The structure described by LiCr4(PO4)3 crystallizes in the tetragonal I-42d space group. Li(1) is bonded to four equivalent O(3) atoms to form LiO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, and corners with four equivalent P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 78-79°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. In the second Cr site, Cr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with four equivalent P(2)O4 tetrahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 60°. There are two inequivalent P sites. In the first P site, P(1) is bonded to four equivalent O(1) atoms to form PO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. In the second P site, P(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form PO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-49°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(2), and one P(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(2), and one P(2) atom. In the third O site, O(3) is bonded to one Li(1), one Cr(1), one Cr(2), and one P(2) atom to form a mixture of distorted corner and edge-sharing OLiCr2P tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiCr4(PO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.727
_cell_length_b   10.727
_cell_length_c   10.727
_cell_angle_alpha   142.675
_cell_angle_beta   142.675
_cell_angle_gamma   53.813
_symmetry_Int_Tables_number   1
_cell_volume   450.889
_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  0.250  0.750  0.500  1.0
  Li  Li1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  0.375  0.372  0.497  1.0
  Cr  Cr3  1  0.775  0.775  0.000  1.0
  Cr  Cr4  1  0.628  0.125  0.003  1.0
  Cr  Cr5  1  0.875  0.878  0.503  1.0
  Cr  Cr6  1  0.225  0.225  0.000  1.0
  Cr  Cr7  1  0.525  0.025  0.500  1.0
  Cr  Cr8  1  0.975  0.475  0.500  1.0
  Cr  Cr9  1  0.122  0.625  0.997  1.0
  P  P10  1  0.000  0.000  0.000  1.0
  P  P11  1  0.875  0.481  0.106  1.0
  P  P12  1  0.375  0.769  0.894  1.0
  P  P13  1  0.231  0.125  0.606  1.0
  P  P14  1  0.750  0.250  0.500  1.0
  P  P15  1  0.519  0.625  0.394  1.0
  O  O16  1  0.231  0.093  0.240  1.0
  O  O17  1  0.675  0.342  0.807  1.0
  O  O18  1  0.075  0.382  0.167  1.0
  O  O19  1  0.618  0.785  0.693  1.0
  O  O20  1  0.279  0.560  0.716  1.0
  O  O21  1  0.471  0.687  0.781  1.0
  O  O22  1  0.906  0.690  0.219  1.0
  O  O23  1  0.844  0.563  0.284  1.0
  O  O24  1  0.092  0.925  0.307  1.0
  O  O25  1  0.907  0.148  0.138  1.0
  O  O26  1  0.440  0.156  0.719  1.0
  O  O27  1  0.215  0.908  0.833  1.0
  O  O28  1  0.535  0.868  0.193  1.0
  O  O29  1  0.313  0.094  0.784  1.0
  O  O30  1  0.741  0.102  0.260  1.0
  O  O31  1  0.898  0.157  0.638  1.0
  O  O32  1  0.852  0.991  0.760  1.0
  O  O33  1  0.132  0.325  0.667  1.0
  O  O34  1  0.658  0.465  0.333  1.0
  O  O35  1  0.519  0.259  0.362  1.0
  O  O36  1  0.843  0.481  0.740  1.0
  O  O37  1  0.310  0.529  0.216  1.0
  O  O38  1  0.437  0.721  0.281  1.0
  O  O39  1  0.009  0.769  0.862  1.0
[/CIF]
.
The structure described by LiCr4(PO4)3 crystallizes in the tetragonal I-42d space group. Li(1) is bonded to four equivalent O(3) atoms to form LiO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, and corners with four equivalent P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 78-79°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one P(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. In the second Cr site, Cr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with four equivalent P(2)O4 tetrahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 60°. There are two inequivalent P sites. In the first P site, P(1) is bonded to four equivalent O(1) atoms to form PO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. In the second P site, P(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form PO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-49°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(2), and one P(1) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Cr(1), one Cr(2), and one P(2) atom. In the third O site, O(3) is bonded to one Li(1), one Cr(1), one Cr(2), and one P(2) atom to form a mixture of distorted corner and edge-sharing OLiCr2P tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiCr4(PO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.727
_cell_length_b   10.727
_cell_length_c   10.727
_cell_angle_alpha   142.675
_cell_angle_beta   142.675
_cell_angle_gamma   53.813
_symmetry_Int_Tables_number   1
_cell_volume   450.889
_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  0.250  0.750  0.500  1.0
  Li  Li1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  0.375  0.372  0.497  1.0
  Cr  Cr3  1  0.775  0.775  0.000  1.0
  Cr  Cr4  1  0.628  0.125  0.003  1.0
  Cr  Cr5  1  0.875  0.878  0.503  1.0
  Cr  Cr6  1  0.225  0.225  0.000  1.0
  Cr  Cr7  1  0.525  0.025  0.500  1.0
  Cr  Cr8  1  0.975  0.475  0.500  1.0
  Cr  Cr9  1  0.122  0.625  0.997  1.0
  P  P10  1  0.000  0.000  0.000  1.0
  P  P11  1  0.875  0.481  0.106  1.0
  P  P12  1  0.375  0.769  0.894  1.0
  P  P13  1  0.231  0.125  0.606  1.0
  P  P14  1  0.750  0.250  0.500  1.0
  P  P15  1  0.519  0.625  0.394  1.0
  O  O16  1  0.231  0.093  0.240  1.0
  O  O17  1  0.675  0.342  0.807  1.0
  O  O18  1  0.075  0.382  0.167  1.0
  O  O19  1  0.618  0.785  0.693  1.0
  O  O20  1  0.279  0.560  0.716  1.0
  O  O21  1  0.471  0.687  0.781  1.0
  O  O22  1  0.906  0.690  0.219  1.0
  O  O23  1  0.844  0.563  0.284  1.0
  O  O24  1  0.092  0.925  0.307  1.0
  O  O25  1  0.907  0.148  0.138  1.0
  O  O26  1  0.440  0.156  0.719  1.0
  O  O27  1  0.215  0.908  0.833  1.0
  O  O28  1  0.535  0.868  0.193  1.0
  O  O29  1  0.313  0.094  0.784  1.0
  O  O30  1  0.741  0.102  0.260  1.0
  O  O31  1  0.898  0.157  0.638  1.0
  O  O32  1  0.852  0.991  0.760  1.0
  O  O33  1  0.132  0.325  0.667  1.0
  O  O34  1  0.658  0.465  0.333  1.0
  O  O35  1  0.519  0.259  0.362  1.0
  O  O36  1  0.843  0.481  0.740  1.0
  O  O37  1  0.310  0.529  0.216  1.0
  O  O38  1  0.437  0.721  0.281  1.0
  O  O39  1  0.009  0.769  0.862  1.0
[/CIF]
.