The structure described by Li4Mn3(FeO4)3 crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(4), one O(5), one O(6), and two equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the second Li site, Li(2) is bonded to one O(2), one O(4), one O(5), one O(6), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with three equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with four equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with three equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. In the second Mn site, Mn(2) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with three equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second Fe site, Fe(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Mn(1), one Mn(2), and one Fe(1) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(1)Li2Mn2Fe square pyramid, corners with two equivalent O(5)Li2Mn2Fe square pyramids, corners with two equivalent O(6)Li2Mn2Fe square pyramids, corners with two equivalent O(2)Li2MnFe2 square pyramids, corners with two equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(2)Li2MnFe2 square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid, edges with two equivalent O(6)Li2Mn2Fe square pyramids, and edges with two equivalent O(4)Li2MnFe2 square pyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Mn(1), one Fe(1), and one Fe(2) atom to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(2)Li2MnFe2 square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid, edges with two equivalent O(6)Li2Mn2Fe square pyramids, edges with two equivalent O(3)Li2MnFe2 square pyramids, and edges with three equivalent O(5)Li2Mn2Fe square pyramids. In the third O site, O(3) is bonded to two equivalent Li(2), one Mn(1), one Fe(1), and one Fe(2) atom to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(3)Li2MnFe2 square pyramid, corners with two equivalent O(5)Li2Mn2Fe square pyramids, corners with two equivalent O(6)Li2Mn2Fe square pyramids, corners with two equivalent O(2)Li2MnFe2 square pyramids, corners with two equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(6)Li2Mn2Fe square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(5)Li2Mn2Fe square pyramids, and edges with two equivalent O(2)Li2MnFe2 square pyramids. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Mn(2), and two equivalent Fe(1) atoms to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(4)Li2MnFe2 square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(2)Li2MnFe2 square pyramids,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(1)Li2Mn2Fe square pyramids, and edges with three equivalent O(6)Li2Mn2Fe square pyramids. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), two equivalent Mn(1), and one Fe(2) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(5)Li2Mn2Fe square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(6)Li2Mn2Fe square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(3)Li2MnFe2 square pyramids, and edges with three equivalent O(2)Li2MnFe2 square pyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(2), one Mn(1), one Mn(2), and one Fe(1) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(6)Li2Mn2Fe square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(5)Li2Mn2Fe square pyramids,  an edgeedge with one O(3)Li2MnFe2 square pyramid, edges with two equivalent O(1)Li2Mn2Fe square pyramids, edges with two equivalent O(2)Li2MnFe2 square pyramids, and edges with three equivalent O(4)Li2MnFe2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Mn3(FeO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.134
_cell_length_b   6.007
_cell_length_c   7.944
_cell_angle_alpha   78.704
_cell_angle_beta   78.160
_cell_angle_gamma   73.059
_symmetry_Int_Tables_number   1
_cell_volume   226.938
_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  0.500  0.834  0.168  1.0
  Li  Li1  1  0.500  0.166  0.832  1.0
  Li  Li2  1  0.003  0.667  0.335  1.0
  Li  Li3  1  0.997  0.333  0.665  1.0
  Mn  Mn4  1  0.004  0.830  0.670  1.0
  Mn  Mn5  1  0.000  0.500  0.000  1.0
  Mn  Mn6  1  0.996  0.170  0.330  1.0
  Fe  Fe7  1  0.498  0.667  0.833  1.0
  Fe  Fe8  1  0.502  0.333  0.167  1.0
  Fe  Fe9  1  0.500  0.000  0.500  1.0
  O  O10  1  0.758  0.802  0.916  1.0
  O  O11  1  0.262  0.976  0.732  1.0
  O  O12  1  0.761  0.687  0.596  1.0
  O  O13  1  0.748  0.361  0.925  1.0
  O  O14  1  0.230  0.867  0.414  1.0
  O  O15  1  0.225  0.515  0.772  1.0
  O  O16  1  0.775  0.485  0.228  1.0
  O  O17  1  0.770  0.133  0.586  1.0
  O  O18  1  0.252  0.639  0.075  1.0
  O  O19  1  0.239  0.313  0.404  1.0
  O  O20  1  0.738  0.024  0.268  1.0
  O  O21  1  0.242  0.198  0.084  1.0
[/CIF]
.
