The crystal structure described by Li3Fe5O12 crystallizes in the triclinic P1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(10), one O(17), one O(19), one O(5), and one O(9) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-64°. In the second Li site, Li(2) is bonded to one O(12), one O(13), one O(21), one O(23), and one O(8) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Li(3)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with two equivalent Fe(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-64°. In the third Li site, Li(3) is bonded to one O(12), one O(13), one O(15), one O(24), and one O(4) atom to form distorted LiO5 trigonal bipyramids that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-76°. In the fourth Li site, Li(4) is bonded in a 4-coordinate geometry to one O(1), one O(10), one O(11), one O(14), one O(20), and one O(9) atom. In the fifth Li site, Li(5) is bonded to one O(10), one O(17), one O(19), one O(20), one O(5), and one O(9) atom to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with three equivalent Fe(9)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 15-18°. In the sixth Li site, Li(6) is bonded to one O(12), one O(13), one O(21), one O(23), one O(24), and one O(8) atom to form distorted LiO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Fe(10)O6 octahedra,  an edgeedge with one Li(3)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 17-20°. There are ten inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(11), one O(14), one O(18), one O(2), and one O(3) atom to form a mixture of edge and corner-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 20-22°. In the second Fe site, Fe(2) is bonded to one O(17), one O(19), one O(22), one O(5), one O(6), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(8)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra,  an edgeedge with one Fe(9)O6 octahedra, and  an edgeedge with one Li(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 7-24°. In the third Fe site, Fe(3) is bonded to one O(15), one O(16), one O(22), one O(4), one O(6), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Li(3)O5 trigonal bipyramids,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, and edges with three equivalent Fe(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 19-22°. In the fourth Fe site, Fe(4) is bonded to one O(18), one O(2), one O(21), one O(23), one O(3), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(7)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra, and  an edgeedge with one Li(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-27°. In the fifth Fe site, Fe(5) is bonded to one O(1), one O(10), one O(11), one O(14), one O(20), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(7)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra,  an edgeedge with one Fe(9)O6 octahedra, and  an edgeedge with one Li(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 11-22°. In the sixth Fe site, Fe(6) is bonded to one O(12), one O(13), one O(15), one O(16), one O(24), and one O(4) atom to form FeO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(8)O6 octahedra,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra,  an edgeedge with one Li(2)O5 trigonal bipyramid, and edges with two equivalent Li(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 7-25°. In the seventh Fe site, Fe(7) is bonded to one O(1), one O(11), one O(14), one O(18), one O(2), and one O(3) atom to form a mixture of distorted edge and corner-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 19-27°. In the eighth Fe site, Fe(8) is bonded to one O(15), one O(16), one O(22), one O(4), one O(6), and one O(7) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 24-25°. In the ninth Fe site, Fe(9) is bonded to one O(10), one O(17), one O(19), one O(20), one O(5), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with three equivalent Li(5)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 7-11°. In the tenth Fe site, Fe(10) is bonded to one O(12), one O(13), one O(21), one O(23), one O(24), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(3)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 6-7°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom to form distorted OLiFe3 trigonal pyramids that share corners with two equivalent O(10)Li3Fe2 square pyramids, corners with two equivalent O(20)Li2Fe2 trigonal pyramids,  an edgeedge with one O(9)Li3Fe2 square pyramid, and edges with two equivalent O(14)LiFe3 trigonal pyramids. