The crystal structure described by MgCo4(HgO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(3), one O(6), one O(7), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O5 trigonal bipyramids, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-85°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Co(2)O5 trigonal bipyramid, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Co(2)O5 trigonal bipyramid. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(8) atom to form CoO5 trigonal bipyramids that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 63°. In the third Co site, Co(3) is bonded in a rectangular see-saw-like geometry to one O(1), one O(5), one O(6), and one O(7) atom. In the fourth Co site, Co(4) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form distorted CoO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra,  an edgeedge with one Mg(1)O4 tetrahedra, and edges with two equivalent Co(2)O5 trigonal bipyramids. There are two inequivalent Hg sites. In the first Hg site, Hg(1) is bonded in a linear geometry to one O(2) and one O(3) atom. In the second Hg site, Hg(2) is bonded in a 4-coordinate geometry to one O(1), one O(4), one O(5), and one O(8) atom. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Co(1), one Co(2), one Co(3), and one Hg(2) atom to form distorted OCo3Hg tetrahedra that share  a cornercorner with one O(5)Co3Hg tetrahedra,  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids, corners with two equivalent O(7)MgCo3 trigonal pyramids, and  an edgeedge with one O(5)Co3Hg tetrahedra. In the second O site, O(2) is bonded to one Co(1), one Co(2), one Co(4), and one Hg(1) atom to form OCo3Hg tetrahedra that share  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(5)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids,  an edgeedge with one O(3)MgCo2Hg tetrahedra, and  an edgeedge with one O(7)MgCo3 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(1), one Co(2), one Co(4), and one Hg(1) atom to form distorted OMgCo2Hg tetrahedra that share  a cornercorner with one O(1)Co3Hg tetrahedra,  a cornercorner with one O(2)Co3Hg tetrahedra,  a cornercorner with one O(5)Co3Hg tetrahedra, corners with two equivalent O(7)MgCo3 trigonal pyramids, corners with three equivalent O(8)MgCo2Hg trigonal pyramids, and  an edgeedge with one O(2)Co3Hg tetrahedra. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(2), one Co(4), and one Hg(2) atom. In the fifth O site, O(5) is bonded to one Co(1), one Co(3), one Co(4), and one Hg(2) atom to form distorted OCo3Hg tetrahedra that share  a cornercorner with one O(1)Co3Hg tetrahedra,  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids, corners with three equivalent O(7)MgCo3 trigonal pyramids, and  an edgeedge with one O(1)Co3Hg tetrahedra. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(1), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Mg(1), one Co(1), one Co(3), and one Co(4) atom to form distorted OMgCo3 trigonal pyramids that share corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(3)MgCo2Hg tetrahedra, corners with three equivalent O(5)Co3Hg tetrahedra,  an edgeedge with one O(2)Co3Hg tetrahedra, and  an edgeedge with one O(8)MgCo2Hg trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Co(2), one Co(4), and one Hg(2) atom to form distorted OMgCo2Hg trigonal pyramids that share corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(5)Co3Hg tetrahedra, corners with three equivalent O(3)MgCo2Hg tetrahedra, and  an edgeedge with one O(7)MgCo3 trigonal pyramid. is represented by the CIF file [CIF]
data_MgCo4(HgO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.098
_cell_length_b   7.190
_cell_length_c   6.299
_cell_angle_alpha   52.508
_cell_angle_beta   102.241
_cell_angle_gamma   129.997
_symmetry_Int_Tables_number   1
_cell_volume   186.705
_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  0.163  0.891  0.960  1.0
  Co  Co1  1  0.632  0.277  0.091  1.0
  Co  Co2  1  0.654  0.242  0.572  1.0
  Co  Co3  1  0.627  0.756  0.621  1.0
  Co  Co4  1  0.151  0.759  0.592  1.0
  Hg  Hg5  1  0.881  0.998  0.086  1.0
  Hg  Hg6  1  0.261  0.427  0.343  1.0
  O  O7  1  0.821  0.183  0.435  1.0
  O  O8  1  0.813  0.292  0.851  1.0
  O  O9  1  0.967  0.720  0.301  1.0
  O  O10  1  0.444  0.257  0.333  1.0
  O  O11  1  0.406  0.787  0.411  1.0
  O  O12  1  0.432  0.343  0.786  1.0
  O  O13  1  0.890  0.767  0.772  1.0
  O  O14  1  0.334  0.802  0.872  1.0
[/CIF]
.
