25  1  0.820  0.340  0.909  1.0
  O  O26  1  0.522  0.522  0.170  1.0
  O  O27  1  0.340  0.820  0.909  1.0
[/CIF]
.