The material described by LiFePO4 crystallizes in the trigonal P31c space group. Li(1) is bonded to one O(1), one O(3), one O(4), and one O(6) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, and corners with three equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(5) atom to form FeO5 trigonal bipyramids that share  a cornercorner with one P(2)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. There are three inequivalent P sites. In the first P site, P(1) is bonded to one O(5) and three equivalent O(1) atoms to form PO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. In the second P site, P(2) is bonded to one O(6) and three equivalent O(3) atoms to form PO4 tetrahedra that share corners with six equivalent Li(1)O4 tetrahedra and corners with three equivalent Fe(1)O5 trigonal bipyramids. In the third P site, P(3) is bonded to one O(2) and three equivalent O(4) atoms to form PO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(6) is bonded in a tetrahedral geometry to three equivalent Li(1) and one P(2) atom. In the second O site, O(1) is bonded in a distorted trigonal planar geometry to one Li(1), one Fe(1), and one P(1) atom. In the third O site, O(2) is bonded in a rectangular see-saw-like geometry to three equivalent Fe(1) and one P(3) atom. In the fourth O site, O(3) is bonded in a distorted trigonal planar geometry to one Li(1), one Fe(1), and one P(2) atom. In the fifth O site, O(4) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one P(3) atom. In the sixth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Fe(1) and one P(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiFePO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.437
_cell_length_b   7.437
_cell_length_c   9.616
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   460.630
_cell_formula_units_Z   6
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  0.206  0.949  0.259  1.0
  Li  Li1  1  0.949  0.206  0.759  1.0
  Li  Li2  1  0.794  0.742  0.759  1.0
  Li  Li3  1  0.742  0.794  0.259  1.0
  Li  Li4  1  0.258  0.051  0.759  1.0
  Li  Li5  1  0.051  0.258  0.259  1.0
  Fe  Fe6  1  0.927  0.523  0.986  1.0
  Fe  Fe7  1  0.596  0.073  0.986  1.0
  Fe  Fe8  1  0.477  0.404  0.986  1.0
  Fe  Fe9  1  0.404  0.477  0.486  1.0
  Fe  Fe10  1  0.523  0.927  0.486  1.0
  Fe  Fe11  1  0.073  0.596  0.486  1.0
  P  P12  1  0.333  0.667  0.177  1.0
  P  P13  1  0.000  0.000  0.507  1.0
  P  P14  1  0.333  0.667  0.787  1.0
  P  P15  1  0.000  0.000  0.007  1.0
  P  P16  1  0.667  0.333  0.287  1.0
  P  P17  1  0.667  0.333  0.677  1.0
  O  O18  1  0.550  0.839  0.129  1.0
  O  O19  1  0.667  0.333  0.119  1.0
  O  O20  1  0.898  0.774  0.949  1.0
  O  O21  1  0.839  0.550  0.629  1.0
  O  O22  1  0.711  0.161  0.629  1.0
  O  O23  1  0.886  0.385  0.332  1.0
  O  O24  1  0.102  0.876  0.449  1.0
  O  O25  1  0.161  0.711  0.129  1.0
  O  O26  1  0.114  0.499  0.832  1.0
  O  O27  1  0.385  0.886  0.832  1.0
  O  O28  1  0.333  0.667  0.344  1.0
  O  O29  1  0.667  0.333  0.844  1.0
  O  O30  1  0.333  0.667  0.619  1.0
  O  O31  1  0.124  0.226  0.449  1.0
  O  O32  1  0.289  0.450  0.129  1.0
  O  O33  1  0.000  0.000  0.668  1.0
  O  O34  1  0.226  0.124  0.949  1.0
  O  O35  1  0.501  0.615  0.832  1.0
  O  O36  1  0.450  0.289  0.629  1.0
  O  O37  1  0.774  0.898  0.449  1.0
  O  O38  1  0.615  0.501  0.332  1.0
  O  O39  1  0.499  0.114  0.332  1.0
  O  O40  1  0.000  0.000  0.168  1.0
  O  O41  1  0.876  0.102  0.949  1.0
[/CIF]
.
