The material described by Li4Cr2Mn3Co3O16 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 Mn(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-63°. 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 Co(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-66°. In the third Li site, Li(3) is bonded in a distorted 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 Co(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. In the second Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. 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(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Mn(1)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 are 51°. In the second Co site, Co(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. 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 Cr(1), one Mn(2), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Co(1) atoms to form distorted OLiCrCo2 tetrahedra that share corners with two equivalent O(4)LiMnCo2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra,  a cornercorner with one O(10)LiMn2Co trigonal pyramid, edges with two equivalent O(6)LiMnCrCo tetrahedra, and  an edgeedge with one O(3)LiMnCo2 trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), one Mn(1), and two equivalent Co(1) atoms to form distorted OLiMnCo2 trigonal pyramids that share  a cornercorner with one O(12)LiMn2Cr tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra, corners with three equivalent O(4)LiMnCo2 tetrahedra,  an edgeedge with one O(2)LiCrCo2 tetrahedra, and edges with two equivalent O(6)LiMnCrCo tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Co(1) atoms to form distorted OLiMnCo2 tetrahedra that share corners with two equivalent O(2)LiCrCo2 tetrahedra, corners with four equivalent O(6)LiMnCrCo tetrahedra, and corners with three equivalent O(3)LiMnCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co tetrahedra that share corners with two equivalent O(12)LiMn2Cr tetrahedra, corners with four equivalent O(9)LiMnCrCo tetrahedra, and corners with three equivalent O(10)LiMn2Co trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Mn(1), and one Co(1) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(2)LiCrCo2 tetrahedra,  a cornercorner with one O(6)LiMnCrCo tetrahedra, corners with two equivalent O(4)LiMnCo2 tetrahedra,  a cornercorner with one O(10)LiMn2Co trigonal pyramid,  an edgeedge with one O(2)LiCrCo2 tetrahedra,  an edgeedge with one O(6)LiMnCrCo tetrahedra, and  an edgeedge with one O(3)LiMnCo2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Co(2) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(12)LiMn2Cr tetrahedra,  a cornercorner with one O(9)LiMnCrCo tetrahedra, corners with two equivalent O(5)LiMn2Co tetrahedra,  a cornercorner with one O(3)LiMnCo2 trigonal pyramid,  an edgeedge with one O(12)LiMn2Cr tetrahedra,  an edgeedge with one O(9)LiMnCrCo tetrahedra, and  an edgeedge with one O(10)LiMn2Co trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co trigonal pyramids that share  a cornercorner with one O(2)LiCrCo2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra, corners with three equivalent O(5)LiMn2Co tetrahedra,  an edgeedge with one O(12)LiMn2Cr tetrahedra, and edges with two equivalent O(9)LiMnCrCo tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Mn(1), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(5)LiMn2Co tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra,  a cornercorner with one O(3)LiMnCo2 trigonal pyramid, edges with two equivalent O(9)LiMnCrCo tetrahedra, and  an edgeedge with one O(10)LiMn2Co trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Mn3Cr2Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.776
_cell_length_b   5.776
_cell_length_c   9.485
_cell_angle_alpha   89.597
_cell_angle_beta   89.597
_cell_angle_gamma   60.324
_symmetry_Int_Tables_number   1
_cell_volume   274.882
_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  0.333  0.333  0.105  1.0
  Li  Li1  1  0.997  0.997  0.001  1.0
  Li  Li2  1  0.996  0.996  0.505  1.0
  Li  Li3  1  0.667  0.667  0.610  1.0
  Mn  Mn4  1  0.170  0.170  0.785  1.0
  Mn  Mn5  1  0.832  0.339  0.285  1.0
  Mn  Mn6  1  0.339  0.832  0.285  1.0
  Cr  Cr7  1  0.338  0.338  0.516  1.0
  Cr  Cr8  1  0.669  0.669  0.014  1.0
  Co  Co9  1  0.663  0.171  0.787  1.0
  Co  Co10  1  0.171  0.663  0.787  1.0
  Co  Co11  1  0.833  0.833  0.289  1.0
  O  O12  1  0.675  0.170  0.399  1.0
  O  O13  1  0.482  0.482  0.664  1.0
  O  O14  1  0.335  0.335  0.890  1.0
  O  O15  1  1.000  1.000  0.693  1.0
  O  O16  1  0.000  0.000  0.190  1.0
  O  O17  1  0.170  0.675  0.399  1.0
  O  O18  1  0.482  0.038  0.665  1.0
  O  O19  1  0.038  0.482  0.665  1.0
  O  O20  1  0.837  0.837  0.895  1.0
  O  O21  1  0.162  0.162  0.397  1.0
  O  O22  1  0.963  0.513  0.158  1.0
  O  O23  1  0.513  0.963  0.158  1.0
  O  O24  1  0.667  0.667  0.390  1.0
  O  O25  1  0.838  0.323  0.896  1.0
  O  O26  1  0.519  0.519  0.164  1.0
  O  O27  1  0.323  0.838  0.896  1.0
[/CIF]
.
