The crystal structure described by Li4Fe3(CoO4)3 crystallizes in the triclinic P-1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(4), one O(5), one O(6), and two equivalent O(2) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with five equivalent Fe(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-15°. In the second Li site, Li(2) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the third Li site, Li(3) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Co(1)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, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-12°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with five equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-15°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form CoO6 octahedra that share corners with four equivalent Li(3)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, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-10°. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(3), one O(5), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(2), one Co(1), and one Co(2) atom. In the second O site, O(2) is bonded to two equivalent Li(1), one Fe(1), one Fe(2), and one Co(2) atom to form OLi2Fe2Co square pyramids that share  a cornercorner with one O(4)Li3Fe2Co octahedra,  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(3)Li2FeCo2 square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with three equivalent O(5)Li2Fe2Co square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid,  an edgeedge with one O(3)Li2FeCo2 square pyramid, and edges with two equivalent O(6)Li2FeCo2 square pyramids. The corner-sharing octahedral tilt angles are 7°. In the third O site, O(3) is bonded to one Li(2), one Li(3), one Fe(1), one Co(1), and one Co(2) atom to form OLi2FeCo2 square pyramids that share  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid, corners with two equivalent O(6)Li2FeCo2 square pyramids, corners with four equivalent O(3)Li2FeCo2 square pyramids, edges with four equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid, and  an edgeedge with one O(6)Li2FeCo2 square pyramid. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Li(3), one Fe(1), one Fe(2), and one Co(1) atom to form OLi3Fe2Co octahedra that share corners with four equivalent O(4)Li3Fe2Co octahedra,  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid, edges with two equivalent O(2)Li2Fe2Co square pyramids, edges with two equivalent O(5)Li2Fe2Co square pyramids, edges with two equivalent O(6)Li2FeCo2 square pyramids, and edges with four equivalent O(3)Li2FeCo2 square pyramids. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), two equivalent Fe(2), and one Co(2) atom to form OLi2Fe2Co square pyramids that share  a cornercorner with one O(4)Li3Fe2Co octahedra,  a cornercorner with one O(5)Li2Fe2Co square pyramid,  a cornercorner with one O(3)Li2FeCo2 square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with three equivalent O(2)Li2Fe2Co square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid,  an edgeedge with one O(3)Li2FeCo2 square pyramid, and edges with two equivalent O(6)Li2FeCo2 square pyramids. The corner-sharing octahedral tilt angles are 3°. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Fe(2), and two equivalent Co(2) atoms to form OLi2FeCo2 square pyramids that share  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with two equivalent O(3)Li2FeCo2 square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(3)Li2FeCo2 square pyramid,  an edgeedge with one O(6)Li2FeCo2 square pyramid, edges with two equivalent O(2)Li2Fe2Co square pyramids, and edges with two equivalent O(5)Li2Fe2Co square pyramids. is represented by the CIF card [CIF]
data_Li4Fe3(CoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.727
_cell_length_b   5.903
_cell_length_c   6.610
_cell_angle_alpha   105.619
_cell_angle_beta   102.722
_cell_angle_gamma   88.982
_symmetry_Int_Tables_number   1
_cell_volume   209.696
_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  0.179  0.152  0.652  1.0
  Li  Li1  1  0.821  0.848  0.348  1.0
  Li  Li2  1  0.500  0.500  0.000  1.0
  Li  Li3  1  0.000  0.500  0.000  1.0
  Fe  Fe4  1  0.000  0.000  0.000  1.0
  Fe  Fe5  1  0.664  0.668  0.664  1.0
  Fe  Fe6  1  0.336  0.332  0.336  1.0
  Co  Co7  1  0.500  0.000  0.000  1.0
  Co  Co8  1  0.167  0.667  0.662  1.0
  Co  Co9  1  0.833  0.333  0.338  1.0
  O  O10  1  0.417  0.891  0.689  1.0
  O  O11  1  0.919  0.889  0.672  1.0
  O  O12  1  0.583  0.109  0.311  1.0
  O  O13  1  0.254  0.760  0.971  1.0
  O  O14  1  0.081  0.111  0.328  1.0
  O  O15  1  0.740  0.759  0.982  1.0
  O  O16  1  0.590  0.560  0.353  1.0
  O  O17  1  0.260  0.241  0.018  1.0
  O  O18  1  0.082  0.553  0.347  1.0
  O  O19  1  0.746  0.240  0.029  1.0
  O  O20  1  0.410  0.440  0.647  1.0
  O  O21  1  0.918  0.447  0.653  1.0
[/CIF]
.
