The material structure described by MgMn2O4 crystallizes in the monoclinic P2/c space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-19°. In the second Mg site, Mg(2) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted MnO6 octahedra that share corners with three equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. In the second Mn site, Mn(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share edges with two equivalent Mn(3)O6 octahedra, edges with four equivalent Mn(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. In the third Mn site, Mn(3) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MnO6 octahedra that share edges with two equivalent Mn(2)O6 octahedra, edges with four equivalent Mn(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Mn(1), one Mn(2), and one Mn(3) atom to form OMgMn3 trigonal pyramids that share corners with two equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(1)MgMn3 trigonal pyramids, edges with two equivalent O(3)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(4)Mg2Mn3 trigonal bipyramids. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mn(1), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), one Mn(2), and two equivalent Mn(1) atoms to form distorted OMg2Mn3 trigonal bipyramids that share corners with two equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(1)MgMn3 trigonal pyramids,  an edgeedge with one O(3)Mg2Mn3 trigonal bipyramid, edges with three equivalent O(4)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(1)MgMn3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), one Mn(3), and two equivalent Mn(1) atoms to form OMg2Mn3 trigonal bipyramids that share corners with two equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(1)MgMn3 trigonal pyramids,  an edgeedge with one O(4)Mg2Mn3 trigonal bipyramid, edges with three equivalent O(3)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(1)MgMn3 trigonal pyramids. is represented by the CIF file [CIF]
data_MgMn2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.151
_cell_length_b   6.027
_cell_length_c   11.769
_cell_angle_alpha   60.933
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   319.315
_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  0.149  0.000  0.250  1.0
  Mg  Mg1  1  0.851  0.000  0.750  1.0
  Mg  Mg2  1  0.511  0.500  0.750  1.0
  Mg  Mg3  1  0.489  0.500  0.250  1.0
  Mn  Mn4  1  0.488  0.765  0.984  1.0
  Mn  Mn5  1  0.488  0.235  0.516  1.0
  Mn  Mn6  1  0.512  0.235  0.016  1.0
  Mn  Mn7  1  0.512  0.765  0.484  1.0
  Mn  Mn8  1  0.000  0.500  0.000  1.0
  Mn  Mn9  1  0.000  0.500  0.500  1.0
  Mn  Mn10  1  0.000  0.000  0.000  1.0
  Mn  Mn11  1  0.000  0.000  0.500  1.0
  O  O12  1  0.142  0.843  0.898  1.0
  O  O13  1  0.142  0.157  0.602  1.0
  O  O14  1  0.858  0.157  0.102  1.0
  O  O15  1  0.858  0.843  0.398  1.0
  O  O16  1  0.766  0.649  0.103  1.0
  O  O17  1  0.766  0.351  0.397  1.0
  O  O18  1  0.234  0.351  0.897  1.0
  O  O19  1  0.234  0.649  0.603  1.0
  O  O20  1  0.318  0.365  0.119  1.0
  O  O21  1  0.318  0.635  0.381  1.0
  O  O22  1  0.691  0.128  0.888  1.0
  O  O23  1  0.691  0.872  0.612  1.0
  O  O24  1  0.682  0.635  0.881  1.0
  O  O25  1  0.682  0.365  0.619  1.0
  O  O26  1  0.309  0.872  0.112  1.0
  O  O27  1  0.309  0.128  0.388  1.0
[/CIF]
.
The material structure described by MgMn2O4 crystallizes in the monoclinic P2/c space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-19°. In the second Mg site, Mg(2) is bonded in a 6-coordinate geometry to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted MnO6 octahedra that share corners with three equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. In the second Mn site, Mn(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share edges with two equivalent Mn(3)O6 octahedra, edges with four equivalent Mn(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. In the third Mn site, Mn(3) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MnO6 octahedra that share edges with two equivalent Mn(2)O6 octahedra, edges with four equivalent Mn(1)O6 octahedra, and edges with two equivalent Mg(1)O6 pentagonal pyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Mn(1), one Mn(2), and one Mn(3) atom to form OMgMn3 trigonal pyramids that share corners with two equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(1)MgMn3 trigonal pyramids, edges with two equivalent O(3)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(4)Mg2Mn3 trigonal bipyramids. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mn(1), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), one Mn(2), and two equivalent Mn(1) atoms to form distorted OMg2Mn3 trigonal bipyramids that share corners with two equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(1)MgMn3 trigonal pyramids,  an edgeedge with one O(3)Mg2Mn3 trigonal bipyramid, edges with three equivalent O(4)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(1)MgMn3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), one Mn(3), and two equivalent Mn(1) atoms to form OMg2Mn3 trigonal bipyramids that share corners with two equivalent O(3)Mg2Mn3 trigonal bipyramids, corners with three equivalent O(4)Mg2Mn3 trigonal bipyramids, corners with two equivalent O(1)MgMn3 trigonal pyramids,  an edgeedge with one O(4)Mg2Mn3 trigonal bipyramid, edges with three equivalent O(3)Mg2Mn3 trigonal bipyramids, and edges with two equivalent O(1)MgMn3 trigonal pyramids. is represented by the CIF file [CIF]
data_MgMn2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.151
_cell_length_b   6.027
_cell_length_c   11.769
_cell_angle_alpha   60.933
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   319.315
_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  0.149  0.000  0.250  1.0
  Mg  Mg1  1  0.851  0.000  0.750  1.0
  Mg  Mg2  1  0.511  0.500  0.750  1.0
  Mg  Mg3  1  0.489  0.500  0.250  1.0
  Mn  Mn4  1  0.488  0.765  0.984  1.0
  Mn  Mn5  1  0.488  0.235  0.516  1.0
  Mn  Mn6  1  0.512  0.235  0.016  1.0
  Mn  Mn7  1  0.512  0.765  0.484  1.0
  Mn  Mn8  1  0.000  0.500  0.000  1.0
  Mn  Mn9  1  0.000  0.500  0.500  1.0
  Mn  Mn10  1  0.000  0.000  0.000  1.0
  Mn  Mn11  1  0.000  0.000  0.500  1.0
  O  O12  1  0.142  0.843  0.898  1.0
  O  O13  1  0.142  0.157  0.602  1.0
  O  O14  1  0.858  0.157  0.102  1.0
  O  O15  1  0.858  0.843  0.398  1.0
  O  O16  1  0.766  0.649  0.103  1.0
  O  O17  1  0.766  0.351  0.397  1.0
  O  O18  1  0.234  0.351  0.897  1.0
  O  O19  1  0.234  0.649  0.603  1.0
  O  O20  1  0.318  0.365  0.119  1.0
  O  O21  1  0.318  0.635  0.381  1.0
  O  O22  1  0.691  0.128  0.888  1.0
  O  O23  1  0.691  0.872  0.612  1.0
  O  O24  1  0.682  0.635  0.881  1.0
  O  O25  1  0.682  0.365  0.619  1.0
  O  O26  1  0.309  0.872  0.112  1.0
  O  O27  1  0.309  0.128  0.388  1.0
[/CIF]
.