The crystal structure described by Li9Cr3(WO4)7 crystallizes in the trigonal R3m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom. In the second Li site, Li(2) is bonded in a 5-coordinate geometry to one O(1), one O(7), two equivalent O(6), and two equivalent O(8) atoms. There are three inequivalent W sites. In the first W site, W(2) is bonded to three equivalent O(2) and three equivalent O(5) atoms to form distorted WO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra and edges with three equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second W site, W(1) is bonded to one O(1), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form distorted WO6 octahedra that share  an edgeedge with one W(2)O6 octahedra, edges with two equivalent W(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. In the third W site, W(3) is bonded to one O(4), one O(8), and two equivalent O(3) atoms to form WO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. Cr(1) is bonded to one O(2), one O(5), two equivalent O(3), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent W(2)O6 octahedra, corners with two equivalent W(3)O4 tetrahedra, and edges with two equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are eight inequivalent O sites. In the first O site, O(5) is bonded to two equivalent Li(1), one W(2), two equivalent W(1), and one Cr(1) atom to form edge-sharing OLi2CrW3 octahedra. In the second O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Li(2), one W(1), and one Cr(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(1), one W(3), and one Cr(1) atom. In the fourth O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Li(2) and three equivalent W(1) atoms. In the fifth O site, O(8) is bonded in a trigonal planar geometry to two equivalent Li(2) and one W(3) atom. In the sixth O site, O(1) is bonded in a distorted see-saw-like geometry to one Li(2), two equivalent Li(1), and one W(1) atom. In the seventh O site, O(2) is bonded in a distorted see-saw-like geometry to two equivalent Li(1), one W(2), and one Cr(1) atom. In the eighth O site, O(4) is bonded in a trigonal planar geometry to two equivalent Li(1) and one W(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li9Cr3(WO4)7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.500
_cell_length_b   8.500
_cell_length_c   8.500
_cell_angle_alpha   89.622
_cell_angle_beta   89.622
_cell_angle_gamma   89.622
_symmetry_Int_Tables_number   1
_cell_volume   614.075
_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  0.907  0.349  0.645  1.0
  Li  Li1  1  0.907  0.645  0.349  1.0
  Li  Li2  1  0.645  0.349  0.907  1.0
  Li  Li3  1  0.645  0.907  0.349  1.0
  Li  Li4  1  0.359  0.093  0.359  1.0
  Li  Li5  1  0.359  0.359  0.093  1.0
  Li  Li6  1  0.349  0.645  0.907  1.0
  Li  Li7  1  0.349  0.907  0.645  1.0
  Li  Li8  1  0.093  0.359  0.359  1.0
  Cr  Cr9  1  0.626  0.106  0.626  1.0
  Cr  Cr10  1  0.626  0.626  0.106  1.0
  Cr  Cr11  1  0.106  0.626  0.626  1.0
  W  W12  1  0.648  0.362  0.362  1.0
  W  W13  1  0.643  0.643  0.643  1.0
  W  W14  1  0.362  0.362  0.648  1.0
  W  W15  1  0.362  0.648  0.362  1.0
  W  W16  1  0.998  0.998  0.499  1.0
  W  W17  1  0.998  0.499  0.998  1.0
  W  W18  1  0.499  0.998  0.998  1.0
  O  O19  1  0.859  0.384  0.384  1.0
  O  O20  1  0.857  0.620  0.620  1.0
  O  O21  1  0.866  0.118  0.622  1.0
  O  O22  1  0.866  0.622  0.118  1.0
  O  O23  1  0.880  0.373  0.880  1.0
  O  O24  1  0.880  0.880  0.373  1.0
  O  O25  1  0.622  0.118  0.866  1.0
  O  O26  1  0.622  0.866  0.118  1.0
  O  O27  1  0.618  0.386  0.618  1.0
  O  O28  1  0.618  0.618  0.386  1.0
  O  O29  1  0.619  0.136  0.393  1.0
  O  O30  1  0.619  0.393  0.136  1.0
  O  O31  1  0.620  0.620  0.857  1.0
  O  O32  1  0.620  0.857  0.620  1.0
  O  O33  1  0.393  0.136  0.619  1.0
  O  O34  1  0.393  0.619  0.136  1.0
  O  O35  1  0.384  0.384  0.859  1.0
  O  O36  1  0.384  0.859  0.384  1.0
  O  O37  1  0.400  0.400  0.400  1.0
  O  O38  1  0.386  0.618  0.618  1.0
  O  O39  1  0.385  0.124  0.124  1.0
  O  O40  1  0.373  0.880  0.880  1.0
  O  O41  1  0.124  0.124  0.385  1.0
  O  O42  1  0.124  0.385  0.124  1.0
  O  O43  1  0.118  0.622  0.866  1.0
  O  O44  1  0.118  0.866  0.622  1.0
  O  O45  1  0.136  0.393  0.619  1.0
  O  O46  1  0.136  0.619  0.393  1.0
[/CIF]
.
