The material described by MgCr4O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form MgO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-53°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with two equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-57°. In the second Cr site, Cr(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-57°. In the third Cr site, Cr(3) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(5), one O(7), and one O(8) atom. In the fourth Cr site, Cr(4) is bonded to one O(1), one O(2), one O(3), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 15-56°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Cr(2), one Cr(3), and one Cr(4) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Cr(1), one Cr(3), and one Cr(4) atom. In the third O site, O(3) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Cr(4) atom to form OMgCr3 trigonal pyramids that share  a cornercorner with one O(8)Cr4 trigonal pyramid,  a cornercorner with one O(4)MgCr3 trigonal pyramid,  an edgeedge with one O(8)Cr4 trigonal pyramid, and  an edgeedge with one O(4)MgCr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Cr(3) atom to form OMgCr3 trigonal pyramids that share  a cornercorner with one O(3)MgCr3 trigonal pyramid, corners with three equivalent O(8)Cr4 trigonal pyramids, and  an edgeedge with one O(3)MgCr3 trigonal pyramid. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Mg(1), one Cr(1), and one Cr(4) atom. In the seventh O site, O(7) is bonded in a 5-coordinate geometry to one Mg(1), one Cr(1), one Cr(2), one Cr(3), and one Cr(4) atom. In the eighth O site, O(8) is bonded to one Cr(1), one Cr(2), one Cr(3), and one Cr(4) atom to form a mixture of corner and edge-sharing OCr4 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.076
_cell_length_b   4.975
_cell_length_c   5.523
_cell_angle_alpha   88.075
_cell_angle_beta   84.327
_cell_angle_gamma   80.920
_symmetry_Int_Tables_number   1
_cell_volume   137.021
_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  0.797  0.941  0.871  1.0
  Cr  Cr1  1  0.500  0.483  0.983  1.0
  Cr  Cr2  1  0.479  0.989  0.502  1.0
  Cr  Cr3  1  0.916  0.468  0.398  1.0
  Cr  Cr4  1  0.213  0.009  0.109  1.0
  O  O5  1  0.131  0.843  0.418  1.0
  O  O6  1  0.864  0.273  0.085  1.0
  O  O7  1  0.394  0.169  0.830  1.0
  O  O8  1  0.665  0.658  0.670  1.0
  O  O9  1  0.805  0.149  0.549  1.0
  O  O10  1  0.156  0.728  0.938  1.0
  O  O11  1  0.582  0.802  0.171  1.0
  O  O12  1  0.303  0.308  0.296  1.0
[/CIF]
.
The material described by MgCr4O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form MgO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(4)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-53°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with two equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 7-57°. In the second Cr site, Cr(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(4)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 40-57°. In the third Cr site, Cr(3) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(5), one O(7), and one O(8) atom. In the fourth Cr site, Cr(4) is bonded to one O(1), one O(2), one O(3), one O(6), one O(7), and one O(8) atom to form CrO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Cr(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  a faceface with one Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 15-56°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Cr(2), one Cr(3), and one Cr(4) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Cr(1), one Cr(3), and one Cr(4) atom. In the third O site, O(3) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Cr(4) atom to form OMgCr3 trigonal pyramids that share  a cornercorner with one O(8)Cr4 trigonal pyramid,  a cornercorner with one O(4)MgCr3 trigonal pyramid,  an edgeedge with one O(8)Cr4 trigonal pyramid, and  an edgeedge with one O(4)MgCr3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one Cr(1), one Cr(2), and one Cr(3) atom to form OMgCr3 trigonal pyramids that share  a cornercorner with one O(3)MgCr3 trigonal pyramid, corners with three equivalent O(8)Cr4 trigonal pyramids, and  an edgeedge with one O(3)MgCr3 trigonal pyramid. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Mg(1), one Cr(1), and one Cr(4) atom. In the seventh O site, O(7) is bonded in a 5-coordinate geometry to one Mg(1), one Cr(1), one Cr(2), one Cr(3), and one Cr(4) atom. In the eighth O site, O(8) is bonded to one Cr(1), one Cr(2), one Cr(3), and one Cr(4) atom to form a mixture of corner and edge-sharing OCr4 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.076
_cell_length_b   4.975
_cell_length_c   5.523
_cell_angle_alpha   88.075
_cell_angle_beta   84.327
_cell_angle_gamma   80.920
_symmetry_Int_Tables_number   1
_cell_volume   137.021
_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  0.797  0.941  0.871  1.0
  Cr  Cr1  1  0.500  0.483  0.983  1.0
  Cr  Cr2  1  0.479  0.989  0.502  1.0
  Cr  Cr3  1  0.916  0.468  0.398  1.0
  Cr  Cr4  1  0.213  0.009  0.109  1.0
  O  O5  1  0.131  0.843  0.418  1.0
  O  O6  1  0.864  0.273  0.085  1.0
  O  O7  1  0.394  0.169  0.830  1.0
  O  O8  1  0.665  0.658  0.670  1.0
  O  O9  1  0.805  0.149  0.549  1.0
  O  O10  1  0.156  0.728  0.938  1.0
  O  O11  1  0.582  0.802  0.171  1.0
  O  O12  1  0.303  0.308  0.296  1.0
[/CIF]
.