The material described by Li4Cr2Mn3Co3O16 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 Mn(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-63°. 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 Co(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-66°. In the third Li site, Li(3) is bonded in a distorted 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 Co(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. In the second Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. 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(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Mn(1)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 are 51°. In the second Co site, Co(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. 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 Cr(1), one Mn(2), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Co(1) atoms to form distorted OLiCrCo2 tetrahedra that share corners with two equivalent O(4)LiMnCo2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra,  a cornercorner with one O(10)LiMn2Co trigonal pyramid, edges with two equivalent O(6)LiMnCrCo tetrahedra, and  an edgeedge with one O(3)LiMnCo2 trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), one Mn(1), and two equivalent Co(1) atoms to form distorted OLiMnCo2 trigonal pyramids that share  a cornercorner with one O(12)LiMn2Cr tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra, corners with three equivalent O(4)LiMnCo2 tetrahedra,  an edgeedge with one O(2)LiCrCo2 tetrahedra, and edges with two equivalent O(6)LiMnCrCo tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Co(1) atoms to form distorted OLiMnCo2 tetrahedra that share corners with two equivalent O(2)LiCrCo2 tetrahedra, corners with four equivalent O(6)LiMnCrCo tetrahedra, and corners with three equivalent O(3)LiMnCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co tetrahedra that share corners with two equivalent O(12)LiMn2Cr tetrahedra, corners with four equivalent O(9)LiMnCrCo tetrahedra, and corners with three equivalent O(10)LiMn2Co trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Mn(1), and one Co(1) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(2)LiCrCo2 tetrahedra,  a cornercorner with one O(6)LiMnCrCo tetrahedra, corners with two equivalent O(4)LiMnCo2 tetrahedra,  a cornercorner with one O(10)LiMn2Co trigonal pyramid,  an edgeedge with one O(2)LiCrCo2 tetrahedra,  an edgeedge with one O(6)LiMnCrCo tetrahedra, and  an edgeedge with one O(3)LiMnCo2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Co(2) atom to form distorted OLiMnCrCo tetrahedra that share  a cornercorner with one O(12)LiMn2Cr tetrahedra,  a cornercorner with one O(9)LiMnCrCo tetrahedra, corners with two equivalent O(5)LiMn2Co tetrahedra,  a cornercorner with one O(3)LiMnCo2 trigonal pyramid,  an edgeedge with one O(12)LiMn2Cr tetrahedra,  an edgeedge with one O(9)LiMnCrCo tetrahedra, and  an edgeedge with one O(10)LiMn2Co trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Mn(2), and one Co(2) atom to form distorted OLiMn2Co trigonal pyramids that share  a cornercorner with one O(2)LiCrCo2 tetrahedra, corners with two equivalent O(6)LiMnCrCo tetrahedra, corners with three equivalent O(5)LiMn2Co tetrahedra,  an edgeedge with one O(12)LiMn2Cr tetrahedra, and edges with two equivalent O(9)LiMnCrCo tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Mn(1), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(5)LiMn2Co tetrahedra, corners with two equivalent O(9)LiMnCrCo tetrahedra,  a cornercorner with one O(3)LiMnCo2 trigonal pyramid, edges with two equivalent O(9)LiMnCrCo tetrahedra, and  an edgeedge with one O(10)LiMn2Co trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Mn3Cr2Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.776
_cell_length_b   5.776
_cell_length_c   9.485
_cell_angle_alpha   89.597
_cell_angle_beta   89.597
_cell_angle_gamma   60.324
_symmetry_Int_Tables_number   1
_cell_volume   274.882
_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  0.333  0.333  0.105  1.0
  Li  Li1  1  0.997  0.997  0.001  1.0
  Li  Li2  1  0.996  0.996  0.505  1.0
  Li  Li3  1  0.667  0.667  0.610  1.0
  Mn  Mn4  1  0.170  0.170  0.785  1.0
  Mn  Mn5  1  0.832  0.339  0.285  1.0
  Mn  Mn6  1  0.339  0.832  0.285  1.0
  Cr  Cr7  1  0.338  0.338  0.516  1.0
  Cr  Cr8  1  0.669  0.669  0.014  1.0
  Co  Co9  1  0.663  0.171  0.787  1.0
  Co  Co10  1  0.171  0.663  0.787  1.0
  Co  Co11  1  0.833  0.833  0.289  1.0
  O  O12  1  0.675  0.170  0.399  1.0
  O  O13  1  0.482  0.482  0.664  1.0
  O  O14  1  0.335  0.335  0.890  1.0
  O  O15  1  1.000  1.000  0.693  1.0
  O  O16  1  0.000  0.000  0.190  1.0
  O  O17  1  0.170  0.675  0.399  1.0
  O  O18  1  0.482  0.038  0.665  1.0
  O  O19  1  0.038  0.482  0.665  1.0
  O  O20  1  0.837  0.837  0.895  1.0
  O  O21  1  0.162  0.162  0.397  1.0
  O  O22  1  0.963  0.513  0.158  1.0
  O  O23  1  0.513  0.963  0.158  1.0
  O  O24  1  0.667  0.667  0.390  1.0
  O  O25  1  0.838  0.323  0.896  1.0
  O  O26  1  0.519  0.519  0.164  1.0
  O  O27  1  0.323  0.838  0.896  1.0
[/CIF]
.