The structure described by Li4Ti3Cr3(NiO8)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 Ni(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. 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 in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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 Ni(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-64°. 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 Ni(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 Ni(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ni(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. 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 Ni(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. 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 Ni(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ni(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, 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 51-55°. In the second Ni site, Ni(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form NiO6 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,  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 50-54°. 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 Cr(2), and one Ni(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Ni(1) atom to form distorted OLiTi2Ni tetrahedra that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrNi tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid, and edges with two equivalent O(6)LiTiCrNi tetrahedra. 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)LiTi2Ni tetrahedra, corners with four equivalent O(6)LiTiCrNi tetrahedra, and  a cornercorner with one O(8)LiCr2Ni 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)LiCr2Ni tetrahedra, corners with four equivalent O(9)LiTiCrNi tetrahedra, and  an edgeedge with one O(8)LiCr2Ni trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Ni(1) atom to form distorted OLiTiCrNi tetrahedra that share  a cornercorner with one O(2)LiTi2Ni tetrahedra,  a cornercorner with one O(6)LiTiCrNi tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid,  an edgeedge with one O(2)LiTi2Ni tetrahedra, and  an edgeedge with one O(6)LiTiCrNi tetrahedra. 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 Ni(2) atom. In the eighth O site, O(8) is bonded to one Li(3), two equivalent Cr(2), and one Ni(1) atom to form distorted OLiCr2Ni trigonal pyramids that share  a cornercorner with one O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2Ni tetrahedra, corners with two equivalent O(12)LiCr2Ni tetrahedra, corners with two equivalent O(6)LiTiCrNi tetrahedra, corners with two equivalent O(9)LiTiCrNi tetrahedra, and  an edgeedge with one O(5)LiTiCr2 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Ni(2) atom to form distorted OLiTiCrNi tetrahedra that share  a cornercorner with one O(12)LiCr2Ni tetrahedra,  a cornercorner with one O(9)LiTiCrNi tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid,  an edgeedge with one O(12)LiCr2Ni tetrahedra, and  an edgeedge with one O(9)LiTiCrNi tetrahedra. 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 Cr(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(1), and one Ni(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Cr(2), and one Ni(2) atom to form distorted OLiCr2Ni tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiCrNi tetrahedra, corners with two equivalent O(8)LiCr2Ni trigonal pyramids, and edges with two equivalent O(9)LiTiCrNi tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Cr3(NiO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.863
_cell_length_b   5.863
_cell_length_c   9.659
_cell_angle_alpha   89.978
_cell_angle_beta   89.978
_cell_angle_gamma   60.146
_symmetry_Int_Tables_number   1
_cell_volume   287.966
_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  0.331  0.331  0.893  1.0
  Li  Li1  1  0.006  0.006  0.996  1.0
  Li  Li2  1  0.005  0.005  0.498  1.0
  Li  Li3  1  0.664  0.664  0.395  1.0
  Ti  Ti4  1  0.165  0.659  0.217  1.0
  Ti  Ti5  1  0.659  0.165  0.217  1.0
  Ti  Ti6  1  0.825  0.825  0.721  1.0
  Cr  Cr7  1  0.167  0.167  0.211  1.0
  Cr  Cr8  1  0.334  0.828  0.711  1.0
  Cr  Cr9  1  0.828  0.334  0.711  1.0
  Ni  Ni10  1  0.334  0.334  0.490  1.0
  Ni  Ni11  1  0.667  0.667  0.989  1.0
  O  O12  1  0.166  0.682  0.606  1.0
  O  O13  1  0.481  0.481  0.331  1.0
  O  O14  1  0.337  0.337  0.102  1.0
  O  O15  1  1.000  1.000  0.314  1.0
  O  O16  1  0.998  0.998  0.813  1.0
  O  O17  1  0.682  0.166  0.606  1.0
  O  O18  1  0.035  0.478  0.331  1.0
  O  O19  1  0.478  0.035  0.331  1.0
  O  O20  1  0.842  0.842  0.105  1.0
  O  O21  1  0.161  0.161  0.613  1.0
  O  O22  1  0.514  0.964  0.831  1.0
  O  O23  1  0.964  0.514  0.831  1.0
  O  O24  1  0.669  0.669  0.602  1.0
  O  O25  1  0.320  0.848  0.108  1.0
  O  O26  1  0.519  0.519  0.826  1.0
  O  O27  1  0.848  0.320  0.108  1.0
[/CIF]
.
