The structure described by Fe3O4 is Spinel-derived structured and crystallizes in the triclinic P-1 space group. There are nine 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 Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(4)O6 octahedra, edges with two equivalent Fe(7)O6 octahedra, and edges with two equivalent Fe(8)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with three equivalent Fe(5)O4 tetrahedra, corners with three equivalent Fe(6)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra, and  an edgeedge with one Fe(9)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-60°. In the sixth Fe site, Fe(6) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-61°. In the seventh Fe site, Fe(7) 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 Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(8)O6 octahedra. In the eighth Fe site, Fe(8) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(7)O6 octahedra. In the ninth Fe site, Fe(9) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(5), one Fe(7), and one Fe(8) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(6), and one Fe(9) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(4), one Fe(5), and one Fe(9) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(4), one Fe(6), one Fe(7), and one Fe(8) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(4), and one Fe(5) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(8) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(4), one Fe(5), and one Fe(9) atom. is represented by the CIF file [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.047
_cell_length_b   10.499
_cell_length_c   6.035
_cell_angle_alpha   73.561
_cell_angle_beta   119.774
_cell_angle_gamma   89.783
_symmetry_Int_Tables_number   1
_cell_volume   314.140
_cell_formula_units_Z   4
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
  Fe  Fe0  1  0.500  0.000  0.500  1.0
  Fe  Fe1  1  1.000  0.000  0.500  1.0
  Fe  Fe2  1  0.000  0.500  0.000  1.0
  Fe  Fe3  1  0.254  0.251  0.504  1.0
  Fe  Fe4  1  0.746  0.749  0.496  1.0
  Fe  Fe5  1  0.936  0.190  0.876  1.0
  Fe  Fe6  1  0.433  0.691  0.872  1.0
  Fe  Fe7  1  0.064  0.810  0.124  1.0
  Fe  Fe8  1  0.567  0.309  0.128  1.0
  Fe  Fe9  1  1.000  0.500  0.500  1.0
  Fe  Fe10  1  0.500  0.500  0.500  1.0
  Fe  Fe11  1  0.500  1.000  0.000  1.0
  O  O12  1  0.877  0.384  0.755  1.0
  O  O13  1  0.358  0.883  0.741  1.0
  O  O14  1  0.123  0.616  0.245  1.0
  O  O15  1  0.642  0.117  0.259  1.0
  O  O16  1  0.893  0.376  0.246  1.0
  O  O17  1  0.392  0.871  0.269  1.0
  O  O18  1  0.631  0.632  0.260  1.0
  O  O19  1  0.122  0.123  0.267  1.0
  O  O20  1  0.369  0.368  0.740  1.0
  O  O21  1  0.878  0.877  0.733  1.0
  O  O22  1  0.647  0.626  0.755  1.0
  O  O23  1  0.120  0.126  0.728  1.0
  O  O24  1  0.107  0.624  0.754  1.0
  O  O25  1  0.608  0.129  0.731  1.0
  O  O26  1  0.353  0.374  0.245  1.0
  O  O27  1  0.880  0.874  0.272  1.0
[/CIF]
.
The structure described by Fe3O4 is Spinel-derived structured and crystallizes in the triclinic P-1 space group. There are nine 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 Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(9)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(4)O6 octahedra, edges with two equivalent Fe(7)O6 octahedra, and edges with two equivalent Fe(8)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with three equivalent Fe(5)O4 tetrahedra, corners with three equivalent Fe(6)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(7)O6 octahedra,  an edgeedge with one Fe(8)O6 octahedra, and  an edgeedge with one Fe(9)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-60°. In the sixth Fe site, Fe(6) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 53-61°. In the seventh Fe site, Fe(7) 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 Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(8)O6 octahedra. In the eighth Fe site, Fe(8) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Fe(5)O4 tetrahedra, corners with four equivalent Fe(6)O4 tetrahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(7)O6 octahedra. In the ninth Fe site, Fe(9) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Fe(6)O4 tetrahedra, corners with four equivalent Fe(5)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(5), one Fe(7), and one Fe(8) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(6), and one Fe(9) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(4), one Fe(5), and one Fe(9) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(4), one Fe(6), one Fe(7), and one Fe(8) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(4), and one Fe(5) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(8) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(4), one Fe(5), and one Fe(9) atom. is represented by the CIF file [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.047
_cell_length_b   10.499
_cell_length_c   6.035
_cell_angle_alpha   73.561
_cell_angle_beta   119.774
_cell_angle_gamma   89.783
_symmetry_Int_Tables_number   1
_cell_volume   314.140
_cell_formula_units_Z   4
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
  Fe  Fe0  1  0.500  0.000  0.500  1.0
  Fe  Fe1  1  1.000  0.000  0.500  1.0
  Fe  Fe2  1  0.000  0.500  0.000  1.0
  Fe  Fe3  1  0.254  0.251  0.504  1.0
  Fe  Fe4  1  0.746  0.749  0.496  1.0
  Fe  Fe5  1  0.936  0.190  0.876  1.0
  Fe  Fe6  1  0.433  0.691  0.872  1.0
  Fe  Fe7  1  0.064  0.810  0.124  1.0
  Fe  Fe8  1  0.567  0.309  0.128  1.0
  Fe  Fe9  1  1.000  0.500  0.500  1.0
  Fe  Fe10  1  0.500  0.500  0.500  1.0
  Fe  Fe11  1  0.500  1.000  0.000  1.0
  O  O12  1  0.877  0.384  0.755  1.0
  O  O13  1  0.358  0.883  0.741  1.0
  O  O14  1  0.123  0.616  0.245  1.0
  O  O15  1  0.642  0.117  0.259  1.0
  O  O16  1  0.893  0.376  0.246  1.0
  O  O17  1  0.392  0.871  0.269  1.0
  O  O18  1  0.631  0.632  0.260  1.0
  O  O19  1  0.122  0.123  0.267  1.0
  O  O20  1  0.369  0.368  0.740  1.0
  O  O21  1  0.878  0.877  0.733  1.0
  O  O22  1  0.647  0.626  0.755  1.0
  O  O23  1  0.120  0.126  0.728  1.0
  O  O24  1  0.107  0.624  0.754  1.0
  O  O25  1  0.608  0.129  0.731  1.0
  O  O26  1  0.353  0.374  0.245  1.0
  O  O27  1  0.880  0.874  0.272  1.0
[/CIF]
.