The material structure described by Fe15O16 crystallizes in the trigonal R-3m space group. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to six equivalent O(4) atoms to form FeO6 octahedra that share corners with six equivalent Fe(5)O6 octahedra, corners with six equivalent Fe(4)O4 tetrahedra, and edges with six equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Fe site, Fe(2) is bonded to six equivalent O(3) atoms to form a mixture of corner and edge-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the third Fe site, Fe(3) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with three equivalent Fe(6)O6 octahedra, corners with three equivalent Fe(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(5)O6 octahedra, edges with two equivalent Fe(6)O6 octahedra, and edges with four equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth Fe site, Fe(4) is bonded to one O(1) and three equivalent O(4) atoms to form a mixture of face and corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-63°. In the fifth Fe site, Fe(5) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form distorted FeO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, edges with three equivalent Fe(6)O6 octahedra, edges with six equivalent Fe(3)O6 octahedra, and  a faceface with one Fe(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the sixth Fe site, Fe(6) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form a mixture of corner and edge-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Fe(4) and three equivalent Fe(3) atoms to form distorted OFe4 tetrahedra that share corners with three equivalent O(2)Fe6 octahedra, corners with nine equivalent O(4)Fe5 square pyramids, and edges with three equivalent O(3)Fe6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to three equivalent Fe(3) and three equivalent Fe(6) atoms to form OFe6 octahedra that share corners with three equivalent O(2)Fe6 octahedra, corners with three equivalent O(1)Fe4 tetrahedra, edges with nine equivalent O(3)Fe6 octahedra, and edges with three equivalent O(4)Fe5 square pyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Fe(2), one Fe(5), two equivalent Fe(3), and two equivalent Fe(6) atoms to form OFe6 octahedra that share corners with three equivalent O(3)Fe6 octahedra, corners with three equivalent O(4)Fe5 square pyramids, edges with three equivalent O(2)Fe6 octahedra, edges with six equivalent O(3)Fe6 octahedra, edges with two equivalent O(4)Fe5 square pyramids, and  an edgeedge with one O(1)Fe4 tetrahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to one Fe(1), one Fe(4), one Fe(5), and two equivalent Fe(3) atoms to form distorted OFe5 square pyramids that share corners with three equivalent O(3)Fe6 octahedra, corners with three equivalent O(4)Fe5 square pyramids, corners with three equivalent O(1)Fe4 tetrahedra,  an edgeedge with one O(2)Fe6 octahedra, edges with two equivalent O(3)Fe6 octahedra, and edges with four equivalent O(4)Fe5 square pyramids. The corner-sharing octahedral tilt angles range from 4-10°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Fe15O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.891
_cell_length_b   10.891
_cell_length_c   10.891
_cell_angle_alpha   33.159
_cell_angle_beta   33.159
_cell_angle_gamma   33.159
_symmetry_Int_Tables_number   1
_cell_volume   344.001
_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
  Fe  Fe0  1  0.500  0.500  0.500  1.0
  Fe  Fe1  1  0.000  0.000  0.000  1.0
  Fe  Fe2  1  0.749  0.749  0.247  1.0
  Fe  Fe3  1  0.251  0.251  0.753  1.0
  Fe  Fe4  1  0.749  0.247  0.749  1.0
  Fe  Fe5  1  0.251  0.753  0.251  1.0
  Fe  Fe6  1  0.247  0.749  0.749  1.0
  Fe  Fe7  1  0.753  0.251  0.251  1.0
  Fe  Fe8  1  0.820  0.820  0.820  1.0
  Fe  Fe9  1  0.180  0.180  0.180  1.0
  Fe  Fe10  1  0.259  0.259  0.259  1.0
  Fe  Fe11  1  0.741  0.741  0.741  1.0
  Fe  Fe12  1  0.500  0.500  0.000  1.0
  Fe  Fe13  1  0.500  0.000  0.500  1.0
  Fe  Fe14  1  0.000  0.500  0.500  1.0
  O  O15  1  0.881  0.881  0.881  1.0
  O  O16  1  0.375  0.375  0.375  1.0
  O  O17  1  0.127  0.127  0.626  1.0
  O  O18  1  0.629  0.629  0.116  1.0
  O  O19  1  0.127  0.626  0.127  1.0
  O  O20  1  0.629  0.116  0.629  1.0
  O  O21  1  0.626  0.127  0.127  1.0
  O  O22  1  0.116  0.629  0.629  1.0
  O  O23  1  0.625  0.625  0.625  1.0
  O  O24  1  0.119  0.119  0.119  1.0
  O  O25  1  0.371  0.371  0.884  1.0
  O  O26  1  0.873  0.873  0.374  1.0
  O  O27  1  0.371  0.884  0.371  1.0
  O  O28  1  0.873  0.374  0.873  1.0
  O  O29  1  0.884  0.371  0.371  1.0
  O  O30  1  0.374  0.873  0.873  1.0
[/CIF]
.
