The structure described by Li4MnFe3(PO4)4 is Hausmannite-derived structured and crystallizes in the monoclinic Pm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(10), one O(11), one O(12), one O(2), and one O(3) atom to form LiO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra,  an edgeedge with one P(1)O4 tetrahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-69°. In the second Li site, Li(2) is bonded to one O(4), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form LiO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra,  an edgeedge with one P(2)O4 tetrahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-69°. Mn(1) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, edges with two equivalent Li(1)O6 octahedra, and  an edgeedge with one P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-69°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, edges with two equivalent Li(2)O6 octahedra, and  an edgeedge with one P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-69°. In the second Fe site, Fe(2) is bonded to one O(11), one O(7), two equivalent O(10), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, corners with four equivalent Fe(3)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, edges with two equivalent Li(1)O6 octahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-69°. In the third Fe site, Fe(3) is bonded to one O(12), one O(8), two equivalent O(10), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, edges with two equivalent Li(2)O6 octahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-69°. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(12), one O(2), and two equivalent O(3) atoms to form PO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-59°. In the second P site, P(2) is bonded to one O(5), one O(7), and two equivalent O(4) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-59°. In the third P site, P(3) is bonded to one O(6), one O(8), and two equivalent O(9) atoms to form PO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-60°. In the fourth P site, P(4) is bonded to one O(1), one O(11), and two equivalent O(10) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-59°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to two equivalent Li(1), one Fe(1), and one P(4) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(1), one Mn(1), and one P(1) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(1), one Fe(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Mn(1), one Fe(1), and one P(2) atom. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(2), one Fe(1), and one P(2) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to two equivalent Li(2), one Mn(1), and one P(3) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to two equivalent Li(2), one Fe(2), and one P(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(2), one Fe(3), and one P(3) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Fe(2), one Fe(3), and one P(3) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(2), one Fe(3), and one P(4) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(1), one Fe(2), and one P(4) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to two equivalent Li(1), one Fe(3), and one P(1) atom. is represented by the CIF file [CIF]
data_Li4MnFe3(PO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.105
_cell_length_b   4.762
_cell_length_c   10.467
_cell_angle_alpha   89.876
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   304.307
_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  0.249  1.000  0.001  1.0
  Li  Li1  1  0.751  1.000  0.001  1.0
  Li  Li2  1  0.249  0.500  0.500  1.0
  Li  Li3  1  0.751  0.500  0.500  1.0
  Mn  Mn4  1  0.500  0.978  0.719  1.0
  Fe  Fe5  1  0.000  0.475  0.782  1.0
  Fe  Fe6  1  0.000  0.025  0.281  1.0
  Fe  Fe7  1  0.500  0.525  0.219  1.0
  P  P8  1  0.500  0.420  0.907  1.0
  P  P9  1  0.000  0.916  0.594  1.0
  P  P10  1  0.500  0.082  0.404  1.0
  P  P11  1  0.000  0.582  0.095  1.0
  O  O12  1  0.000  0.707  0.957  1.0
  O  O13  1  0.500  0.742  0.905  1.0
  O  O14  1  0.297  0.289  0.836  1.0
  O  O15  1  0.703  0.289  0.836  1.0
  O  O16  1  0.798  0.780  0.664  1.0
  O  O17  1  0.202  0.780  0.664  1.0
  O  O18  1  0.000  0.238  0.597  1.0
  O  O19  1  0.500  0.209  0.541  1.0
  O  O20  1  0.000  0.794  0.456  1.0
  O  O21  1  0.500  0.760  0.403  1.0
  O  O22  1  0.297  0.215  0.334  1.0
  O  O23  1  0.703  0.215  0.334  1.0
  O  O24  1  0.797  0.714  0.166  1.0
  O  O25  1  0.203  0.714  0.166  1.0
  O  O26  1  0.000  0.259  0.097  1.0
  O  O27  1  0.500  0.292  0.044  1.0
[/CIF]
.