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the third O site, O(3) is bonded in a T-shaped geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(3), one Fe(3), one Fe(6), and one Fe(8) atom. In the fifth O site, O(5) is bonded in a see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the sixth O site, O(6) is bonded in a trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the eighth O site, O(8) is bonded in a see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the ninth O site, O(9) is bonded to one Li(1), one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form distorted OLi3Fe2 square pyramids that share  a cornercorner with one O(10)Li3Fe2 square pyramid, corners with two equivalent O(20)Li2Fe2 trigonal pyramids, corners with two equivalent O(14)LiFe3 trigonal pyramids, edges with two equivalent O(10)Li3Fe2 square pyramids,  an edgeedge with one O(20)Li2Fe2 trigonal pyramid, and  an edgeedge with one O(1)LiFe3 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(1), one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(9)Li3Fe2 square pyramid, corners with two equivalent O(1)LiFe3 trigonal pyramids, edges with two equivalent O(9)Li3Fe2 square pyramids,  an edgeedge with one O(14)LiFe3 trigonal pyramid, and edges with two equivalent O(20)Li2Fe2 trigonal pyramids. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom. In the twelfth O site, O(12) is bonded to one Li(2), one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(13)Li3Fe2 square pyramid, edges with two equivalent O(13)Li3Fe2 square pyramids,  an edgeedge with one O(15)LiFe3 trigonal pyramid, and edges with two equivalent O(24)Li2Fe2 trigonal pyramids. In the thirteenth O site, O(13) is bonded to one Li(2), one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(12)Li3Fe2 square pyramid, corners with two equivalent O(24)Li2Fe2 trigonal pyramids, corners with two equivalent O(15)LiFe3 trigonal pyramids, edges with two equivalent O(12)Li3Fe2 square pyramids, and  an edgeedge with one O(24)Li2Fe2 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom to form OLiFe3 trigonal pyramids that share corners with two equivalent O(9)Li3Fe2 square pyramids, corners with two equivalent O(20)Li2Fe2 trigonal pyramids,  an edgeedge with one O(10)Li3Fe2 square pyramid, and edges with two equivalent O(1)LiFe3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Li(3), one Fe(3), one Fe(6), and one Fe(8) atom to form distorted OLiFe3 trigonal pyramids that share corners with two equivalent O(13)Li3Fe2 square pyramids, corners with two equivalent O(24)Li2Fe2 trigonal pyramids, and  an edgeedge with one O(12)Li3Fe2 square pyramid. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one Fe(3), one Fe(6), and one Fe(8) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the eighteenth O site, O(18) is bonded in a distorted T-shaped geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the nineteenth O site, O(19) is bonded in a see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the twentieth O site, O(20) is bonded to one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form OLi2Fe2 trigonal pyramids that share corners with two equivalent O(9)Li3Fe2 square pyramids, corners with two equivalent O(1)LiFe3 trigonal pyramids, corners with two equivalent O(14)LiFe3 trigonal pyramids,  an edgeedge with one O(9)Li3Fe2 square pyramid, and edges with two equivalent O(10)Li3Fe2 square pyramids. In the twenty-first O site, O(21) is bonded in a rectangular see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the twenty-second O site, O(22) is bonded in a distorted T-shaped geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the twenty-third O site, O(23) is bonded in a see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the twenty-fourth O site, O(24) is bonded to one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi2Fe2 trigonal pyramids that share corners with two equivalent O(13)Li3Fe2 square pyramids, corners with two equivalent O(15)LiFe3 trigonal pyramids,  an edgeedge with one O(13)Li3Fe2 square pyramid, and edges with two equivalent O(12)Li3Fe2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Fe5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.027
_cell_length_b   5.072
