The material structure described by Li4Cr3Mn5O16 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(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. 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 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-65°. 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 trigonal pyramids that share  a cornercorner with one Mn(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-67°. 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 Cr(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. There are two inequivalent Cr sites. In the first Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 52°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with four equivalent Mn(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Mn site, Mn(2) 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Mn(1)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the third Mn site, Mn(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Mn site, Mn(4) 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 Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Mn(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. 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(2), one Mn(1), and one Mn(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Mn(1) atom to form distorted corner-sharing OLiMnCr2 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Mn(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Mn(2) atom to form distorted corner-sharing OLiMnCr2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Mn(4) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(12)LiMn3 tetrahedra and corners with four equivalent O(9)LiMn2Cr tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Cr(1), one Mn(1), and one Mn(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Mn(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(3), and one Mn(4) atom to form distorted OLiMn2Cr tetrahedra that share  a cornercorner with one O(9)LiMn2Cr tetrahedra,  a cornercorner with one O(12)LiMn3 tetrahedra, corners with two equivalent O(5)LiMn2Cr tetrahedra,  an edgeedge with one O(9)LiMn2Cr tetrahedra, and  an edgeedge with one O(12)LiMn3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Mn(4) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Mn(2), and one Mn(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(3), and two equivalent Mn(4) atoms to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.878
_cell_length_c   9.502
_cell_angle_alpha   89.049
_cell_angle_beta   89.049
_cell_angle_gamma   59.707
_symmetry_Int_Tables_number   1
_cell_volume   283.431
_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  0.670  0.670  0.899  1.0
  Li  Li1  1  0.999  0.999  0.997  1.0
  Li  Li2  1  0.999  0.999  0.494  1.0
  Li  Li3  1  0.335  0.335  0.394  1.0
  Mn  Mn4  1  0.664  0.664  0.486  1.0
  Mn  Mn5  1  0.829  0.829  0.214  1.0
  Mn  Mn6  1  0.331  0.331  0.990  1.0
  Mn  Mn7  1  0.665  0.171  0.715  1.0
  Mn  Mn8  1  0.171  0.665  0.715  1.0
  Cr  Cr9  1  0.827  0.339  0.213  1.0
  Cr  Cr10  1  0.339  0.827  0.213  1.0
  Cr  Cr11  1  0.171  0.171  0.714  1.0
  O  O12  1  0.835  0.325  0.600  1.0
  O  O13  1  0.514  0.514  0.335  1.0
  O  O14  1  0.673  0.673  0.106  1.0
  O  O15  1  0.992  0.992  0.308  1.0
  O  O16  1  0.997  0.997  0.810  1.0
  O  O17  1  0.325  0.835  0.600  1.0
  O  O18  1  0.958  0.522  0.340  1.0
  O  O19  1  0.522  0.958  0.340  1.0
  O  O20  1  0.162  0.162  0.094  1.0
  O  O21  1  0.839  0.839  0.608  1.0
  O  O22  1  0.485  0.043  0.841  1.0
  O  O23  1  0.043  0.485  0.841  1.0
  O  O24  1  0.341  0.341  0.609  1.0
  O  O25  1  0.670  0.159  0.098  1.0
  O  O26  1  0.482  0.482  0.839  1.0
  O  O27  1  0.159  0.670  0.098  1.0
[/CIF]
.
The material structure described by Li4Cr3Mn5O16 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(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. 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 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-65°. 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 trigonal pyramids that share  a cornercorner with one Mn(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-67°. 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 Cr(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. There are two inequivalent Cr sites. In the first Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 52°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with four equivalent Mn(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Mn site, Mn(2) 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Mn(1)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the third Mn site, Mn(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Mn site, Mn(4) 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 Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Mn(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. 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(2), one Mn(1), and one Mn(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Mn(1) atom to form distorted corner-sharing OLiMnCr2 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Mn(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Mn(2) atom to form distorted corner-sharing OLiMnCr2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Mn(4) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(12)LiMn3 tetrahedra and corners with four equivalent O(9)LiMn2Cr tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Cr(1), one Mn(1), and one Mn(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Mn(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(3), and one Mn(4) atom to form distorted OLiMn2Cr tetrahedra that share  a cornercorner with one O(9)LiMn2Cr tetrahedra,  a cornercorner with one O(12)LiMn3 tetrahedra, corners with two equivalent O(5)LiMn2Cr tetrahedra,  an edgeedge with one O(9)LiMn2Cr tetrahedra, and  an edgeedge with one O(12)LiMn3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Mn(4) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Mn(2), and one Mn(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(3), and two equivalent Mn(4) atoms to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.878
_cell_length_c   9.502
_cell_angle_alpha   89.049
_cell_angle_beta   89.049
_cell_angle_gamma   59.707
_symmetry_Int_Tables_number   1
_cell_volume   283.431
_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  0.670  0.670  0.899  1.0
  Li  Li1  1  0.999  0.999  0.997  1.0
  Li  Li2  1  0.999  0.999  0.494  1.0
  Li  Li3  1  0.335  0.335  0.394  1.0
  Mn  Mn4  1  0.664  0.664  0.486  1.0
  Mn  Mn5  1  0.829  0.829  0.214  1.0
  Mn  Mn6  1  0.331  0.331  0.990  1.0
  Mn  Mn7  1  0.665  0.171  0.715  1.0
  Mn  Mn8  1  0.171  0.665  0.715  1.0
  Cr  Cr9  1  0.827  0.339  0.213  1.0
  Cr  Cr10  1  0.339  0.827  0.213  1.0
  Cr  Cr11  1  0.171  0.171  0.714  1.0
  O  O12  1  0.835  0.325  0.600  1.0
  O  O13  1  0.514  0.514  0.335  1.0
  O  O14  1  0.673  0.673  0.106  1.0
  O  O15  1  0.992  0.992  0.308  1.0
  O  O16  1  0.997  0.997  0.810  1.0
  O  O17  1  0.325  0.835  0.600  1.0
  O  O18  1  0.958  0.522  0.340  1.0
  O  O19  1  0.522  0.958  0.340  1.0
  O  O20  1  0.162  0.162  0.094  1.0
  O  O21  1  0.839  0.839  0.608  1.0
  O  O22  1  0.485  0.043  0.841  1.0
  O  O23  1  0.043  0.485  0.841  1.0
  O  O24  1  0.341  0.341  0.609  1.0
  O  O25  1  0.670  0.159  0.098  1.0
  O  O26  1  0.482  0.482  0.839  1.0
  O  O27  1  0.159  0.670  0.098  1.0
[/CIF]
.