The structure described by MgCr4O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 8-coordinate geometry to one O(7), one O(8), two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(5), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-55°. In the second Cr site, Cr(2) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-39°. In the third Cr site, Cr(3) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-55°. In the fourth Cr site, Cr(4) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-39°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Cr(4), and two equivalent Cr(3) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with two equivalent O(7)MgCr4 square pyramids, corners with two equivalent O(8)MgCr4 square pyramids, corners with four equivalent O(5)Mg2Cr2 tetrahedra, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(8)MgCr4 square pyramids,  an edgeedge with one O(5)Mg2Cr2 tetrahedra,  an edgeedge with one O(4)Mg2Cr3 trigonal bipyramid, and edges with two equivalent O(1)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Cr(3) and two equivalent Cr(4) atoms. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Cr(1) and two equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(1), one Cr(2), and two equivalent Cr(1) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with two equivalent O(7)MgCr4 square pyramids, corners with two equivalent O(8)MgCr4 square pyramids, corners with four equivalent O(5)Mg2Cr2 tetrahedra, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(7)MgCr4 square pyramids,  an edgeedge with one O(5)Mg2Cr2 tetrahedra,  an edgeedge with one O(1)Mg2Cr3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Cr3 trigonal bipyramids. In the fifth O site, O(5) is bonded to two equivalent Mg(1), one Cr(1), and one Cr(3) atom to form OMg2Cr2 tetrahedra that share corners with two equivalent O(5)Mg2Cr2 tetrahedra, corners with four equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with four equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(7)MgCr4 square pyramids, edges with two equivalent O(8)MgCr4 square pyramids,  an edgeedge with one O(1)Mg2Cr3 trigonal bipyramid, and  an edgeedge with one O(4)Mg2Cr3 trigonal bipyramid. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(4) atom. In the seventh O site, O(7) is bonded to one Mg(1), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr4 square pyramids that share  a cornercorner with one O(8)MgCr4 square pyramid, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(7)MgCr4 square pyramids, edges with two equivalent O(5)Mg2Cr2 tetrahedra, and edges with three equivalent O(4)Mg2Cr3 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Mg(1), two equivalent Cr(3), and two equivalent Cr(4) atoms to form distorted OMgCr4 square pyramids that share  a cornercorner with one O(7)MgCr4 square pyramid, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(8)MgCr4 square pyramids, edges with two equivalent O(5)Mg2Cr2 tetrahedra, and edges with three equivalent O(1)Mg2Cr3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.920
_cell_length_b   5.035
_cell_length_c   9.788
_cell_angle_alpha   89.858
_cell_angle_beta   90.429
_cell_angle_gamma   106.833
_symmetry_Int_Tables_number   1
_cell_volume   137.746
_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
  Mg  Mg0  1  0.604  0.213  0.250  1.0
  Cr  Cr1  1  0.864  0.731  0.071  1.0
  Cr  Cr2  1  0.140  0.264  0.924  1.0
  Cr  Cr3  1  0.867  0.731  0.430  1.0
  Cr  Cr4  1  0.124  0.264  0.576  1.0
  O  O5  1  0.229  0.457  0.387  1.0
  O  O6  1  0.744  0.513  0.603  1.0
  O  O7  1  0.769  0.514  0.897  1.0
  O  O8  1  0.227  0.457  0.114  1.0
  O  O9  1  0.958  0.922  0.250  1.0
  O  O10  1  0.069  0.137  0.750  1.0
  O  O11  1  0.488  0.010  0.006  1.0
  O  O12  1  0.522  0.010  0.494  1.0
[/CIF]
.
The structure described by MgCr4O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded in a 8-coordinate geometry to one O(7), one O(8), two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(5), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-55°. In the second Cr site, Cr(2) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-39°. In the third Cr site, Cr(3) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-55°. In the fourth Cr site, Cr(4) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(8) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 6-39°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Cr(4), and two equivalent Cr(3) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with two equivalent O(7)MgCr4 square pyramids, corners with two equivalent O(8)MgCr4 square pyramids, corners with four equivalent O(5)Mg2Cr2 tetrahedra, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(8)MgCr4 square pyramids,  an edgeedge with one O(5)Mg2Cr2 tetrahedra,  an edgeedge with one O(4)Mg2Cr3 trigonal bipyramid, and edges with two equivalent O(1)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Cr(3) and two equivalent Cr(4) atoms. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Cr(1) and two equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(1), one Cr(2), and two equivalent Cr(1) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with two equivalent O(7)MgCr4 square pyramids, corners with two equivalent O(8)MgCr4 square pyramids, corners with four equivalent O(5)Mg2Cr2 tetrahedra, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(7)MgCr4 square pyramids,  an edgeedge with one O(5)Mg2Cr2 tetrahedra,  an edgeedge with one O(1)Mg2Cr3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Cr3 trigonal bipyramids. In the fifth O site, O(5) is bonded to two equivalent Mg(1), one Cr(1), and one Cr(3) atom to form OMg2Cr2 tetrahedra that share corners with two equivalent O(5)Mg2Cr2 tetrahedra, corners with four equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with four equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(7)MgCr4 square pyramids, edges with two equivalent O(8)MgCr4 square pyramids,  an edgeedge with one O(1)Mg2Cr3 trigonal bipyramid, and  an edgeedge with one O(4)Mg2Cr3 trigonal bipyramid. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Cr(2) and one Cr(4) atom. In the seventh O site, O(7) is bonded to one Mg(1), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr4 square pyramids that share  a cornercorner with one O(8)MgCr4 square pyramid, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(7)MgCr4 square pyramids, edges with two equivalent O(5)Mg2Cr2 tetrahedra, and edges with three equivalent O(4)Mg2Cr3 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Mg(1), two equivalent Cr(3), and two equivalent Cr(4) atoms to form distorted OMgCr4 square pyramids that share  a cornercorner with one O(7)MgCr4 square pyramid, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids, corners with two equivalent O(4)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(8)MgCr4 square pyramids, edges with two equivalent O(5)Mg2Cr2 tetrahedra, and edges with three equivalent O(1)Mg2Cr3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.920
_cell_length_b   5.035
_cell_length_c   9.788
_cell_angle_alpha   89.858
_cell_angle_beta   90.429
_cell_angle_gamma   106.833
_symmetry_Int_Tables_number   1
_cell_volume   137.746
_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
  Mg  Mg0  1  0.604  0.213  0.250  1.0
  Cr  Cr1  1  0.864  0.731  0.071  1.0
  Cr  Cr2  1  0.140  0.264  0.924  1.0
  Cr  Cr3  1  0.867  0.731  0.430  1.0
  Cr  Cr4  1  0.124  0.264  0.576  1.0
  O  O5  1  0.229  0.457  0.387  1.0
  O  O6  1  0.744  0.513  0.603  1.0
  O  O7  1  0.769  0.514  0.897  1.0
  O  O8  1  0.227  0.457  0.114  1.0
  O  O9  1  0.958  0.922  0.250  1.0
  O  O10  1  0.069  0.137  0.750  1.0
  O  O11  1  0.488  0.010  0.006  1.0
  O  O12  1  0.522  0.010  0.494  1.0
[/CIF]
.