The structure described by MgCrCo3O8 is beta indium sulfide-derived structured and crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(5), one O(6), one O(7), and one O(8) atom to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with three equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. Cr(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 CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. There are three inequivalent Co sites. In the first Co site, Co(1) 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 CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. In the third Co site, Co(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(1), and one Co(2) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(1), and one Co(3) atom. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Cr(1), one Co(2), and one Co(3) atom to form distorted OMgCrCo2 trigonal pyramids that share  a cornercorner with one O(6)MgCrCo2 tetrahedra,  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(7)MgCrCo2 trigonal pyramid,  an edgeedge with one O(6)MgCrCo2 tetrahedra,  an edgeedge with one O(8)MgCo3 trigonal pyramid, and  an edgeedge with one O(7)MgCrCo2 trigonal pyramid. In the sixth O site, O(6) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(3) atom to form distorted OMgCrCo2 tetrahedra that share  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(5)MgCrCo2 trigonal pyramid,  a cornercorner with one O(7)MgCrCo2 trigonal pyramid,  an edgeedge with one O(8)MgCo3 trigonal pyramid,  an edgeedge with one O(5)MgCrCo2 trigonal pyramid, and  an edgeedge with one O(7)MgCrCo2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted OMgCrCo2 trigonal pyramids that share  a cornercorner with one O(6)MgCrCo2 tetrahedra,  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(5)MgCrCo2 trigonal pyramid,  an edgeedge with one O(6)MgCrCo2 tetrahedra,  an edgeedge with one O(8)MgCo3 trigonal pyramid, and  an edgeedge with one O(5)MgCrCo2 trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Co(1), one Co(2), and one Co(3) atom to form a mixture of distorted edge and corner-sharing OMgCo3 trigonal pyramids. is represented by the CIF file [CIF]
data_MgCrCo3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.964
_cell_length_b   5.827
_cell_length_c   5.970
_cell_angle_alpha   60.424
_cell_angle_beta   58.315
_cell_angle_gamma   59.747
_symmetry_Int_Tables_number   1
_cell_volume   144.913
_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  0.876  0.883  0.867  1.0
  Cr  Cr1  1  0.501  0.495  0.500  1.0
  Co  Co2  1  0.009  0.503  0.494  1.0
  Co  Co3  1  0.498  0.006  0.497  1.0
  Co  Co4  1  0.497  0.501  0.003  1.0
  O  O5  1  0.261  0.247  0.293  1.0
  O  O6  1  0.271  0.247  0.707  1.0
  O  O7  1  0.261  0.703  0.275  1.0
  O  O8  1  0.702  0.245  0.266  1.0
  O  O9  1  0.289  0.747  0.737  1.0
  O  O10  1  0.738  0.293  0.730  1.0
  O  O11  1  0.733  0.747  0.283  1.0
  O  O12  1  0.740  0.752  0.717  1.0
[/CIF]
.
The structure described by MgCrCo3O8 is beta indium sulfide-derived structured and crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(5), one O(6), one O(7), and one O(8) atom to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with three equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. Cr(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 CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. There are three inequivalent Co sites. In the first Co site, Co(1) 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 CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. In the third Co site, Co(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(1), and one Co(2) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(1), and one Co(3) atom. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Cr(1), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Cr(1), one Co(2), and one Co(3) atom to form distorted OMgCrCo2 trigonal pyramids that share  a cornercorner with one O(6)MgCrCo2 tetrahedra,  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(7)MgCrCo2 trigonal pyramid,  an edgeedge with one O(6)MgCrCo2 tetrahedra,  an edgeedge with one O(8)MgCo3 trigonal pyramid, and  an edgeedge with one O(7)MgCrCo2 trigonal pyramid. In the sixth O site, O(6) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(3) atom to form distorted OMgCrCo2 tetrahedra that share  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(5)MgCrCo2 trigonal pyramid,  a cornercorner with one O(7)MgCrCo2 trigonal pyramid,  an edgeedge with one O(8)MgCo3 trigonal pyramid,  an edgeedge with one O(5)MgCrCo2 trigonal pyramid, and  an edgeedge with one O(7)MgCrCo2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted OMgCrCo2 trigonal pyramids that share  a cornercorner with one O(6)MgCrCo2 tetrahedra,  a cornercorner with one O(8)MgCo3 trigonal pyramid,  a cornercorner with one O(5)MgCrCo2 trigonal pyramid,  an edgeedge with one O(6)MgCrCo2 tetrahedra,  an edgeedge with one O(8)MgCo3 trigonal pyramid, and  an edgeedge with one O(5)MgCrCo2 trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Co(1), one Co(2), and one Co(3) atom to form a mixture of distorted edge and corner-sharing OMgCo3 trigonal pyramids. is represented by the CIF file [CIF]
data_MgCrCo3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.964
_cell_length_b   5.827
_cell_length_c   5.970
_cell_angle_alpha   60.424
_cell_angle_beta   58.315
_cell_angle_gamma   59.747
_symmetry_Int_Tables_number   1
_cell_volume   144.913
_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  0.876  0.883  0.867  1.0
  Cr  Cr1  1  0.501  0.495  0.500  1.0
  Co  Co2  1  0.009  0.503  0.494  1.0
  Co  Co3  1  0.498  0.006  0.497  1.0
  Co  Co4  1  0.497  0.501  0.003  1.0
  O  O5  1  0.261  0.247  0.293  1.0
  O  O6  1  0.271  0.247  0.707  1.0
  O  O7  1  0.261  0.703  0.275  1.0
  O  O8  1  0.702  0.245  0.266  1.0
  O  O9  1  0.289  0.747  0.737  1.0
  O  O10  1  0.738  0.293  0.730  1.0
  O  O11  1  0.733  0.747  0.283  1.0
  O  O12  1  0.740  0.752  0.717  1.0
[/CIF]
.