The crystal structure described by Fe3O4 is Hausmannite-like structured and crystallizes in the monoclinic P2/m space group. There are seven inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(1) and four equivalent O(3) 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, and edges with four equivalent Fe(7)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(2) and four equivalent O(3) 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, and edges with four equivalent Fe(7)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(6) and four equivalent O(4) 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, and edges with four equivalent Fe(7)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to two equivalent O(5) and four equivalent O(4) 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, and edges with four equivalent Fe(7)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(5), one O(6), and two equivalent O(3) atoms 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(1), one O(2), and two equivalent O(4) atoms to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the seventh Fe site, Fe(7) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) 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(4)O6 octahedra, and edges with two equivalent Fe(7)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(6), and two equivalent Fe(7) atoms. In the second O site, O(2) is bonded to one Fe(2), one Fe(6), and two equivalent Fe(7) atoms to form distorted corner-sharing OFe4 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(5), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(7) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(4), one Fe(5), and two equivalent Fe(7) atoms. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(5), and two equivalent Fe(7) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.063
_cell_length_b   6.066
_cell_length_c   6.095
_cell_angle_alpha   119.840
_cell_angle_beta   119.655
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   159.717
_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
  Fe  Fe0  1  0.500  0.500  0.000  1.0
  Fe  Fe1  1  0.000  0.500  0.000  1.0
  Fe  Fe2  1  0.627  0.878  0.756  1.0
  Fe  Fe3  1  0.373  0.122  0.244  1.0
  Fe  Fe4  1  0.000  0.500  0.500  1.0
  Fe  Fe5  1  0.000  0.000  0.500  1.0
  O  O6  1  0.765  0.745  0.490  1.0
  O  O7  1  0.775  0.258  0.516  1.0
  O  O8  1  0.225  0.742  0.484  1.0
  O  O9  1  0.235  0.255  0.510  1.0
  O  O10  1  0.763  0.277  0.028  1.0
  O  O11  1  0.237  0.249  0.972  1.0
  O  O12  1  0.237  0.723  0.972  1.0
  O  O13  1  0.763  0.751  0.028  1.0
[/CIF]
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The crystal structure described by Fe3O4 is Hausmannite-like structured and crystallizes in the monoclinic P2/m space group. There are seven inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(1) and four equivalent O(3) 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, and edges with four equivalent Fe(7)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(2) and four equivalent O(3) 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, and edges with four equivalent Fe(7)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(6) and four equivalent O(4) 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, and edges with four equivalent Fe(7)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to two equivalent O(5) and four equivalent O(4) 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, and edges with four equivalent Fe(7)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to one O(5), one O(6), and two equivalent O(3) atoms 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(1), one O(2), and two equivalent O(4) atoms to form corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the seventh Fe site, Fe(7) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) 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(4)O6 octahedra, and edges with two equivalent Fe(7)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(6), and two equivalent Fe(7) atoms. In the second O site, O(2) is bonded to one Fe(2), one Fe(6), and two equivalent Fe(7) atoms to form distorted corner-sharing OFe4 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Fe(1), one Fe(2), one Fe(5), and one Fe(7) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Fe(3), one Fe(4), one Fe(6), and one Fe(7) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(4), one Fe(5), and two equivalent Fe(7) atoms. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Fe(3), one Fe(5), and two equivalent Fe(7) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Fe3O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.063
_cell_length_b   6.066
_cell_length_c   6.095
_cell_angle_alpha   119.840
_cell_angle_beta   119.655
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   159.717
_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
  Fe  Fe0  1  0.500  0.500  0.000  1.0
  Fe  Fe1  1  0.000  0.500  0.000  1.0
  Fe  Fe2  1  0.627  0.878  0.756  1.0
  Fe  Fe3  1  0.373  0.122  0.244  1.0
  Fe  Fe4  1  0.000  0.500  0.500  1.0
  Fe  Fe5  1  0.000  0.000  0.500  1.0
  O  O6  1  0.765  0.745  0.490  1.0
  O  O7  1  0.775  0.258  0.516  1.0
  O  O8  1  0.225  0.742  0.484  1.0
  O  O9  1  0.235  0.255  0.510  1.0
  O  O10  1  0.763  0.277  0.028  1.0
  O  O11  1  0.237  0.249  0.972  1.0
  O  O12  1  0.237  0.723  0.972  1.0
  O  O13  1  0.763  0.751  0.028  1.0
[/CIF]
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