The crystal structure described by MgZn4(Co3O8)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(14), one O(5), and one O(7) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with three equivalent Zn(4)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-58°. There are six inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(11), one O(13), one O(15), one O(4), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. In the second Co site, Co(2) is bonded to one O(10), one O(12), one O(14), one O(16), one O(2), and one O(3) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 47-50°. In the third Co site, Co(3) is bonded to one O(1), one O(11), one O(13), one O(15), one O(5), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra, corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. In the fourth Co site, Co(4) is bonded to one O(12), one O(14), one O(16), one O(2), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-55°. In the fifth Co site, Co(5) is bonded to one O(10), one O(12), one O(16), one O(3), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 51-54°. In the sixth Co site, Co(6) is bonded to one O(11), one O(13), one O(4), one O(5), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 5-coordinate geometry to one O(1), one O(15), one O(4), one O(5), and one O(8) atom. In the second Zn site, Zn(2) is bonded to one O(15), one O(2), one O(3), one O(6), one O(8), and one O(9) atom to form ZnO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, corners with three equivalent Zn(3)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-55°. In the third Zn site, Zn(3) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form distorted ZnO4 tetrahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(6)O6 octahedra, and corners with three equivalent Zn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-74°. In the fourth Zn site, Zn(4) is bonded to one O(10), one O(13), one O(14), and one O(7) atom to form ZnO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, and corners with three equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-69°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Co(1), one Co(3), and one Zn(1) atom to form OMgZnCo2 trigonal pyramids that share corners with three equivalent O(15)Zn3Co2 square pyramids,  a cornercorner with one O(10)MgZnCo2 trigonal pyramid,  a cornercorner with one O(14)MgZnCo2 trigonal pyramid, and  an edgeedge with one O(8)Zn3Co2 square pyramid. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Co(2), one Co(4), and one Zn(2) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Co(2), one Co(5), and one Zn(2) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Co(1), one Co(6), and one Zn(1) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(3), one Co(6), and one Zn(1) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Co(4), one Co(5), and one Zn(2) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Co(4), one Co(5), and one Zn(4) atom. In the eighth O site, O(8) is bonded to one Co(3), one Co(6), one Zn(1), one Zn(2), and one Zn(3) atom to form distorted OZn3Co2 square pyramids that share  a cornercorner with one O(16)ZnCo3 tetrahedra, edges with two equivalent O(15)Zn3Co2 square pyramids, and  an edgeedge with one O(1)MgZnCo2 trigonal pyramid. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Co(1), one Co(6), one Zn(2), and one Zn(3) atom. In the tenth O site, O(10) is bonded to one Mg(1), one Co(2), one Co(5), and one Zn(4) atom to form distorted OMgZnCo2 trigonal pyramids that share  a cornercorner with one O(1)MgZnCo2 trigonal pyramid,  a cornercorner with one O(14)MgZnCo2 trigonal pyramid,  an edgeedge with one O(16)ZnCo3 tetrahedra, and  an edgeedge with one O(14)MgZnCo2 trigonal pyramid. