The material described by Li4Ti3Cr3(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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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(2)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. 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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(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 56-63°. 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, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 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 four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the second Cr site, Cr(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 CrO6 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 CoO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. 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 Cr(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Ti(2), one Cr(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)LiTi2Cr tetrahedra,  a cornercorner with one O(8)LiCr2Co trigonal pyramid, and  a cornercorner with one O(10)LiTiCr2 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra and  a cornercorner with one O(8)LiCr2Co trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiCr2Co tetrahedra, corners with three equivalent O(10)LiTiCr2 trigonal pyramids, and  an edgeedge with one O(8)LiCr2Co trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Cr(1), and one Co(1) atom. In the seventh O site, O(7) is bonded in a distorted 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 to one Li(3), two equivalent Cr(2), and one Co(1) atom to form distorted OLiCr2Co trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi2Cr tetrahedra, corners with two equivalent O(12)LiCr2Co tetrahedra, corners with two equivalent O(10)LiTiCr2 trigonal pyramids, and  an edgeedge with one O(5)LiTiCr2 tetrahedra. 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 Cr(2), and one Co(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra, corners with three equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(8)LiCr2Co trigonal pyramids, and  an edgeedge with one O(12)LiCr2Co tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Cr(2), and one Co(2) atom to form distorted OLiCr2Co tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(8)LiCr2Co trigonal pyramids, and  an edgeedge with one O(10)LiTiCr2 trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Ti3Cr3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.814
_cell_length_b   5.855
_cell_length_c   9.396
_cell_angle_alpha   90.009
_cell_angle_beta   90.123
_cell_angle_gamma   120.237
_symmetry_Int_Tables_number   1
_cell_volume   276.332
_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  0.337  0.668  0.893  1.0
  Li  Li1  1  0.990  0.995  0.995  1.0
  Li  Li2  1  1.000  1.000  0.498  1.0
  Li  Li3  1  0.666  0.333  0.396  1.0
  Ti  Ti4  1  0.167  0.831  0.212  1.0
  Ti  Ti5  1  0.167  0.336  0.212  1.0
  Ti  Ti6  1  0.340  0.170  0.716  1.0
  Cr  Cr7  1  0.653  0.827  0.213  1.0
  Cr  Cr8  1  0.830  0.659  0.709  1.0
  Cr  Cr9  1  0.830  0.170  0.709  1.0
  Co  Co10  1  0.334  0.667  0.484  1.0
  Co  Co11  1  0.672  0.336  0.980  1.0
  O  O12  1  0.170  0.832  0.603  1.0
  O  O13  1  0.045  0.523  0.343  1.0
  O  O14  1  0.325  0.663  0.100  1.0
  O  O15  1  0.997  0.999  0.311  1.0
  O  O16  1  0.999  0.999  0.808  1.0
  O  O17  1  0.170  0.338  0.603  1.0
  O  O18  1  0.477  0.955  0.344  1.0
  O  O19  1  0.477  0.523  0.344  1.0
  O  O20  1  0.338  0.169  0.103  1.0
  O  O21  1  0.667  0.834  0.605  1.0
  O  O22  1  0.528  0.481  0.844  1.0
  O  O23  1  0.528  0.047  0.844  1.0
  O  O24  1  0.663  0.332  0.600  1.0
  O  O25  1  0.837  0.665  0.101  1.0
  O  O26  1  0.955  0.477  0.839  1.0
  O  O27  1  0.837  0.171  0.101  1.0
[/CIF]
.
The material described by Li4Ti3Cr3(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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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(2)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. 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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(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 56-63°. 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, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 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 four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the second Cr site, Cr(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 CrO6 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 CoO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. 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 Cr(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Ti(2), one Cr(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)LiTi2Cr tetrahedra,  a cornercorner with one O(8)LiCr2Co trigonal pyramid, and  a cornercorner with one O(10)LiTiCr2 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra and  a cornercorner with one O(8)LiCr2Co trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiCr2Co tetrahedra, corners with three equivalent O(10)LiTiCr2 trigonal pyramids, and  an edgeedge with one O(8)LiCr2Co trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Cr(1), and one Co(1) atom. In the seventh O site, O(7) is bonded in a distorted 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 to one Li(3), two equivalent Cr(2), and one Co(1) atom to form distorted OLiCr2Co trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi2Cr tetrahedra, corners with two equivalent O(12)LiCr2Co tetrahedra, corners with two equivalent O(10)LiTiCr2 trigonal pyramids, and  an edgeedge with one O(5)LiTiCr2 tetrahedra. 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 Cr(2), and one Co(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra, corners with three equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(8)LiCr2Co trigonal pyramids, and  an edgeedge with one O(12)LiCr2Co tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(1), and one Co(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Cr(2), and one Co(2) atom to form distorted OLiCr2Co tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(8)LiCr2Co trigonal pyramids, and  an edgeedge with one O(10)LiTiCr2 trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Ti3Cr3(CoO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.814
_cell_length_b   5.855
_cell_length_c   9.396
_cell_angle_alpha   90.009
_cell_angle_beta   90.123
_cell_angle_gamma   120.237
_symmetry_Int_Tables_number   1
_cell_volume   276.332
_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  0.337  0.668  0.893  1.0
  Li  Li1  1  0.990  0.995  0.995  1.0
  Li  Li2  1  1.000  1.000  0.498  1.0
  Li  Li3  1  0.666  0.333  0.396  1.0
  Ti  Ti4  1  0.167  0.831  0.212  1.0
  Ti  Ti5  1  0.167  0.336  0.212  1.0
  Ti  Ti6  1  0.340  0.170  0.716  1.0
  Cr  Cr7  1  0.653  0.827  0.213  1.0
  Cr  Cr8  1  0.830  0.659  0.709  1.0
  Cr  Cr9  1  0.830  0.170  0.709  1.0
  Co  Co10  1  0.334  0.667  0.484  1.0
  Co  Co11  1  0.672  0.336  0.980  1.0
  O  O12  1  0.170  0.832  0.603  1.0
  O  O13  1  0.045  0.523  0.343  1.0
  O  O14  1  0.325  0.663  0.100  1.0
  O  O15  1  0.997  0.999  0.311  1.0
  O  O16  1  0.999  0.999  0.808  1.0
  O  O17  1  0.170  0.338  0.603  1.0
  O  O18  1  0.477  0.955  0.344  1.0
  O  O19  1  0.477  0.523  0.344  1.0
  O  O20  1  0.338  0.169  0.103  1.0
  O  O21  1  0.667  0.834  0.605  1.0
  O  O22  1  0.528  0.481  0.844  1.0
  O  O23  1  0.528  0.047  0.844  1.0
  O  O24  1  0.663  0.332  0.600  1.0
  O  O25  1  0.837  0.665  0.101  1.0
  O  O26  1  0.955  0.477  0.839  1.0
  O  O27  1  0.837  0.171  0.101  1.0
[/CIF]
.