The material described by LiFePO4 crystallizes in the trigonal P31c space group. Li(1) is bonded to one O(1), one O(3), one O(4), and one O(6) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one P(1)O4 tetrahedra,  a cornercorner with one P(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent P(2)O4 tetrahedra, and corners with three equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(5) atom to form FeO5 trigonal bipyramids that share  a cornercorner with one P(2)O4 tetrahedra, corners with two equivalent P(1)O4 tetrahedra, corners with two equivalent P(3)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. There are three inequivalent P sites. In the first P site, P(1) is bonded to one O(5) and three equivalent O(1) atoms to form PO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. In the second P site, P(2) is bonded to one O(6) and three equivalent O(3) atoms to form PO4 tetrahedra that share corners with six equivalent Li(1)O4 tetrahedra and corners with three equivalent Fe(1)O5 trigonal bipyramids. In the third P site, P(3) is bonded to one O(2) and three equivalent O(4) atoms to form PO4 tetrahedra that share corners with three equivalent Li(1)O4 tetrahedra and corners with six equivalent Fe(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(6) is bonded in a tetrahedral geometry to three equivalent Li(1) and one P(2) atom. In the second O site, O(1) is bonded in a distorted trigonal planar geometry to one Li(1), one Fe(1), and one P(1) atom. In the third O site, O(2) is bonded in a rectangular see-saw-like geometry to three equivalent Fe(1) and one P(3) atom. In the fourth O site, O(3) is bonded in a distorted trigonal planar geometry to one Li(1), one Fe(1), and one P(2) atom. In the fifth O site, O(4) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one P(3) atom. In the sixth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Fe(1) and one P(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiFePO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.437
_cell_length_b   7.437
_cell_length_c   9.616
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   460.630
_cell_formula_units_Z   6
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  0.206  0.949  0.259  1.0
  Li  Li1  1  0.949  0.206  0.759  1.0
  Li  Li2  1  0.794  0.742  0.759  1.0
  Li  Li3  1  0.742  0.794  0.259  1.0
  Li  Li4  1  0.258  0.051  0.759  1.0
  Li  Li5  1  0.051  0.258  0.259  1.0
  Fe  Fe6  1  0.927  0.523  0.986  1.0
  Fe  Fe7  1  0.596  0.073  0.986  1.0
  Fe  Fe8  1  0.477  0.404  0.986  1.0
  Fe  Fe9  1  0.404  0.477  0.486  1.0
  Fe  Fe10  1  0.523  0.927  0.486  1.0
  Fe  Fe11  1  0.073  0.596  0.486  1.0
  P  P12  1  0.333  0.667  0.177  1.0
  P  P13  1  0.000  0.000  0.507  1.0
  P  P14  1  0.333  0.667  0.787  1.0
  P  P15  1  0.000  0.000  0.007  1.0
  P  P16  1  0.667  0.333  0.287  1.0
  P  P17  1  0.667  0.333  0.677  1.0
  O  O18  1  0.550  0.839  0.129  1.0
  O  O19  1  0.667  0.333  0.119  1.0
  O  O20  1  0.898  0.774  0.949  1.0
  O  O21  1  0.839  0.550  0.629  1.0
  O  O22  1  0.711  0.161  0.629  1.0
  O  O23  1  0.886  0.385  0.332  1.0
  O  O24  1  0.102  0.876  0.449  1.0
  O  O25  1  0.161  0.711  0.129  1.0
  O  O26  1  0.114  0.499  0.832  1.0
  O  O27  1  0.385  0.886  0.832  1.0
  O  O28  1  0.333  0.667  0.344  1.0
  O  O29  1  0.667  0.333  0.844  1.0
  O  O30  1  0.333  0.667  0.619  1.0
  O  O31  1  0.124  0.226  0.449  1.0
  O  O32  1  0.289  0.450  0.129  1.0
  O  O33  1  0.000  0.000  0.668  1.0
  O  O34  1  0.226  0.124  0.949  1.0
  O  O35  1  0.501  0.615  0.832  1.0
  O  O36  1  0.450  0.289  0.629  1.0
  O  O37  1  0.774  0.898  0.449  1.0
  O  O38  1  0.615  0.501  0.332  1.0
  O  O39  1  0.499  0.114  0.332  1.0
  O  O40  1  0.000  0.000  0.168  1.0
  O  O41  1  0.876  0.102  0.949  1.0
[/CIF]
.