The structure described by Li4Mn3Co2Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. 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 Mn(2)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-66°. 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 Ni(1)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-67°. 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 Mn(2)O6 octahedra, corners with two equivalent Ni(1)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. There are two inequivalent Mn sites. In the first Mn site, Mn(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 MnO6 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 Mn(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 49-51°. In the second Mn site, Mn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form MnO6 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 Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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 Mn(2)O6 octahedra, corners with four equivalent Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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 Ni(1)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 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 Mn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. In the second Ni site, Ni(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 NiO6 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 Mn(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. 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 distorted rectangular see-saw-like geometry to one Li(3), one Mn(2), one Co(1), and one Ni(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Mn(1), and one Co(1) atom to form distorted OLiMn2Co trigonal pyramids that share corners with two equivalent O(4)LiMn2Ni tetrahedra, corners with two equivalent O(6)LiMnCoNi tetrahedra,  a cornercorner with one O(10)LiMnNi2 trigonal pyramid, and edges with two equivalent O(6)LiMnCoNi tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Mn(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Mn(1), and one Ni(1) atom to form OLiMn2Ni tetrahedra that share corners with four equivalent O(6)LiMnCoNi tetrahedra and corners with two equivalent O(2)LiMn2Co trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Mn(2), and two equivalent Ni(2) atoms to form OLiMnNi2 tetrahedra that share corners with two equivalent O(12)LiCoNi2 tetrahedra and corners with three equivalent O(10)LiMnNi2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Co(1), and one Ni(1) atom to form distorted OLiMnCoNi tetrahedra that share  a cornercorner with one O(6)LiMnCoNi tetrahedra, corners with two equivalent O(4)LiMn2Ni tetrahedra,  a cornercorner with one O(2)LiMn2Co trigonal pyramid,  a cornercorner with one O(10)LiMnNi2 trigonal pyramid,  an edgeedge with one O(6)LiMnCoNi tetrahedra, and  an edgeedge with one O(2)LiMn2Co trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Mn(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), one Co(1), and two equivalent Ni(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(2), one Co(2), and one Ni(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Mn(2), and two equivalent Ni(2) atoms to form distorted OLiMnNi2 trigonal pyramids that share corners with two equivalent O(6)LiMnCoNi tetrahedra, corners with three equivalent O(5)LiMnNi2 tetrahedra,  a cornercorner with one O(2)LiMn2Co trigonal pyramid, and  an edgeedge with one O(12)LiCoNi2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Co(2), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(2), and two equivalent Ni(2) atoms to form a mixture of distorted edge and corner-sharing OLiCoNi2 tetrahedra. is represented by the CIF card [CIF]
data_Li4Mn3Co2Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.807
_cell_length_b   5.758
_cell_length_c   9.292
_cell_angle_alpha   90.001
_cell_angle_beta   91.371
_cell_angle_gamma   119.727
_symmetry_Int_Tables_number   1
_cell_volume   269.682
_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  0.666  0.896  1.0
  Li  Li1  1  0.991  0.995  0.992  1.0
  Li  Li2  1  0.996  0.998  0.497  1.0
  Li  Li3  1  0.666  0.333  0.398  1.0
  Mn  Mn4  1  0.172  0.832  0.213  1.0
  Mn  Mn5  1  0.172  0.341  0.213  1.0
  Mn  Mn6  1  0.344  0.172  0.714  1.0
  Co  Co7  1  0.341  0.670  0.487  1.0
  Co  Co8  1  0.677  0.339  0.983  1.0
  Ni  Ni9  1  0.660  0.830  0.212  1.0
  Ni  Ni10  1  0.830  0.660  0.711  1.0
  Ni  Ni11  1  0.830  0.170  0.711  1.0
  O  O12  1  0.179  0.840  0.598  1.0
  O  O13  1  0.040  0.520  0.338  1.0
  O  O14  1  0.319  0.660  0.106  1.0
  O  O15  1  0.011  0.006  0.307  1.0
  O  O16  1  0.005  0.002  0.801  1.0
  O  O17  1  0.179  0.340  0.598  1.0
  O  O18  1  0.469  0.959  0.347  1.0
  O  O19  1  0.469  0.511  0.347  1.0
  O  O20  1  0.328  0.164  0.102  1.0
  O  O21  1  0.663  0.832  0.595  1.0
  O  O22  1  0.512  0.470  0.848  1.0
  O  O23  1  0.512  0.042  0.848  1.0
  O  O24  1  0.660  0.330  0.608  1.0
  O  O25  1  0.841  0.664  0.096  1.0
  O  O26  1  0.956  0.478  0.847  1.0
  O  O27  1  0.841  0.178  0.095  1.0
[/CIF]
.
