The compound described by Li4Ti3Fe3(CoO8)2 is Spinel-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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. 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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-62°. 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) 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 Co(2)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 Co(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Ti site, Ti(2) 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 Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Co(2)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 Co(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-51°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted CoO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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(2), one Fe(2), and one Co(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiFeCo tetrahedra, edges with two equivalent O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(3)LiTi2Fe trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe trigonal pyramids that share  a cornercorner with one O(12)LiFe2Co tetrahedra, corners with three equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Co tetrahedra, and edges with two equivalent O(6)LiTiFeCo tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra, corners with four equivalent O(6)LiTiFeCo tetrahedra, and corners with three equivalent O(3)LiTi2Fe trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form corner-sharing OLiTiFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Co(1) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(6)LiTiFeCo tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Co tetrahedra,  an edgeedge with one O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(3)LiTi2Fe trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Fe(2), and one Co(1) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Fe(2), and one Co(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Fe(2), and one Co(2) atom to form distorted OLiFe2Co tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra and  a cornercorner with one O(3)LiTi2Fe trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Fe3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.933
_cell_length_b   5.933
_cell_length_c   9.620
_cell_angle_alpha   89.303
_cell_angle_beta   89.303
_cell_angle_gamma   60.283
_symmetry_Int_Tables_number   1
_cell_volume   294.039
_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  0.665  0.665  0.892  1.0
  Li  Li1  1  0.999  0.999  0.994  1.0
  Li  Li2  1  0.002  0.002  0.497  1.0
  Li  Li3  1  0.331  0.331  0.396  1.0
  Ti  Ti4  1  0.828  0.340  0.214  1.0
  Ti  Ti5  1  0.340  0.828  0.214  1.0
  Ti  Ti6  1  0.171  0.171  0.717  1.0
  Fe  Fe7  1  0.830  0.830  0.216  1.0
  Fe  Fe8  1  0.660  0.170  0.712  1.0
  Fe  Fe9  1  0.170  0.660  0.712  1.0
  Co  Co10  1  0.676  0.676  0.492  1.0
  Co  Co11  1  0.337  0.337  0.988  1.0
  O  O12  1  0.834  0.332  0.601  1.0
  O  O13  1  0.518  0.518  0.333  1.0
  O  O14  1  0.664  0.664  0.104  1.0
  O  O15  1  0.003  0.003  0.312  1.0
  O  O16  1  1.000  1.000  0.807  1.0
  O  O17  1  0.332  0.834  0.601  1.0
  O  O18  1  0.956  0.515  0.341  1.0
  O  O19  1  0.515  0.956  0.341  1.0
  O  O20  1  0.169  0.169  0.104  1.0
  O  O21  1  0.834  0.834  0.594  1.0
  O  O22  1  0.476  0.036  0.837  1.0
  O  O23  1  0.036  0.476  0.837  1.0
  O  O24  1  0.329  0.329  0.601  1.0
  O  O25  1  0.676  0.171  0.104  1.0
  O  O26  1  0.476  0.476  0.844  1.0
  O  O27  1  0.171  0.676  0.104  1.0
[/CIF]
.
The compound described by Li4Ti3Fe3(CoO8)2 is Spinel-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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. 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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-62°. 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) 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 Co(2)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 Co(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Ti site, Ti(2) 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 Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 54°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Co(2)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 Co(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-51°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted CoO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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(2), one Fe(2), and one Co(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiFeCo tetrahedra, edges with two equivalent O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(3)LiTi2Fe trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe trigonal pyramids that share  a cornercorner with one O(12)LiFe2Co tetrahedra, corners with three equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Co tetrahedra, and edges with two equivalent O(6)LiTiFeCo tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra, corners with four equivalent O(6)LiTiFeCo tetrahedra, and corners with three equivalent O(3)LiTi2Fe trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form corner-sharing OLiTiFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Co(1) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(6)LiTiFeCo tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Co tetrahedra,  an edgeedge with one O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(3)LiTi2Fe trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Fe(2), and one Co(1) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Fe(2), and one Co(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Fe(2), and one Co(2) atom to form distorted OLiFe2Co tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra and  a cornercorner with one O(3)LiTi2Fe trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Fe3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.933
_cell_length_b   5.933
_cell_length_c   9.620
_cell_angle_alpha   89.303
_cell_angle_beta   89.303
_cell_angle_gamma   60.283
_symmetry_Int_Tables_number   1
_cell_volume   294.039
_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  0.665  0.665  0.892  1.0
  Li  Li1  1  0.999  0.999  0.994  1.0
  Li  Li2  1  0.002  0.002  0.497  1.0
  Li  Li3  1  0.331  0.331  0.396  1.0
  Ti  Ti4  1  0.828  0.340  0.214  1.0
  Ti  Ti5  1  0.340  0.828  0.214  1.0
  Ti  Ti6  1  0.171  0.171  0.717  1.0
  Fe  Fe7  1  0.830  0.830  0.216  1.0
  Fe  Fe8  1  0.660  0.170  0.712  1.0
  Fe  Fe9  1  0.170  0.660  0.712  1.0
  Co  Co10  1  0.676  0.676  0.492  1.0
  Co  Co11  1  0.337  0.337  0.988  1.0
  O  O12  1  0.834  0.332  0.601  1.0
  O  O13  1  0.518  0.518  0.333  1.0
  O  O14  1  0.664  0.664  0.104  1.0
  O  O15  1  0.003  0.003  0.312  1.0
  O  O16  1  1.000  1.000  0.807  1.0
  O  O17  1  0.332  0.834  0.601  1.0
  O  O18  1  0.956  0.515  0.341  1.0
  O  O19  1  0.515  0.956  0.341  1.0
  O  O20  1  0.169  0.169  0.104  1.0
  O  O21  1  0.834  0.834  0.594  1.0
  O  O22  1  0.476  0.036  0.837  1.0
  O  O23  1  0.036  0.476  0.837  1.0
  O  O24  1  0.329  0.329  0.601  1.0
  O  O25  1  0.676  0.171  0.104  1.0
  O  O26  1  0.476  0.476  0.844  1.0
  O  O27  1  0.171  0.676  0.104  1.0
[/CIF]
.