The structure described by MgFe2O4 crystallizes in the orthorhombic Pmmn space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and edges with two equivalent Mg(2)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 3-17°. In the second Mg site, Mg(2) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form distorted MgO6 pentagonal pyramids that share corners with four equivalent Fe(1)O6 octahedra, corners with eight equivalent Fe(2)O6 octahedra, edges with two equivalent Mg(1)O6 pentagonal pyramids, and faces with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), and four equivalent O(3) atoms to form FeO6 octahedra that share corners with two equivalent Mg(2)O6 pentagonal pyramids, corners with three equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra,  an edgeedge with one Mg(1)O6 pentagonal pyramid, and  a faceface with one Mg(2)O6 pentagonal pyramid. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share corners with four equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. There are three inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Fe(1), and two equivalent Fe(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Fe(1), and two equivalent Fe(2) atoms. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), one Fe(2), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2Fe3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.130
_cell_length_b   5.896
_cell_length_c   10.329
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   312.407
_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
  Mg  Mg0  1  0.853  0.000  0.500  1.0
  Mg  Mg1  1  0.147  0.500  0.000  1.0
  Mg  Mg2  1  0.516  0.000  0.000  1.0
  Mg  Mg3  1  0.484  0.500  0.500  1.0
  Fe  Fe4  1  0.509  0.500  0.230  1.0
  Fe  Fe5  1  0.509  0.500  0.770  1.0
  Fe  Fe6  1  0.491  0.000  0.270  1.0
  Fe  Fe7  1  0.491  0.000  0.730  1.0
  Fe  Fe8  1  0.000  0.250  0.250  1.0
  Fe  Fe9  1  0.000  0.750  0.750  1.0
  Fe  Fe10  1  0.000  0.750  0.250  1.0
  Fe  Fe11  1  0.000  0.250  0.750  1.0
  O  O12  1  0.855  0.500  0.141  1.0
  O  O13  1  0.855  0.500  0.859  1.0
  O  O14  1  0.145  0.000  0.359  1.0
  O  O15  1  0.145  0.000  0.641  1.0
  O  O16  1  0.198  0.500  0.349  1.0
  O  O17  1  0.198  0.500  0.651  1.0
  O  O18  1  0.802  0.000  0.151  1.0
  O  O19  1  0.802  0.000  0.849  1.0
  O  O20  1  0.668  0.254  0.365  1.0
  O  O21  1  0.668  0.746  0.635  1.0
  O  O22  1  0.332  0.754  0.135  1.0
  O  O23  1  0.332  0.246  0.865  1.0
  O  O24  1  0.332  0.246  0.135  1.0
  O  O25  1  0.332  0.754  0.865  1.0
  O  O26  1  0.668  0.746  0.365  1.0
  O  O27  1  0.668  0.254  0.635  1.0
[/CIF]
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The structure described by MgFe2O4 crystallizes in the orthorhombic Pmmn space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and edges with two equivalent Mg(2)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 3-17°. In the second Mg site, Mg(2) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form distorted MgO6 pentagonal pyramids that share corners with four equivalent Fe(1)O6 octahedra, corners with eight equivalent Fe(2)O6 octahedra, edges with two equivalent Mg(1)O6 pentagonal pyramids, and faces with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), and four equivalent O(3) atoms to form FeO6 octahedra that share corners with two equivalent Mg(2)O6 pentagonal pyramids, corners with three equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra,  an edgeedge with one Mg(1)O6 pentagonal pyramid, and  a faceface with one Mg(2)O6 pentagonal pyramid. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share corners with four equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. There are three inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Fe(1), and two equivalent Fe(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Fe(1), and two equivalent Fe(2) atoms. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), one Fe(2), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2Fe3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.130
_cell_length_b   5.896
_cell_length_c   10.329
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   312.407
_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
  Mg  Mg0  1  0.853  0.000  0.500  1.0
  Mg  Mg1  1  0.147  0.500  0.000  1.0
  Mg  Mg2  1  0.516  0.000  0.000  1.0
  Mg  Mg3  1  0.484  0.500  0.500  1.0
  Fe  Fe4  1  0.509  0.500  0.230  1.0
  Fe  Fe5  1  0.509  0.500  0.770  1.0
  Fe  Fe6  1  0.491  0.000  0.270  1.0
  Fe  Fe7  1  0.491  0.000  0.730  1.0
  Fe  Fe8  1  0.000  0.250  0.250  1.0
  Fe  Fe9  1  0.000  0.750  0.750  1.0
  Fe  Fe10  1  0.000  0.750  0.250  1.0
  Fe  Fe11  1  0.000  0.250  0.750  1.0
  O  O12  1  0.855  0.500  0.141  1.0
  O  O13  1  0.855  0.500  0.859  1.0
  O  O14  1  0.145  0.000  0.359  1.0
  O  O15  1  0.145  0.000  0.641  1.0
  O  O16  1  0.198  0.500  0.349  1.0
  O  O17  1  0.198  0.500  0.651  1.0
  O  O18  1  0.802  0.000  0.151  1.0
  O  O19  1  0.802  0.000  0.849  1.0
  O  O20  1  0.668  0.254  0.365  1.0
  O  O21  1  0.668  0.746  0.635  1.0
  O  O22  1  0.332  0.754  0.135  1.0
  O  O23  1  0.332  0.246  0.865  1.0
  O  O24  1  0.332  0.246  0.135  1.0
  O  O25  1  0.332  0.754  0.865  1.0
  O  O26  1  0.668  0.746  0.365  1.0
  O  O27  1  0.668  0.254  0.635  1.0
[/CIF]
.