The structure described by Li4MnFe3(PO4)4 is Hausmannite-derived structured and crystallizes in the monoclinic Pm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(10), one O(11), one O(12), one O(2), and one O(3) atom to form LiO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra,  an edgeedge with one P(1)O4 tetrahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-69°. In the second Li site, Li(2) is bonded to one O(4), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form LiO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra,  an edgeedge with one P(2)O4 tetrahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-69°. Mn(1) is bonded to one O(2), one O(6), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, edges with two equivalent Li(1)O6 octahedra, and  an edgeedge with one P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-69°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, edges with two equivalent Li(2)O6 octahedra, and  an edgeedge with one P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-69°. In the second Fe site, Fe(2) is bonded to one O(11), one O(7), two equivalent O(10), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, corners with four equivalent Fe(3)O6 octahedra,  a cornercorner with one P(2)O4 tetrahedra,  a cornercorner with one P(4)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, edges with two equivalent Li(1)O6 octahedra, and  an edgeedge with one P(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-69°. In the third Fe site, Fe(3) is bonded to one O(12), one O(8), two equivalent O(10), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra,  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent P(4)O4 tetrahedra, edges with two equivalent Li(2)O6 octahedra, and  an edgeedge with one P(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-69°. There are four inequivalent P sites. In the first P site, P(1) is bonded to one O(12), one O(2), and two equivalent O(3) atoms to form PO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-59°. In the second P site, P(2) is bonded to one O(5), one O(7), and two equivalent O(4) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-59°. In the third P site, P(3) is bonded to one O(6), one O(8), and two equivalent O(9) atoms to form PO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with two equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-60°. In the fourth P site, P(4) is bonded to one O(1), one O(11), and two equivalent O(10) atoms to form PO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-59°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to two equivalent Li(1), one Fe(1), and one P(4) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(1), one Mn(1), and one P(1) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(1), one Fe(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Mn(1), one Fe(1), and one P(2) atom. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(2), one Fe(1), and one P(2) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to two equivalent Li(2), one Mn(1), and one P(3) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to two equivalent Li(2), one Fe(2), and one P(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(2), one Fe(3), and one P(3) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Fe(2), one Fe(3), and one P(3) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(2), one Fe(3), and one P(4) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Li(1), one Fe(2), and one P(4) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to two equivalent Li(1), one Fe(3), and one P(1) atom. is represented by the CIF file [CIF]
data_Li4MnFe3(PO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.105
_cell_length_b   4.762
_cell_length_c   10.467
_cell_angle_alpha   89.876
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   304.307
_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  0.249  1.000  0.001  1.0
  Li  Li1  1  0.751  1.000  0.001  1.0
  Li  Li2  1  0.249  0.500  0.500  1.0
  Li  Li3  1  0.751  0.500  0.500  1.0
  Mn  Mn4  1  0.500  0.978  0.719  1.0
  Fe  Fe5  1  0.000  0.475  0.782  1.0
  Fe  Fe6  1  0.000  0.025  0.281  1.0
  Fe  Fe7  1  0.500  0.525  0.219  1.0
  P  P8  1  0.500  0.420  0.907  1.0
  P  P9  1  0.000  0.916  0.594  1.0
  P  P10  1  0.500  0.082  0.404  1.0
  P  P11  1  0.000  0.582  0.095  1.0
  O  O12  1  0.000  0.707  0.957  1.0
  O  O13  1  0.500  0.742  0.905  1.0
  O  O14  1  0.297  0.289  0.836  1.0
  O  O15  1  0.703  0.289  0.836  1.0
  O  O16  1  0.798  0.780  0.664  1.0
  O  O17  1  0.202  0.780  0.664  1.0
  O  O18  1  0.000  0.238  0.597  1.0
  O  O19  1  0.500  0.209  0.541  1.0
  O  O20  1  0.000  0.794  0.456  1.0
  O  O21  1  0.500  0.760  0.403  1.0
  O  O22  1  0.297  0.215  0.334  1.0
  O  O23  1  0.703  0.215  0.334  1.0
  O  O24  1  0.797  0.714  0.166  1.0
  O  O25  1  0.203  0.714  0.166  1.0
  O  O26  1  0.000  0.259  0.097  1.0
  O  O27  1  0.500  0.292  0.044  1.0
[/CIF]
.