_cell_length_c   18.527
_cell_angle_alpha   93.654
_cell_angle_beta   92.611
_cell_angle_gamma   113.990
_symmetry_Int_Tables_number   1
_cell_volume   429.411
_cell_formula_units_Z   2
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  0.679  0.195  0.107  1.0
  Li  Li1  1  0.692  0.182  0.606  1.0
  Li  Li2  1  0.830  0.619  0.742  1.0
  Li  Li3  1  0.146  0.350  0.249  1.0
  Li  Li4  1  0.067  0.927  0.125  1.0
  Li  Li5  1  0.080  0.938  0.624  1.0
  Fe  Fe6  1  0.929  0.059  0.378  1.0
  Fe  Fe7  1  0.018  0.534  0.004  1.0
  Fe  Fe8  1  0.937  0.073  0.877  1.0
  Fe  Fe9  1  0.018  0.523  0.505  1.0
  Fe  Fe10  1  0.486  1.000  0.247  1.0
  Fe  Fe11  1  0.484  0.996  0.747  1.0
  Fe  Fe12  1  0.577  0.429  0.378  1.0
  Fe  Fe13  1  0.572  0.429  0.878  1.0
  Fe  Fe14  1  0.432  0.583  0.124  1.0
  Fe  Fe15  1  0.425  0.570  0.625  1.0
  O  O16  1  0.812  0.290  0.308  1.0
  O  O17  1  0.704  0.202  0.444  1.0
  O  O18  1  0.911  0.739  0.433  1.0
  O  O19  1  0.803  0.305  0.808  1.0
  O  O20  1  0.730  0.565  0.071  1.0
  O  O21  1  0.708  0.206  0.945  1.0
  O  O22  1  0.905  0.744  0.933  1.0
  O  O23  1  0.738  0.558  0.569  1.0
  O  O24  1  0.724  0.928  0.179  1.0
  O  O25  1  0.421  0.275  0.181  1.0
  O  O26  1  0.596  0.748  0.324  1.0
  O  O27  1  0.723  0.901  0.680  1.0
  O  O28  1  0.474  0.292  0.681  1.0
  O  O29  1  0.259  0.108  0.317  1.0
  O  O30  1  0.623  0.757  0.820  1.0
  O  O31  1  0.260  0.093  0.820  1.0
  O  O32  1  0.333  0.821  0.058  1.0
  O  O33  1  0.236  0.384  0.431  1.0
  O  O34  1  0.092  0.295  0.071  1.0
  O  O35  1  0.196  0.683  0.195  1.0
  O  O36  1  0.338  0.813  0.559  1.0
  O  O37  1  0.245  0.402  0.929  1.0
  O  O38  1  0.092  0.282  0.572  1.0
  O  O39  1  0.190  0.692  0.696  1.0
[/CIF]
.
The crystal structure described by Li3Fe5O12 crystallizes in the triclinic P1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(10), one O(17), one O(19), one O(5), and one O(9) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-64°. In the second Li site, Li(2) is bonded to one O(12), one O(13), one O(21), one O(23), and one O(8) atom to form LiO5 trigonal bipyramids that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Li(3)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with two equivalent Li(6)O6 octahedra, and edges with two equivalent Fe(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-64°. In the third Li site, Li(3) is bonded to one O(12), one O(13), one O(15), one O(24), and one O(4) atom to form distorted LiO5 trigonal bipyramids that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-76°. In the fourth Li site, Li(4) is bonded in a 4-coordinate geometry to one O(1), one O(10), one O(11), one O(14), one O(20), and one O(9) atom. In the fifth Li site, Li(5) is bonded to one O(10), one O(17), one O(19), one O(20), one O(5), and one O(9) atom to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with three equivalent Fe(9)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 15-18°. In the sixth Li site, Li(6) is bonded to one O(12), one O(13), one O(21), one O(23), one O(24), and one O(8) atom to form distorted LiO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Fe(10)O6 octahedra,  an edgeedge with one Li(3)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 17-20°. There are ten inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(11), one O(14), one O(18), one O(2), and one O(3) atom to form a mixture of edge and corner-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 20-22°. In the second Fe site, Fe(2) is bonded to one O(17), one O(19), one O(22), one O(5), one O(6), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(8)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra,  an edgeedge with one Fe(9)O6 octahedra, and  an edgeedge with one Li(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 7-24°. In the third Fe site, Fe(3) is bonded to one O(15), one O(16), one O(22), one O(4), one O(6), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Li(3)O5 trigonal bipyramids,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, and edges with three equivalent Fe(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 19-22°. In the fourth Fe site, Fe(4) is bonded to one O(18), one O(2), one O(21), one O(23), one O(3), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(7)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra, and  