The structure described by Li4Ti3Cr3(NiO8)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 Ni(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. 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 in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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 Ni(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-64°. 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 Ni(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 Ni(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ni(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. 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 Ni(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. 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 Ni(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ni(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, 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 51-55°. In the second Ni site, Ni(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form NiO6 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,  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 50-54°. 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 Cr(2), and one Ni(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Ni(1) atom to form distorted OLiTi2Ni tetrahedra that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrNi tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid, and edges with two equivalent O(6)LiTiCrNi tetrahedra. 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)LiTi2Ni tetrahedra, corners with four equivalent O(6)LiTiCrNi tetrahedra, and  a cornercorner with one O(8)LiCr2Ni 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)LiCr2Ni tetrahedra, corners with four equivalent O(9)LiTiCrNi tetrahedra, and  an edgeedge with one O(8)LiCr2Ni trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Ni(1) atom to form distorted OLiTiCrNi tetrahedra that share  a cornercorner with one O(2)LiTi2Ni tetrahedra,  a cornercorner with one O(6)LiTiCrNi tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid,  an edgeedge with one O(2)LiTi2Ni tetrahedra, and  an edgeedge with one O(6)LiTiCrNi tetrahedra. 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 Ni(2) atom. In the eighth O site, O(8) is bonded to one Li(3), two equivalent Cr(2), and one Ni(1) atom to form distorted OLiCr2Ni trigonal pyramids that share  a cornercorner with one O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2Ni tetrahedra, corners with two equivalent O(12)LiCr2Ni tetrahedra, corners with two equivalent O(6)LiTiCrNi tetrahedra, corners with two equivalent O(9)LiTiCrNi tetrahedra, and  an edgeedge with one O(5)LiTiCr2 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Ni(2) atom to form distorted OLiTiCrNi tetrahedra that share  a cornercorner with one O(12)LiCr2Ni tetrahedra,  a cornercorner with one O(9)LiTiCrNi tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  a cornercorner with one O(8)LiCr2Ni trigonal pyramid,  an edgeedge with one O(12)LiCr2Ni tetrahedra, and  an edgeedge with one O(9)LiTiCrNi tetrahedra. 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 Cr(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(1), and one Ni(2) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Cr(2), and one Ni(2) atom to form distorted OLiCr2Ni tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiCrNi tetrahedra, corners with two equivalent O(8)LiCr2Ni trigonal pyramids, and edges with two equivalent O(9)LiTiCrNi tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Cr3(NiO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.863
_cell_length_b   5.863
_cell_length_c   9.659
_cell_angle_alpha   89.978
_cell_angle_beta   89.978
_cell_angle_gamma   60.146
_symmetry_Int_Tables_number   1
_cell_volume   287.966
_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  0.331  0.331  0.893  1.0
  Li  Li1  1  0.006  0.006  0.996  1.0
  Li  Li2  1  0.005  0.005  0.498  1.0
  Li  Li3  1  0.664  0.664  0.395  1.0
  Ti  Ti4  1  0.165  0.659  0.217  1.0
  Ti  Ti5  1  0.659  0.165  0.217  1.0
  Ti  Ti6  1  0.825  0.825  0.721  1.0
  Cr  Cr7  1  0.167  0.167  0.211  1.0
  Cr  Cr8  1  0.334  0.828  0.711  1.0
  Cr  Cr9  1  0.828  0.334  0.711  1.0
  Ni  Ni10  1  0.334  0.334  0.490  1.0
  Ni  Ni11  1  0.667  0.667  0.989  1.0
  O  O12  1  0.166  0.682  0.606  1.0
  O  O13  1  0.481  0.481  0.331  1.0
  O  O14  1  0.337  0.337  0.102  1.0
  O  O15  1  1.000  1.000  0.314  1.0
  O  O16  1  0.998  0.998  0.813  1.0
  O  O17  1  0.682  0.166  0.606  1.0
  O  O18  1  0.035  0.478  0.331  1.0
  O  O19  1  0.478  0.035  0.331  1.0
  O  O20  1  0.842  0.842  0.105  1.0
  O  O21  1  0.161  0.161  0.613  1.0
  O  O22  1  0.514  0.964  0.831  1.0
  O  O23  1  0.964  0.514  0.831  1.0
  O  O24  1  0.669  0.669  0.602  1.0
  O  O25  1  0.320  0.848  0.108  1.0
  O  O26  1  0.519  0.519  0.826  1.0
  O  O27  1  0.848  0.320  0.108  1.0
[/CIF]
.