The material described by MgCo7O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-22°. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(5)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-16°. In the second Co site, Co(2) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form distorted CoO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-19°. In the third Co site, Co(3) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-20°. In the fourth Co site, Co(4) is bonded to one O(10), one O(11), one O(2), one O(3), one O(6), and one O(7) atom to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 14-20°. In the fifth Co site, Co(5) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(1)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-14°. In the sixth Co site, Co(6) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with three equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-22°. In the seventh Co site, Co(7) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(1)O6 octahedra, and edges with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-16°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Co(2), one Co(3), and one Co(6) atom to form a mixture of corner and edge-sharing OMgCo3 trigonal pyramids. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(3), one Co(4), and one Co(6) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(12)MgCo4 square pyramid,  a cornercorner with one O(8)MgCo4 square pyramid, edges with two equivalent O(12)MgCo4 square pyramids, edges with two equivalent O(8)MgCo4 square pyramids, and  an edgeedge with one O(1)MgCo3 trigonal pyramid. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(2), one Co(3), and one Co(6) atom. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Co(3), one Co(4), and one Co(6) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the eighth O site, O(8) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(12)MgCo4 square pyramid,  a cornercorner with one O(4)MgCo4 square pyramid, corners with two equivalent O(1)MgCo3 trigonal pyramids, edges with two equivalent O(12)MgCo4 square pyramids, and edges with two equivalent O(4)MgCo4 square pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(2), one Co(3), and one Co(6) atom. In the tenth O site, O(10) is bonded in a T-shaped geometry to one Co(3), one Co(4), and one Co(6) atom. In the eleventh O site, O(11) is bonded in a distorted see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(4)MgCo4 square pyramid,  a cornercorner with one O(8)MgCo4 square pyramid, corners with two equivalent O(1)MgCo3 trigonal pyramids, edges with two equivalent O(4)MgCo4 square pyramids, and edges with two equivalent O(8)MgCo4 square pyramids. is represented by the CIF file [CIF]
data_MgCo7O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.102
_cell_length_b   5.092
_cell_length_c   9.771
_cell_angle_alpha   84.811
_cell_angle_beta   97.711
_cell_angle_gamma   58.040
_symmetry_Int_Tables_number   1
_cell_volume   209.423
_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  0.296  0.840  0.991  1.0
  Co  Co1  1  0.096  0.075  0.259  1.0
  Co  Co2  1  0.992  0.524  0.987  1.0
  Co  Co3  1  0.245  0.258  0.746  1.0
  Co  Co4  1  0.544  0.983  0.521  1.0
  Co  Co5  1  0.432  0.407  0.256  1.0
  Co  Co6  1  0.552  0.581  0.747  1.0
  Co  Co7  1  0.758  0.748  0.255  1.0
  O  O8  1  0.960  0.256  0.860  1.0
  O  O9  1  0.247  0.971  0.634  1.0
  O  O10  1  0.184  0.349  0.365  1.0
  O  O11  1  0.342  0.125  0.123  1.0
  O  O12  1  0.305  0.531  0.856  1.0
  O  O13  1  0.487  0.306  0.645  1.0
  O  O14  1  0.483  0.730  0.366  1.0
  O  O15  1  0.702  0.474  0.148  1.0
  O  O16  1  0.574  0.861  0.865  1.0
  O  O17  1  0.836  0.614  0.641  1.0
  O  O18  1  0.790  0.027  0.360  1.0
  O  O19  1  0.053  0.768  0.134  1.0
[/CIF]
.
The material described by MgCo7O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-22°. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(5)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-16°. In the second Co site, Co(2) is bonded to one O(1), one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form distorted CoO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with three equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-19°. In the third Co site, Co(3) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-20°. In the fourth Co site, Co(4) is bonded to one O(10), one O(11), one O(2), one O(3), one O(6), and one O(7) atom to form a mixture of distorted corner and edge-sharing CoO6 octahedra. The corner-sharing octahedral tilt angles range from 14-20°. In the fifth Co site, Co(5) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(1)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-14°. In the sixth Co site, Co(6) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with three equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-22°. In the seventh Co site, Co(7) is bonded to one O(11), one O(12), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with three equivalent Co(1)O6 octahedra, and edges with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-16°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Co(2), one Co(3), and one Co(6) atom to form a mixture of corner and edge-sharing OMgCo3 trigonal pyramids. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(3), one Co(4), and one Co(6) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(12)MgCo4 square pyramid,  a cornercorner with one O(8)MgCo4 square pyramid, edges with two equivalent O(12)MgCo4 square pyramids, edges with two equivalent O(8)MgCo4 square pyramids, and  an edgeedge with one O(1)MgCo3 trigonal pyramid. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(2), one Co(3), and one Co(6) atom. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Co(3), one Co(4), and one Co(6) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the eighth O site, O(8) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(12)MgCo4 square pyramid,  a cornercorner with one O(4)MgCo4 square pyramid, corners with two equivalent O(1)MgCo3 trigonal pyramids, edges with two equivalent O(12)MgCo4 square pyramids, and edges with two equivalent O(4)MgCo4 square pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(2), one Co(3), and one Co(6) atom. In the tenth O site, O(10) is bonded in a T-shaped geometry to one Co(3), one Co(4), and one Co(6) atom. In the eleventh O site, O(11) is bonded in a distorted see-saw-like geometry to one Co(1), one Co(4), one Co(5), and one Co(7) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Co(1), one Co(2), one Co(5), and one Co(7) atom to form OMgCo4 square pyramids that share  a cornercorner with one O(4)MgCo4 square pyramid,  a cornercorner with one O(8)MgCo4 square pyramid, corners with two equivalent O(1)MgCo3 trigonal pyramids, edges with two equivalent O(4)MgCo4 square pyramids, and edges with two equivalent O(8)MgCo4 square pyramids. is represented by the CIF file [CIF]
data_MgCo7O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.102
_cell_length_b   5.092
_cell_length_c   9.771
_cell_angle_alpha   84.811
_cell_angle_beta   97.711
_cell_angle_gamma   58.040
_symmetry_Int_Tables_number   1
_cell_volume   209.423
_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  0.296  0.840  0.991  1.0
  Co  Co1  1  0.096  0.075  0.259  1.0
  Co  Co2  1  0.992  0.524  0.987  1.0
  Co  Co3  1  0.245  0.258  0.746  1.0
  Co  Co4  1  0.544  0.983  0.521  1.0
  Co  Co5  1  0.432  0.407  0.256  1.0
  Co  Co6  1  0.552  0.581  0.747  1.0
  Co  Co7  1  0.758  0.748  0.255  1.0
  O  O8  1  0.960  0.256  0.860  1.0
  O  O9  1  0.247  0.971  0.634  1.0
  O  O10  1  0.184  0.349  0.365  1.0
  O  O11  1  0.342  0.125  0.123  1.0
  O  O12  1  0.305  0.531  0.856  1.0
  O  O13  1  0.487  0.306  0.645  1.0
  O  O14  1  0.483  0.730  0.366  1.0
  O  O15  1  0.702  0.474  0.148  1.0
  O  O16  1  0.574  0.861  0.865  1.0
  O  O17  1  0.836  0.614  0.641  1.0
  O  O18  1  0.790  0.027  0.360  1.0
  O  O19  1  0.053  0.768  0.134  1.0
[/CIF]
.