an edgeedge with one Li(2)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-27°. In the fifth Fe site, Fe(5) is bonded to one O(1), one O(10), one O(11), one O(14), one O(20), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Li(5)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(7)O6 octahedra,  a cornercorner with one Fe(9)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra,  an edgeedge with one Fe(9)O6 octahedra, and  an edgeedge with one Li(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 11-22°. In the sixth Fe site, Fe(6) is bonded to one O(12), one O(13), one O(15), one O(16), one O(24), and one O(4) atom to form FeO6 octahedra that share  a cornercorner with one Li(6)O6 octahedra,  a cornercorner with one Fe(10)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(8)O6 octahedra,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Li(6)O6 octahedra,  an edgeedge with one Fe(10)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra,  an edgeedge with one Li(2)O5 trigonal bipyramid, and edges with two equivalent Li(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 7-25°. In the seventh Fe site, Fe(7) is bonded to one O(1), one O(11), one O(14), one O(18), one O(2), and one O(3) atom to form a mixture of distorted edge and corner-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 19-27°. In the eighth Fe site, Fe(8) is bonded to one O(15), one O(16), one O(22), one O(4), one O(6), and one O(7) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 24-25°. In the ninth Fe site, Fe(9) is bonded to one O(10), one O(17), one O(19), one O(20), one O(5), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra,  a cornercorner with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, edges with three equivalent Li(5)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 7-11°. In the tenth Fe site, Fe(10) is bonded to one O(12), one O(13), one O(21), one O(23), one O(24), and one O(8) atom to form FeO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  a cornercorner with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with three equivalent Li(6)O6 octahedra,  an edgeedge with one Li(3)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 6-7°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom to form distorted OLiFe3 trigonal pyramids that share corners with two equivalent O(10)Li3Fe2 square pyramids, corners with two equivalent O(20)Li2Fe2 trigonal pyramids,  an edgeedge with one O(9)Li3Fe2 square pyramid, and edges with two equivalent O(14)LiFe3 trigonal pyramids. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the third O site, O(3) is bonded in a T-shaped geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(3), one Fe(3), one Fe(6), and one Fe(8) atom. In the fifth O site, O(5) is bonded in a see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the sixth O site, O(6) is bonded in a trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the eighth O site, O(8) is bonded in a see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the ninth O site, O(9) is bonded to one Li(1), one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form distorted OLi3Fe2 square pyramids that share  a cornercorner with one O(10)Li3Fe2 square pyramid, corners with two equivalent O(20)Li2Fe2 trigonal pyramids, corners with two equivalent O(14)LiFe3 trigonal pyramids, edges with two equivalent O(10)Li3Fe2 square pyramids,  an edgeedge with one O(20)Li2Fe2 trigonal pyramid, and  an edgeedge with one O(1)LiFe3 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(1), one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(9)Li3Fe2 square pyramid, corners with two equivalent O(1)LiFe3 trigonal pyramids, edges with two equivalent O(9)Li3Fe2 square pyramids,  an edgeedge with one O(14)LiFe3 trigonal pyramid, and edges with two equivalent O(20)Li2Fe2 trigonal pyramids. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom. In the twelfth O site, O(12) is bonded to one Li(2), one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(13)Li3Fe2 square pyramid, edges with two equivalent O(13)Li3Fe2 square pyramids,  an edgeedge with one O(15)LiFe3 trigonal pyramid, and edges with two equivalent O(24)Li2Fe2 trigonal pyramids. In the thirteenth O site, O(13) is bonded to one Li(2), one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi3Fe2 square pyramids that share  a cornercorner with one O(12)Li3Fe2 square pyramid, corners with two equivalent O(24)Li2Fe2 trigonal pyramids, corners with two equivalent O(15)LiFe3 trigonal pyramids, edges with two equivalent O(12)Li3Fe2 square pyramids, and  an edgeedge with one O(24)Li2Fe2 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Li(4), one Fe(1), one Fe(5), and one Fe(7) atom to form OLiFe3 trigonal pyramids that share corners with two equivalent O(9)Li3Fe2 square pyramids, corners with two equivalent O(20)Li2Fe2 trigonal pyramids,  an edgeedge with one O(10)Li3Fe2 square pyramid, and edges with two equivalent O(1)LiFe3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Li(3), one Fe(3), one Fe(6), and one Fe(8) atom to form distorted OLiFe3 trigonal pyramids that share corners with two equivalent O(13)Li3Fe2 square pyramids, corners with two equivalent O(24)Li2Fe2 trigonal pyramids, and  an edgeedge with one O(12)Li3Fe2 square pyramid. In the sixteenth O site, O(16) is bonded in a distorted T-shaped geometry to one Fe(3), one Fe(6), and one Fe(8) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the eighteenth O site, O(18) is bonded in a distorted T-shaped geometry to one Fe(1), one Fe(4), and one Fe(7) atom. In the nineteenth O site, O(19) is bonded in a see-saw-like geometry to one Li(1), one Li(5), one Fe(2), and one Fe(9) atom. In the twentieth O site, O(20) is bonded to one Li(4), one Li(5), one Fe(5), and one Fe(9) atom to form OLi2Fe2 trigonal pyramids that share corners with two equivalent O(9)Li3Fe2 square pyramids, corners with two equivalent O(1)LiFe3 trigonal pyramids, corners with two equivalent O(14)LiFe3 trigonal pyramids,  an edgeedge with one O(9)Li3Fe2 square pyramid, and edges with two equivalent O(10)Li3Fe2 square pyramids. In the twenty-first O site, O(21) is bonded in a rectangular see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the twenty-second O site, O(22) is bonded in a distorted T-shaped geometry to one Fe(2), one Fe(3), and one Fe(8) atom. In the twenty-third O site, O(23) is bonded in a see-saw-like geometry to one Li(2), one Li(6), one Fe(10), and one Fe(4) atom. In the twenty-fourth O site, O(24) is bonded to one Li(3), one Li(6), one Fe(10), and one Fe(6) atom to form OLi2Fe2 trigonal pyramids that share corners with two equivalent O(13)Li3Fe2 square pyramids, corners with two equivalent O(15)LiFe3 trigonal pyramids,  an edgeedge with one O(13)Li3Fe2 square pyramid, and edges with two equivalent O(12)Li3Fe2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Fe5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.027
_cell_length_b   5.072
_cell_length_c   18.527
_cell_angle_alpha   93.654
_cell_angle_beta   92.611
_cell_angle_gamma   113.990
_symmetry_Int_Tables_number   1
_cell_volume   429.411
_cell_formula_units_Z   2
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  0.679  0.195  0.107  1.0
  Li  Li1  1  0.692  0.182  0.606  1.0
  Li  Li2  1  0.830  0.619  0.742  1.0
  Li  Li3  1  0.146  0.350  0.249  1.0
  Li  Li4  1  0.067  0.927  0.125  1.0
  Li  Li5  1  0.080  0.938  0.624  1.0
  Fe  Fe6  1  0.929  0.059  0.378  1.0
  Fe  Fe7  1  0.018  0.534  0.004  1.0
  Fe  Fe8  1  0.937  0.073  0.877  1.0
  Fe  Fe9  1  0.018  0.523  0.505  1.0
  Fe  Fe10  1  0.486  1.000  0.247  1.0
  Fe  Fe11  1  0.484  0.996  0.747  1.0
  Fe  Fe12  1  0.577  0.429  0.378  1.0
  Fe  Fe13  1  0.572  0.429  0.878  1.0
  Fe  Fe14  1  0.432  0.583  0.124  1.0
  Fe  Fe15  1  0.425  0.570  0.625  1.0
  O  O16  1  0.812  0.290  0.308  1.0
  O  O17  1  0.704  0.202  0.444  1.0
  O  O18  1  0.911  0.739  0.433  1.0
  O  O19  1  0.803  0.305  0.808  1.0
  O  O20  1  0.730  0.565  0.071  1.0
  O  O21  1  0.708  0.206  0.945  1.0
  O  O22  1  0.905  0.744  0.933  1.0
  O  O23  1  0.738  0.558  0.569  1.0
  O  O24  1  0.724  0.928  0.179  1.0
  O  O25  1  0.421  0.275  0.181  1.0
  O  O26  1  0.596  0.748  0.324  1.0
  O  O27  1  0.723  0.901  0.680  1.0
  O  O28  1  0.474  0.292  0.681  1.0
  O  O29  1  0.259  0.108  0.317  1.0
  O  O30  1  0.623  0.757  0.820  1.0
  O  O31  1  0.260  0.093  0.820  1.0
  O  O32  1  0.333  0.821  0.058  1.0
  O  O33  1  0.236  0.384  0.431  1.0
  O  O34  1  0.092  0.295  0.071  1.0
  O  O35  1  0.196  0.683  0.195  1.0
  O  O36  1  0.338  0.813  0.559  1.0
  O  O37  1  0.245  0.402  0.929  1.0
  O  O38  1  0.092  0.282  0.572  1.0
  O  O39  1  0.190  0.692  0.696  1.0
[/CIF]
.