The structure described by Li4Mn3Co2Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. 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 Mn(2)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-66°. 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 Ni(1)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-67°. 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 Mn(2)O6 octahedra, corners with two equivalent Ni(1)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. There are two inequivalent Mn sites. In the first Mn site, Mn(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 MnO6 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 Mn(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 49-51°. In the second Mn site, Mn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form MnO6 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 Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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 Mn(2)O6 octahedra, corners with four equivalent Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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 Ni(1)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 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 Mn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. In the second Ni site, Ni(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 NiO6 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 Mn(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. 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 distorted rectangular see-saw-like geometry to one Li(3), one Mn(2), one Co(1), and one Ni(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Mn(1), and one Co(1) atom to form distorted OLiMn2Co trigonal pyramids that share corners with two equivalent O(4)LiMn2Ni tetrahedra, corners with two equivalent O(6)LiMnCoNi tetrahedra,  a cornercorner with one O(10)LiMnNi2 trigonal pyramid, and edges with two equivalent O(6)LiMnCoNi tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Mn(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Mn(1), and one Ni(1) atom to form OLiMn2Ni tetrahedra that share corners with four equivalent O(6)LiMnCoNi tetrahedra and corners with two equivalent O(2)LiMn2Co trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Mn(2), and two equivalent Ni(2) atoms to form OLiMnNi2 tetrahedra that share corners with two equivalent O(12)LiCoNi2 tetrahedra and corners with three equivalent O(10)LiMnNi2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Co(1), and one Ni(1) atom to form distorted OLiMnCoNi tetrahedra that share  a cornercorner with one O(6)LiMnCoNi tetrahedra, corners with two equivalent O(4)LiMn2Ni tetrahedra,  a cornercorner with one O(2)LiMn2Co trigonal pyramid,  a cornercorner with one O(10)LiMnNi2 trigonal pyramid,  an edgeedge with one O(6)LiMnCoNi tetrahedra, and  an edgeedge with one O(2)LiMn2Co trigonal pyramid. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Mn(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), one Co(1), and two equivalent Ni(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(2), one Co(2), and one Ni(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Mn(2), and two equivalent Ni(2) atoms to form distorted OLiMnNi2 trigonal pyramids that share corners with two equivalent O(6)LiMnCoNi tetrahedra, corners with three equivalent O(5)LiMnNi2 tetrahedra,  a cornercorner with one O(2)LiMn2Co trigonal pyramid, and  an edgeedge with one O(12)LiCoNi2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Co(2), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(2), and two equivalent Ni(2) atoms to form a mixture of distorted edge and corner-sharing OLiCoNi2 tetrahedra. is represented by the CIF card [CIF]
data_Li4Mn3Co2Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.807
_cell_length_b   5.758
_cell_length_c   9.292
_cell_angle_alpha   90.001
_cell_angle_beta   91.371
_cell_angle_gamma   119.727
_symmetry_Int_Tables_number   1
_cell_volume   269.682
_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  0.666  0.896  1.0
  Li  Li1  1  0.991  0.995  0.992  1.0
  Li  Li2  1  0.996  0.998  0.497  1.0
  Li  Li3  1  0.666  0.333  0.398  1.0
  Mn  Mn4  1  0.172  0.832  0.213  1.0
  Mn  Mn5  1  0.172  0.341  0.213  1.0
  Mn  Mn6  1  0.344  0.172  0.714  1.0
  Co  Co7  1  0.341  0.670  0.487  1.0
  Co  Co8  1  0.677  0.339  0.983  1.0
  Ni  Ni9  1  0.660  0.830  0.212  1.0
  Ni  Ni10  1  0.830  0.660  0.711  1.0
  Ni  Ni11  1  0.830  0.170  0.711  1.0
  O  O12  1  0.179  0.840  0.598  1.0
  O  O13  1  0.040  0.520  0.338  1.0
  O  O14  1  0.319  0.660  0.106  1.0
  O  O15  1  0.011  0.006  0.307  1.0
  O  O16  1  0.005  0.002  0.801  1.0
  O  O17  1  0.179  0.340  0.598  1.0
  O  O18  1  0.469  0.959  0.347  1.0
  O  O19  1  0.469  0.511  0.347  1.0
  O  O20  1  0.328  0.164  0.102  1.0
  O  O21  1  0.663  0.832  0.595  1.0
  O  O22  1  0.512  0.470  0.848  1.0
  O  O23  1  0.512  0.042  0.848  1.0
  O  O24  1  0.660  0.330  0.608  1.0
  O  O25  1  0.841  0.664  0.096  1.0
  O  O26  1  0.956  0.478  0.847  1.0
  O  O27  1  0.841  0.178  0.095  1.0
[/CIF]
.