The crystal structure described by Li4Cr3O8 crystallizes in the trigonal R32 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to six equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(1) and three equivalent O(2) atoms. In the third Li site, Li(3) is bonded to six equivalent O(2) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. Cr(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Li(2) and three equivalent Cr(1) atoms to form distorted OLiCr3 trigonal pyramids that share corners with nine equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, and edges with three equivalent O(2)Li3Cr2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), and two equivalent Cr(1) atoms to form OLi3Cr2 trigonal bipyramids that share corners with six equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, edges with six equivalent O(2)Li3Cr2 trigonal bipyramids, and  an edgeedge with one O(1)LiCr3 trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Cr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.115
_cell_length_b   10.763
_cell_length_c   10.765
_cell_angle_alpha   31.288
_cell_angle_beta   28.334
_cell_angle_gamma   51.377
_symmetry_Int_Tables_number   1
_cell_volume   149.242
_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  0.001  0.000  1.000  1.0
  Li  Li1  1  0.357  0.357  0.000  1.0
  Li  Li2  1  0.500  0.499  0.000  1.0
  Li  Li3  1  0.643  0.642  1.000  1.0
  Cr  Cr4  1  0.501  1.000  0.999  1.0
  Cr  Cr5  1  0.499  0.499  0.501  1.0
  Cr  Cr6  1  0.501  0.999  0.501  1.0
  O  O7  1  0.236  0.235  1.000  1.0
  O  O8  1  0.216  0.744  1.000  1.0
  O  O9  1  0.217  0.215  0.528  1.0
  O  O10  1  0.273  0.744  0.471  1.0
  O  O11  1  0.765  0.764  0.000  1.0
  O  O12  1  0.785  0.255  0.000  1.0
  O  O13  1  0.785  0.784  0.472  1.0
  O  O14  1  0.728  0.256  0.528  1.0
[/CIF]
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The crystal structure described by Li4Cr3O8 crystallizes in the trigonal R32 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to six equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(1) and three equivalent O(2) atoms. In the third Li site, Li(3) is bonded to six equivalent O(2) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra and edges with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. Cr(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CrO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. There are two inequivalent O sites. In the first O site, O(1) is bonded to one Li(2) and three equivalent Cr(1) atoms to form distorted OLiCr3 trigonal pyramids that share corners with nine equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, and edges with three equivalent O(2)Li3Cr2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), and two equivalent Cr(1) atoms to form OLi3Cr2 trigonal bipyramids that share corners with six equivalent O(2)Li3Cr2 trigonal bipyramids, corners with three equivalent O(1)LiCr3 trigonal pyramids, edges with six equivalent O(2)Li3Cr2 trigonal bipyramids, and  an edgeedge with one O(1)LiCr3 trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Cr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.115
_cell_length_b   10.763
_cell_length_c   10.765
_cell_angle_alpha   31.288
_cell_angle_beta   28.334
_cell_angle_gamma   51.377
_symmetry_Int_Tables_number   1
_cell_volume   149.242
_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  0.001  0.000  1.000  1.0
  Li  Li1  1  0.357  0.357  0.000  1.0
  Li  Li2  1  0.500  0.499  0.000  1.0
  Li  Li3  1  0.643  0.642  1.000  1.0
  Cr  Cr4  1  0.501  1.000  0.999  1.0
  Cr  Cr5  1  0.499  0.499  0.501  1.0
  Cr  Cr6  1  0.501  0.999  0.501  1.0
  O  O7  1  0.236  0.235  1.000  1.0
  O  O8  1  0.216  0.744  1.000  1.0
  O  O9  1  0.217  0.215  0.528  1.0
  O  O10  1  0.273  0.744  0.471  1.0
  O  O11  1  0.765  0.764  0.000  1.0
  O  O12  1  0.785  0.255  0.000  1.0
  O  O13  1  0.785  0.784  0.472  1.0
  O  O14  1  0.728  0.256  0.528  1.0
[/CIF]
.