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(6) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Co(2), one Co(4), and one Co(5) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(3), one Co(6), and one Zn(4) atom. In the fourteenth O site, O(14) is bonded to one Mg(1), one Co(2), one Co(4), and one Zn(4) atom to form distorted OMgZnCo2 trigonal pyramids that share  a cornercorner with one O(1)MgZnCo2 trigonal pyramid,  a cornercorner with one O(10)MgZnCo2 trigonal pyramid,  an edgeedge with one O(16)ZnCo3 tetrahedra, and  an edgeedge with one O(10)MgZnCo2 trigonal pyramid. In the fifteenth O site, O(15) is bonded to one Co(1), one Co(3), one Zn(1), one Zn(2), and one Zn(3) atom to form distorted OZn3Co2 square pyramids that share  a cornercorner with one O(16)ZnCo3 tetrahedra, corners with three equivalent O(1)MgZnCo2 trigonal pyramids, and edges with two equivalent O(8)Zn3Co2 square pyramids. In the sixteenth O site, O(16) is bonded to one Co(2), one Co(4), one Co(5), and one Zn(3) atom to form OZnCo3 tetrahedra that share  a cornercorner with one O(15)Zn3Co2 square pyramid,  a cornercorner with one O(8)Zn3Co2 square pyramid,  an edgeedge with one O(10)MgZnCo2 trigonal pyramid, and  an edgeedge with one O(14)MgZnCo2 trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgZn4(Co3O8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.776
_cell_length_b   5.892
_cell_length_c   9.982
_cell_angle_alpha   87.776
_cell_angle_beta   91.087
_cell_angle_gamma   119.545
_symmetry_Int_Tables_number   1
_cell_volume   295.318
_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  0.650  0.282  0.972  1.0
  Zn  Zn1  1  0.709  0.397  0.219  1.0
  Zn  Zn2  1  0.306  0.649  0.509  1.0
  Zn  Zn3  1  0.656  0.308  0.452  1.0
  Zn  Zn4  1  0.330  0.644  0.917  1.0
  Co  Co5  1  0.688  0.866  0.231  1.0
  Co  Co6  1  0.819  0.142  0.731  1.0
  Co  Co7  1  0.184  0.353  0.230  1.0
  Co  Co8  1  0.825  0.660  0.730  1.0
  Co  Co9  1  0.304  0.145  0.729  1.0
  Co  Co10  1  0.192  0.877  0.221  1.0
  O  O11  1  0.850  0.195  0.124  1.0
  O  O12  1  0.667  0.839  0.635  1.0
  O  O13  1  0.135  0.300  0.631  1.0
  O  O14  1  0.883  0.733  0.122  1.0
  O  O15  1  0.368  0.210  0.117  1.0
  O  O16  1  0.118  0.801  0.631  1.0
  O  O17  1  0.521  0.477  0.843  1.0
  O  O18  1  0.019  0.503  0.358  1.0
  O  O19  1  0.479  0.972  0.353  1.0
  O  O20  1  0.503  0.003  0.838  1.0
  O  O21  1  0.033  0.012  0.326  1.0
  O  O22  1  0.960  0.960  0.831  1.0
  O  O23  1  0.343  0.703  0.122  1.0
  O  O24  1  0.960  0.450  0.841  1.0
  O  O25  1  0.504  0.524  0.351  1.0
  O  O26  1  0.661  0.326  0.638  1.0
[/CIF]
.
The crystal structure described by MgZn4(Co3O8)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(10), one O(14), one O(5), and one O(7) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with three equivalent Zn(4)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-58°. There are six inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(11), one O(13), one O(15), one O(4), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. In the second Co site, Co(2) is bonded to one O(10), one O(12), one O(14), one O(16), one O(2), and one O(3) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 47-50°. In the third Co site, Co(3) is bonded to one O(1), one O(11), one O(13), one O(15), one O(5), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra, corners with two equivalent Mg(1)O5 trigonal bipyramids,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. In the fourth Co site, Co(4) is bonded to one O(12), one O(14), one O(16), one O(2), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-55°. In the fifth Co site, Co(5) is bonded to one O(10), one O(12), one O(16), one O(3), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Zn(2)O6 octahedra,  a cornercorner with one Zn(3)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 51-54°. In the sixth Co site, Co(6) is bonded to one O(11), one O(13), one O(4), one O(5), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Zn(4)O4 tetrahedra, corners with two equivalent Zn(3)O4 tetrahedra,  a cornercorner with one Mg(1)O5 trigonal bipyramid,  an edgeedge with one Zn(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 5-coordinate geometry to one O(1), one O(15), one O(4), one O(5), and one O(8) atom. In the second Zn site, Zn(2) is bonded to one O(15), one O(2), one O(3), one O(6), one O(8), and one O(9) atom to form ZnO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, corners with three equivalent Zn(3)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-55°. In the third Zn site, Zn(3) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form distorted ZnO4 tetrahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(6)O6 octahedra, and corners with three equivalent Zn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-74°. In the fourth Zn site, Zn(4) is bonded to one O(10), one O(13), one O(14), and one O(7) atom to form ZnO4 tetrahedra that share  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, and corners with three equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-69°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Co(1), one Co(3), and one Zn(1) atom to form OMgZnCo2 trigonal pyramids that share corners with three equivalent O(15)Zn3Co2 square pyramids,  a cornercorner with one O(10)MgZnCo2 trigonal pyramid,  a cornercorner with one O(14)MgZnCo2 trigonal pyramid, and  an edgeedge with one O(8)Zn3Co2 square pyramid. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Co(2), one Co(4), and one Zn(2) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Co(2), one Co(5), and one Zn(2) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Co(1), one Co(6), and one Zn(1) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Co(3), one Co(6), and one Zn(1) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Co(4), one Co(5), and one Zn(2) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Co(4), one Co(5), and one Zn(4) atom. In the eighth O site, O(8) is bonded to one Co(3), one Co(6), one Zn(1), one Zn(2), and one Zn(3) atom to form distorted OZn3Co2 square pyramids that share  a cornercorner with one O(16)ZnCo3 tetrahedra, edges with two equivalent O(15)Zn3Co2 square pyramids, and  an edgeedge with one O(1)MgZnCo2 trigonal pyramid. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Co(1), one Co(6), one Zn(2), and one Zn(3) atom. In the tenth O site, O(10) is bonded to one Mg(1), one Co(2), one Co(5), and one Zn(4) atom to form distorted OMgZnCo2 trigonal pyramids that share  a cornercorner with one O(1)MgZnCo2 trigonal pyramid,  a cornercorner with one O(14)MgZnCo2 trigonal pyramid,  an edgeedge with one O(16)ZnCo3 tetrahedra, and  an edgeedge with one O(14)MgZnCo2 trigonal pyramid. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(6) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Co(2), one Co(4), and one Co(5) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(3), one Co(6), and one Zn(4) atom. In the fourteenth O site, O(14) is bonded to one Mg(1), one Co(2), one Co(4), and one Zn(4) atom to form distorted OMgZnCo2 trigonal pyramids that share  a cornercorner with one O(1)MgZnCo2 trigonal pyramid,  a cornercorner with one O(10)MgZnCo2 trigonal pyramid,  an edgeedge with one O(16)ZnCo3 tetrahedra, and  an edgeedge with one O(10)MgZnCo2 trigonal pyramid. In the fifteenth O site, O(15) is bonded to one Co(1), one Co(3), one Zn(1), one Zn(2), and one Zn(3) atom to form distorted OZn3Co2 square pyramids that share  a cornercorner with one O(16)ZnCo3 tetrahedra, corners with three equivalent O(1)MgZnCo2 trigonal pyramids, and edges with two equivalent O(8)Zn3Co2 square pyramids. In the sixteenth O site, O(16) is bonded to one Co(2), one Co(4), one Co(5), and one Zn(3) atom to form OZnCo3 tetrahedra that share  a cornercorner with one O(15)Zn3Co2 square pyramid,  a cornercorner with one O(8)Zn3Co2 square pyramid,  an edgeedge with one O(10)MgZnCo2 trigonal pyramid, and  an edgeedge with one O(14)MgZnCo2 trigonal pyramid. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgZn4(Co3O8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.776
_cell_length_b   5.892
_cell_length_c   9.982
_cell_angle_alpha   87.776
_cell_angle_beta   91.087
_cell_angle_gamma   119.545
_symmetry_Int_Tables_number   1
_cell_volume   295.318
_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  0.650  0.282  0.972  1.0
  Zn  Zn1  1  0.709  0.397  0.219  1.0
  Zn  Zn2  1  0.306  0.649  0.509  1.0
  Zn  Zn3  1  0.656  0.308  0.452  1.0
  Zn  Zn4  1  0.330  0.644  0.917  1.0
  Co  Co5  1  0.688  0.866  0.231  1.0
  Co  Co6  1  0.819  0.142  0.731  1.0
  Co  Co7  1  0.184  0.353  0.230  1.0
  Co  Co8  1  0.825  0.660  0.730  1.0
  Co  Co9  1  0.304  0.145  0.729  1.0
  Co  Co10  1  0.192  0.877  0.221  1.0
  O  O11  1  0.850  0.195  0.124  1.0
  O  O12  1  0.667  0.839  0.635  1.0
  O  O13  1  0.135  0.300  0.631  1.0
  O  O14  1  0.883  0.733  0.122  1.0
  O  O15  1  0.368  0.210  0.117  1.0
  O  O16  1  0.118  0.801  0.631  1.0
  O  O17  1  0.521  0.477  0.843  1.0
  O  O18  1  0.019  0.503  0.358  1.0
  O  O19  1  0.479  0.972  0.353  1.0
  O  O20  1  0.503  0.003  0.838  1.0
  O  O21  1  0.033  0.012  0.326  1.0
  O  O22  1  0.960  0.960  0.831  1.0
  O  O23  1  0.343  0.703  0.122  1.0
  O  O24  1  0.960  0.450  0.841  1.0
  O  O25  1  0.504  0.524  0.351  1.0
  O  O26  1  0.661  0.326  0.638  1.0
[/CIF]
.