The crystal structure described by Li9Cr3(WO4)7 crystallizes in the trigonal R3m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom. In the second Li site, Li(2) is bonded in a 5-coordinate geometry to one O(1), one O(7), two equivalent O(6), and two equivalent O(8) atoms. There are three inequivalent W sites. In the first W site, W(2) is bonded to three equivalent O(2) and three equivalent O(5) atoms to form distorted WO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra and edges with three equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second W site, W(1) is bonded to one O(1), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form distorted WO6 octahedra that share  an edgeedge with one W(2)O6 octahedra, edges with two equivalent W(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. In the third W site, W(3) is bonded to one O(4), one O(8), and two equivalent O(3) atoms to form WO4 tetrahedra that share corners with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. Cr(1) is bonded to one O(2), one O(5), two equivalent O(3), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent W(2)O6 octahedra, corners with two equivalent W(3)O4 tetrahedra, and edges with two equivalent W(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are eight inequivalent O sites. In the first O site, O(5) is bonded to two equivalent Li(1), one W(2), two equivalent W(1), and one Cr(1) atom to form edge-sharing OLi2CrW3 octahedra. In the second O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Li(2), one W(1), and one Cr(1) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Li(1), one W(3), and one Cr(1) atom. In the fourth O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Li(2) and three equivalent W(1) atoms. In the fifth O site, O(8) is bonded in a trigonal planar geometry to two equivalent Li(2) and one W(3) atom. In the sixth O site, O(1) is bonded in a distorted see-saw-like geometry to one Li(2), two equivalent Li(1), and one W(1) atom. In the seventh O site, O(2) is bonded in a distorted see-saw-like geometry to two equivalent Li(1), one W(2), and one Cr(1) atom. In the eighth O site, O(4) is bonded in a trigonal planar geometry to two equivalent Li(1) and one W(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li9Cr3(WO4)7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.500
_cell_length_b   8.500
_cell_length_c   8.500
_cell_angle_alpha   89.622
_cell_angle_beta   89.622
_cell_angle_gamma   89.622
_symmetry_Int_Tables_number   1
_cell_volume   614.075
_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  0.907  0.349  0.645  1.0
  Li  Li1  1  0.907  0.645  0.349  1.0
  Li  Li2  1  0.645  0.349  0.907  1.0
  Li  Li3  1  0.645  0.907  0.349  1.0
  Li  Li4  1  0.359  0.093  0.359  1.0
  Li  Li5  1  0.359  0.359  0.093  1.0
  Li  Li6  1  0.349  0.645  0.907  1.0
  Li  Li7  1  0.349  0.907  0.645  1.0
  Li  Li8  1  0.093  0.359  0.359  1.0
  Cr  Cr9  1  0.626  0.106  0.626  1.0
  Cr  Cr10  1  0.626  0.626  0.106  1.0
  Cr  Cr11  1  0.106  0.626  0.626  1.0
  W  W12  1  0.648  0.362  0.362  1.0
  W  W13  1  0.643  0.643  0.643  1.0
  W  W14  1  0.362  0.362  0.648  1.0
  W  W15  1  0.362  0.648  0.362  1.0
  W  W16  1  0.998  0.998  0.499  1.0
  W  W17  1  0.998  0.499  0.998  1.0
  W  W18  1  0.499  0.998  0.998  1.0
  O  O19  1  0.859  0.384  0.384  1.0
  O  O20  1  0.857  0.620  0.620  1.0
  O  O21  1  0.866  0.118  0.622  1.0
  O  O22  1  0.866  0.622  0.118  1.0
  O  O23  1  0.880  0.373  0.880  1.0
  O  O24  1  0.880  0.880  0.373  1.0
  O  O25  1  0.622  0.118  0.866  1.0
  O  O26  1  0.622  0.866  0.118  1.0
  O  O27  1  0.618  0.386  0.618  1.0
  O  O28  1  0.618  0.618  0.386  1.0
  O  O29  1  0.619  0.136  0.393  1.0
  O  O30  1  0.619  0.393  0.136  1.0
  O  O31  1  0.620  0.620  0.857  1.0
  O  O32  1  0.620  0.857  0.620  1.0
  O  O33  1  0.393  0.136  0.619  1.0
  O  O34  1  0.393  0.619  0.136  1.0
  O  O35  1  0.384  0.384  0.859  1.0
  O  O36  1  0.384  0.859  0.384  1.0
  O  O37  1  0.400  0.400  0.400  1.0
  O  O38  1  0.386  0.618  0.618  1.0
  O  O39  1  0.385  0.124  0.124  1.0
  O  O40  1  0.373  0.880  0.880  1.0
  O  O41  1  0.124  0.124  0.385  1.0
  O  O42  1  0.124  0.385  0.124  1.0
  O  O43  1  0.118  0.622  0.866  1.0
  O  O44  1  0.118  0.866  0.622  1.0
  O  O45  1  0.136  0.393  0.619  1.0
  O  O46  1  0.136  0.619  0.393  1.0
[/CIF]
.