The crystal structure described by Li4Fe3(CoO4)3 crystallizes in the triclinic P-1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(4), one O(5), one O(6), and two equivalent O(2) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with five equivalent Fe(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-15°. In the second Li site, Li(2) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the third Li site, Li(3) is bonded to two equivalent O(3), two equivalent O(4), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Co(1)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, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-12°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms to form FeO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with five equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-15°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form CoO6 octahedra that share corners with four equivalent Li(3)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, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-10°. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(3), one O(5), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(2), one Co(1), and one Co(2) atom. In the second O site, O(2) is bonded to two equivalent Li(1), one Fe(1), one Fe(2), and one Co(2) atom to form OLi2Fe2Co square pyramids that share  a cornercorner with one O(4)Li3Fe2Co octahedra,  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(3)Li2FeCo2 square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with three equivalent O(5)Li2Fe2Co square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid,  an edgeedge with one O(3)Li2FeCo2 square pyramid, and edges with two equivalent O(6)Li2FeCo2 square pyramids. The corner-sharing octahedral tilt angles are 7°. In the third O site, O(3) is bonded to one Li(2), one Li(3), one Fe(1), one Co(1), and one Co(2) atom to form OLi2FeCo2 square pyramids that share  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid, corners with two equivalent O(6)Li2FeCo2 square pyramids, corners with four equivalent O(3)Li2FeCo2 square pyramids, edges with four equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid, and  an edgeedge with one O(6)Li2FeCo2 square pyramid. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Li(3), one Fe(1), one Fe(2), and one Co(1) atom to form OLi3Fe2Co octahedra that share corners with four equivalent O(4)Li3Fe2Co octahedra,  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid, edges with two equivalent O(2)Li2Fe2Co square pyramids, edges with two equivalent O(5)Li2Fe2Co square pyramids, edges with two equivalent O(6)Li2FeCo2 square pyramids, and edges with four equivalent O(3)Li2FeCo2 square pyramids. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), two equivalent Fe(2), and one Co(2) atom to form OLi2Fe2Co square pyramids that share  a cornercorner with one O(4)Li3Fe2Co octahedra,  a cornercorner with one O(5)Li2Fe2Co square pyramid,  a cornercorner with one O(3)Li2FeCo2 square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with three equivalent O(2)Li2Fe2Co square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(2)Li2Fe2Co square pyramid,  an edgeedge with one O(5)Li2Fe2Co square pyramid,  an edgeedge with one O(3)Li2FeCo2 square pyramid, and edges with two equivalent O(6)Li2FeCo2 square pyramids. The corner-sharing octahedral tilt angles are 3°. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Fe(2), and two equivalent Co(2) atoms to form OLi2FeCo2 square pyramids that share  a cornercorner with one O(2)Li2Fe2Co square pyramid,  a cornercorner with one O(5)Li2Fe2Co square pyramid,  a cornercorner with one O(6)Li2FeCo2 square pyramid, corners with two equivalent O(3)Li2FeCo2 square pyramids, edges with two equivalent O(4)Li3Fe2Co octahedra,  an edgeedge with one O(3)Li2FeCo2 square pyramid,  an edgeedge with one O(6)Li2FeCo2 square pyramid, edges with two equivalent O(2)Li2Fe2Co square pyramids, and edges with two equivalent O(5)Li2Fe2Co square pyramids. is represented by the CIF card [CIF]
data_Li4Fe3(CoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.727
_cell_length_b   5.903
_cell_length_c   6.610
_cell_angle_alpha   105.619
_cell_angle_beta   102.722
_cell_angle_gamma   88.982
_symmetry_Int_Tables_number   1
_cell_volume   209.696
_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  0.179  0.152  0.652  1.0
  Li  Li1  1  0.821  0.848  0.348  1.0
  Li  Li2  1  0.500  0.500  0.000  1.0
  Li  Li3  1  0.000  0.500  0.000  1.0
  Fe  Fe4  1  0.000  0.000  0.000  1.0
  Fe  Fe5  1  0.664  0.668  0.664  1.0
  Fe  Fe6  1  0.336  0.332  0.336  1.0
  Co  Co7  1  0.500  0.000  0.000  1.0
  Co  Co8  1  0.167  0.667  0.662  1.0
  Co  Co9  1  0.833  0.333  0.338  1.0
  O  O10  1  0.417  0.891  0.689  1.0
  O  O11  1  0.919  0.889  0.672  1.0
  O  O12  1  0.583  0.109  0.311  1.0
  O  O13  1  0.254  0.760  0.971  1.0
  O  O14  1  0.081  0.111  0.328  1.0
  O  O15  1  0.740  0.759  0.982  1.0
  O  O16  1  0.590  0.560  0.353  1.0
  O  O17  1  0.260  0.241  0.018  1.0
  O  O18  1  0.082  0.553  0.347  1.0
  O  O19  1  0.746  0.240  0.029  1.0
  O  O20  1  0.410  0.440  0.647  1.0
  O  O21  1  0.918  0.447  0.653  1.0
[/CIF]
.