The structure described by Li5Cr2Fe5O12 is beta Polonium-derived structured and crystallizes in the monoclinic C2 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with three equivalent Li(2)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)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 range from 1-8°. In the third Li site, Li(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Li(3)O6 octahedra, and edges with three equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-9°. In the second Cr site, Cr(2) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-5°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form FeO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and edges with three equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-9°. In the third Fe site, Fe(3) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-7°. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Li(3)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. There are six inequivalent O sites. In the first O site, O(5) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(1)Li3CrFe2 octahedra, and edges with four equivalent O(3)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the second O site, O(6) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(2)Li2CrFe3 octahedra, and edges with four equivalent O(4)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 2-9°. In the third O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra, edges with four equivalent O(3)Li3CrFe2 octahedra, and edges with four equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the fourth O site, O(2) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(4)Li2CrFe3 octahedra, and edges with four equivalent O(6)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the fifth O site, O(3) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra, edges with four equivalent O(1)Li3CrFe2 octahedra, and edges with four equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the sixth O site, O(4) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(2)Li2CrFe3 octahedra, and edges with four equivalent O(6)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. is represented by the CIF file [CIF]
data_Li5Cr2Fe5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.171
_cell_length_b   5.171
_cell_length_c   9.779
_cell_angle_alpha   84.587
_cell_angle_beta   84.587
_cell_angle_gamma   121.005
_symmetry_Int_Tables_number   1
_cell_volume   219.953
_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  0.833  0.669  0.254  1.0
  Li  Li1  1  0.669  0.833  0.746  1.0
  Li  Li2  1  0.331  0.167  0.746  1.0
  Li  Li3  1  0.167  0.331  0.254  1.0
  Li  Li4  1  0.081  0.919  0.500  1.0
  Cr  Cr5  1  0.751  0.249  0.500  1.0
  Cr  Cr6  1  0.250  0.750  0.000  1.0
  Fe  Fe7  1  0.918  0.082  0.000  1.0
  Fe  Fe8  1  0.995  0.503  0.747  1.0
  Fe  Fe9  1  0.497  0.005  0.253  1.0
  Fe  Fe10  1  0.576  0.424  0.000  1.0
  Fe  Fe11  1  0.420  0.580  0.500  1.0
  O  O12  1  0.047  0.236  0.619  1.0
  O  O13  1  0.764  0.953  0.381  1.0
  O  O14  1  0.879  0.371  0.125  1.0
  O  O15  1  0.629  0.121  0.875  1.0
  O  O16  1  0.706  0.528  0.618  1.0
  O  O17  1  0.472  0.294  0.382  1.0
  O  O18  1  0.531  0.728  0.124  1.0
  O  O19  1  0.272  0.469  0.876  1.0
  O  O20  1  0.382  0.856  0.617  1.0
  O  O21  1  0.144  0.618  0.383  1.0
  O  O22  1  0.212  0.025  0.126  1.0
  O  O23  1  0.975  0.788  0.874  1.0
[/CIF]
.
The structure described by Li5Cr2Fe5O12 is beta Polonium-derived structured and crystallizes in the monoclinic C2 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with three equivalent Li(2)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)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 range from 1-8°. In the third Li site, Li(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-8°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Li(3)O6 octahedra, and edges with three equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-9°. In the second Cr site, Cr(2) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-5°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. In the second Fe site, Fe(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form FeO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra, edges with three equivalent Li(1)O6 octahedra, and edges with three equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-9°. In the third Fe site, Fe(3) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-7°. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with three equivalent Li(3)O6 octahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. There are six inequivalent O sites. In the first O site, O(5) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(1)Li3CrFe2 octahedra, and edges with four equivalent O(3)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the second O site, O(6) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(2)Li2CrFe3 octahedra, and edges with four equivalent O(4)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 2-9°. In the third O site, O(1) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra, edges with four equivalent O(3)Li3CrFe2 octahedra, and edges with four equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the fourth O site, O(2) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(4)Li2CrFe3 octahedra, and edges with four equivalent O(6)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the fifth O site, O(3) is bonded to one Li(1), one Li(2), one Li(3), one Cr(1), one Fe(2), and one Fe(4) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li2CrFe3 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(6)Li2CrFe3 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra, edges with four equivalent O(1)Li3CrFe2 octahedra, and edges with four equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. In the sixth O site, O(4) is bonded to one Li(1), one Li(2), one Cr(2), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi2CrFe3 octahedra that share  a cornercorner with one O(2)Li2CrFe3 octahedra,  a cornercorner with one O(4)Li2CrFe3 octahedra,  a cornercorner with one O(6)Li2CrFe3 octahedra,  a cornercorner with one O(1)Li3CrFe2 octahedra,  a cornercorner with one O(3)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(4)Li2CrFe3 octahedra,  an edgeedge with one O(1)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra, edges with four equivalent O(2)Li2CrFe3 octahedra, and edges with four equivalent O(6)Li2CrFe3 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. is represented by the CIF file [CIF]
data_Li5Cr2Fe5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.171
_cell_length_b   5.171
_cell_length_c   9.779
_cell_angle_alpha   84.587
_cell_angle_beta   84.587
_cell_angle_gamma   121.005
_symmetry_Int_Tables_number   1
_cell_volume   219.953
_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  0.833  0.669  0.254  1.0
  Li  Li1  1  0.669  0.833  0.746  1.0
  Li  Li2  1  0.331  0.167  0.746  1.0
  Li  Li3  1  0.167  0.331  0.254  1.0
  Li  Li4  1  0.081  0.919  0.500  1.0
  Cr  Cr5  1  0.751  0.249  0.500  1.0
  Cr  Cr6  1  0.250  0.750  0.000  1.0
  Fe  Fe7  1  0.918  0.082  0.000  1.0
  Fe  Fe8  1  0.995  0.503  0.747  1.0
  Fe  Fe9  1  0.497  0.005  0.253  1.0
  Fe  Fe10  1  0.576  0.424  0.000  1.0
  Fe  Fe11  1  0.420  0.580  0.500  1.0
  O  O12  1  0.047  0.236  0.619  1.0
  O  O13  1  0.764  0.953  0.381  1.0
  O  O14  1  0.879  0.371  0.125  1.0
  O  O15  1  0.629  0.121  0.875  1.0
  O  O16  1  0.706  0.528  0.618  1.0
  O  O17  1  0.472  0.294  0.382  1.0
  O  O18  1  0.531  0.728  0.124  1.0
  O  O19  1  0.272  0.469  0.876  1.0
  O  O20  1  0.382  0.856  0.617  1.0
  O  O21  1  0.144  0.618  0.383  1.0
  O  O22  1  0.212  0.025  0.126  1.0
  O  O23  1  0.975  0.788  0.874  1.0
[/CIF]
.