The structure described by Li4Mn3(FeO4)3 crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(4), one O(5), one O(6), and two equivalent O(1) atoms to form LiO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the second Li site, Li(2) is bonded to one O(2), one O(4), one O(5), one O(6), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with three equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with four equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with three equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-11°. In the second Mn site, Mn(2) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(3), one O(6), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with three equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second Fe site, Fe(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Mn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Mn(1), one Mn(2), and one Fe(1) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(1)Li2Mn2Fe square pyramid, corners with two equivalent O(5)Li2Mn2Fe square pyramids, corners with two equivalent O(6)Li2Mn2Fe square pyramids, corners with two equivalent O(2)Li2MnFe2 square pyramids, corners with two equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(2)Li2MnFe2 square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid, edges with two equivalent O(6)Li2Mn2Fe square pyramids, and edges with two equivalent O(4)Li2MnFe2 square pyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Mn(1), one Fe(1), and one Fe(2) atom to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(2)Li2MnFe2 square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid, edges with two equivalent O(6)Li2Mn2Fe square pyramids, edges with two equivalent O(3)Li2MnFe2 square pyramids, and edges with three equivalent O(5)Li2Mn2Fe square pyramids. In the third O site, O(3) is bonded to two equivalent Li(2), one Mn(1), one Fe(1), and one Fe(2) atom to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(3)Li2MnFe2 square pyramid, corners with two equivalent O(5)Li2Mn2Fe square pyramids, corners with two equivalent O(6)Li2Mn2Fe square pyramids, corners with two equivalent O(2)Li2MnFe2 square pyramids, corners with two equivalent O(4)Li2MnFe2 square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(6)Li2Mn2Fe square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(5)Li2Mn2Fe square pyramids, and edges with two equivalent O(2)Li2MnFe2 square pyramids. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Mn(2), and two equivalent Fe(1) atoms to form OLi2MnFe2 square pyramids that share  a cornercorner with one O(4)Li2MnFe2 square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(2)Li2MnFe2 square pyramids,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(3)Li2MnFe2 square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(1)Li2Mn2Fe square pyramids, and edges with three equivalent O(6)Li2Mn2Fe square pyramids. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), two equivalent Mn(1), and one Fe(2) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(5)Li2Mn2Fe square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(6)Li2Mn2Fe square pyramids,  an edgeedge with one O(1)Li2Mn2Fe square pyramid,  an edgeedge with one O(5)Li2Mn2Fe square pyramid,  an edgeedge with one O(4)Li2MnFe2 square pyramid, edges with two equivalent O(3)Li2MnFe2 square pyramids, and edges with three equivalent O(2)Li2MnFe2 square pyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(2), one Mn(1), one Mn(2), and one Fe(1) atom to form OLi2Mn2Fe square pyramids that share  a cornercorner with one O(6)Li2Mn2Fe square pyramid, corners with two equivalent O(1)Li2Mn2Fe square pyramids, corners with two equivalent O(3)Li2MnFe2 square pyramids, corners with four equivalent O(5)Li2Mn2Fe square pyramids,  an edgeedge with one O(3)Li2MnFe2 square pyramid, edges with two equivalent O(1)Li2Mn2Fe square pyramids, edges with two equivalent O(2)Li2MnFe2 square pyramids, and edges with three equivalent O(4)Li2MnFe2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Mn3(FeO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.134
_cell_length_b   6.007
_cell_length_c   7.944
_cell_angle_alpha   78.704
_cell_angle_beta   78.160
_cell_angle_gamma   73.059
_symmetry_Int_Tables_number   1
_cell_volume   226.938
_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  0.500  0.834  0.168  1.0
  Li  Li1  1  0.500  0.166  0.832  1.0
  Li  Li2  1  0.003  0.667  0.335  1.0
  Li  Li3  1  0.997  0.333  0.665  1.0
  Mn  Mn4  1  0.004  0.830  0.670  1.0
  Mn  Mn5  1  0.000  0.500  0.000  1.0
  Mn  Mn6  1  0.996  0.170  0.330  1.0
  Fe  Fe7  1  0.498  0.667  0.833  1.0
  Fe  Fe8  1  0.502  0.333  0.167  1.0
  Fe  Fe9  1  0.500  0.000  0.500  1.0
  O  O10  1  0.758  0.802  0.916  1.0
  O  O11  1  0.262  0.976  0.732  1.0
  O  O12  1  0.761  0.687  0.596  1.0
  O  O13  1  0.748  0.361  0.925  1.0
  O  O14  1  0.230  0.867  0.414  1.0
  O  O15  1  0.225  0.515  0.772  1.0
  O  O16  1  0.775  0.485  0.228  1.0
  O  O17  1  0.770  0.133  0.586  1.0
  O  O18  1  0.252  0.639  0.075  1.0
  O  O19  1  0.239  0.313  0.404  1.0
  O  O20  1  0.738  0.024  0.268  1.0
  O  O21  1  0.242  0.198  0.084  1.0
[/CIF]
.