The material structure described by Fe15O16 crystallizes in the trigonal R-3m space group. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to six equivalent O(4) atoms to form FeO6 octahedra that share corners with six equivalent Fe(5)O6 octahedra, corners with six equivalent Fe(4)O4 tetrahedra, and edges with six equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Fe site, Fe(2) is bonded to six equivalent O(3) atoms to form a mixture of corner and edge-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the third Fe site, Fe(3) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with three equivalent Fe(6)O6 octahedra, corners with three equivalent Fe(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Fe(5)O6 octahedra, edges with two equivalent Fe(6)O6 octahedra, and edges with four equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth Fe site, Fe(4) is bonded to one O(1) and three equivalent O(4) atoms to form a mixture of face and corner-sharing FeO4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-63°. In the fifth Fe site, Fe(5) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form distorted FeO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, edges with three equivalent Fe(6)O6 octahedra, edges with six equivalent Fe(3)O6 octahedra, and  a faceface with one Fe(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the sixth Fe site, Fe(6) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form a mixture of corner and edge-sharing FeO6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Fe(4) and three equivalent Fe(3) atoms to form distorted OFe4 tetrahedra that share corners with three equivalent O(2)Fe6 octahedra, corners with nine equivalent O(4)Fe5 square pyramids, and edges with three equivalent O(3)Fe6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second O site, O(2) is bonded to three equivalent Fe(3) and three equivalent Fe(6) atoms to form OFe6 octahedra that share corners with three equivalent O(2)Fe6 octahedra, corners with three equivalent O(1)Fe4 tetrahedra, edges with nine equivalent O(3)Fe6 octahedra, and edges with three equivalent O(4)Fe5 square pyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Fe(2), one Fe(5), two equivalent Fe(3), and two equivalent Fe(6) atoms to form OFe6 octahedra that share corners with three equivalent O(3)Fe6 octahedra, corners with three equivalent O(4)Fe5 square pyramids, edges with three equivalent O(2)Fe6 octahedra, edges with six equivalent O(3)Fe6 octahedra, edges with two equivalent O(4)Fe5 square pyramids, and  an edgeedge with one O(1)Fe4 tetrahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to one Fe(1), one Fe(4), one Fe(5), and two equivalent Fe(3) atoms to form distorted OFe5 square pyramids that share corners with three equivalent O(3)Fe6 octahedra, corners with three equivalent O(4)Fe5 square pyramids, corners with three equivalent O(1)Fe4 tetrahedra,  an edgeedge with one O(2)Fe6 octahedra, edges with two equivalent O(3)Fe6 octahedra, and edges with four equivalent O(4)Fe5 square pyramids. The corner-sharing octahedral tilt angles range from 4-10°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Fe15O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.891
_cell_length_b   10.891
_cell_length_c   10.891
_cell_angle_alpha   33.159
_cell_angle_beta   33.159
_cell_angle_gamma   33.159
_symmetry_Int_Tables_number   1
_cell_volume   344.001
_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
  Fe  Fe0  1  0.500  0.500  0.500  1.0
  Fe  Fe1  1  0.000  0.000  0.000  1.0
  Fe  Fe2  1  0.749  0.749  0.247  1.0
  Fe  Fe3  1  0.251  0.251  0.753  1.0
  Fe  Fe4  1  0.749  0.247  0.749  1.0
  Fe  Fe5  1  0.251  0.753  0.251  1.0
  Fe  Fe6  1  0.247  0.749  0.749  1.0
  Fe  Fe7  1  0.753  0.251  0.251  1.0
  Fe  Fe8  1  0.820  0.820  0.820  1.0
  Fe  Fe9  1  0.180  0.180  0.180  1.0
  Fe  Fe10  1  0.259  0.259  0.259  1.0
  Fe  Fe11  1  0.741  0.741  0.741  1.0
  Fe  Fe12  1  0.500  0.500  0.000  1.0
  Fe  Fe13  1  0.500  0.000  0.500  1.0
  Fe  Fe14  1  0.000  0.500  0.500  1.0
  O  O15  1  0.881  0.881  0.881  1.0
  O  O16  1  0.375  0.375  0.375  1.0
  O  O17  1  0.127  0.127  0.626  1.0
  O  O18  1  0.629  0.629  0.116  1.0
  O  O19  1  0.127  0.626  0.127  1.0
  O  O20  1  0.629  0.116  0.629  1.0
  O  O21  1  0.626  0.127  0.127  1.0
  O  O22  1  0.116  0.629  0.629  1.0
  O  O23  1  0.625  0.625  0.625  1.0
  O  O24  1  0.119  0.119  0.119  1.0
  O  O25  1  0.371  0.371  0.884  1.0
  O  O26  1  0.873  0.873  0.374  1.0
  O  O27  1  0.371  0.884  0.371  1.0
  O  O28  1  0.873  0.374  0.873  1.0
  O  O29  1  0.884  0.371  0.371  1.0
  O  O30  1  0.374  0.873  0.873  1.0
[/CIF]
.