The crystal structure described by MgCo4(HgO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(3), one O(6), one O(7), and one O(8) atom to form MgO4 tetrahedra that share  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O5 trigonal bipyramids, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-85°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Co(2)O5 trigonal bipyramid, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Co(2)O5 trigonal bipyramid. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(8) atom to form CoO5 trigonal bipyramids that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 63°. In the third Co site, Co(3) is bonded in a rectangular see-saw-like geometry to one O(1), one O(5), one O(6), and one O(7) atom. In the fourth Co site, Co(4) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form distorted CoO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra,  an edgeedge with one Mg(1)O4 tetrahedra, and edges with two equivalent Co(2)O5 trigonal bipyramids. There are two inequivalent Hg sites. In the first Hg site, Hg(1) is bonded in a linear geometry to one O(2) and one O(3) atom. In the second Hg site, Hg(2) is bonded in a 4-coordinate geometry to one O(1), one O(4), one O(5), and one O(8) atom. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Co(1), one Co(2), one Co(3), and one Hg(2) atom to form distorted OCo3Hg tetrahedra that share  a cornercorner with one O(5)Co3Hg tetrahedra,  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids, corners with two equivalent O(7)MgCo3 trigonal pyramids, and  an edgeedge with one O(5)Co3Hg tetrahedra. In the second O site, O(2) is bonded to one Co(1), one Co(2), one Co(4), and one Hg(1) atom to form OCo3Hg tetrahedra that share  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(5)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids,  an edgeedge with one O(3)MgCo2Hg tetrahedra, and  an edgeedge with one O(7)MgCo3 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(1), one Co(2), one Co(4), and one Hg(1) atom to form distorted OMgCo2Hg tetrahedra that share  a cornercorner with one O(1)Co3Hg tetrahedra,  a cornercorner with one O(2)Co3Hg tetrahedra,  a cornercorner with one O(5)Co3Hg tetrahedra, corners with two equivalent O(7)MgCo3 trigonal pyramids, corners with three equivalent O(8)MgCo2Hg trigonal pyramids, and  an edgeedge with one O(2)Co3Hg tetrahedra. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Co(1), one Co(2), one Co(4), and one Hg(2) atom. In the fifth O site, O(5) is bonded to one Co(1), one Co(3), one Co(4), and one Hg(2) atom to form distorted OCo3Hg tetrahedra that share  a cornercorner with one O(1)Co3Hg tetrahedra,  a cornercorner with one O(3)MgCo2Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(8)MgCo2Hg trigonal pyramids, corners with three equivalent O(7)MgCo3 trigonal pyramids, and  an edgeedge with one O(1)Co3Hg tetrahedra. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(1), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Mg(1), one Co(1), one Co(3), and one Co(4) atom to form distorted OMgCo3 trigonal pyramids that share corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(3)MgCo2Hg tetrahedra, corners with three equivalent O(5)Co3Hg tetrahedra,  an edgeedge with one O(2)Co3Hg tetrahedra, and  an edgeedge with one O(8)MgCo2Hg trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Co(2), one Co(4), and one Hg(2) atom to form distorted OMgCo2Hg trigonal pyramids that share corners with two equivalent O(1)Co3Hg tetrahedra, corners with two equivalent O(2)Co3Hg tetrahedra, corners with two equivalent O(5)Co3Hg tetrahedra, corners with three equivalent O(3)MgCo2Hg tetrahedra, and  an edgeedge with one O(7)MgCo3 trigonal pyramid. is represented by the CIF file [CIF]
data_MgCo4(HgO4)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.098
_cell_length_b   7.190
_cell_length_c   6.299
_cell_angle_alpha   52.508
_cell_angle_beta   102.241
_cell_angle_gamma   129.997
_symmetry_Int_Tables_number   1
_cell_volume   186.705
_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  0.163  0.891  0.960  1.0
  Co  Co1  1  0.632  0.277  0.091  1.0
  Co  Co2  1  0.654  0.242  0.572  1.0
  Co  Co3  1  0.627  0.756  0.621  1.0
  Co  Co4  1  0.151  0.759  0.592  1.0
  Hg  Hg5  1  0.881  0.998  0.086  1.0
  Hg  Hg6  1  0.261  0.427  0.343  1.0
  O  O7  1  0.821  0.183  0.435  1.0
  O  O8  1  0.813  0.292  0.851  1.0
  O  O9  1  0.967  0.720  0.301  1.0
  O  O10  1  0.444  0.257  0.333  1.0
  O  O11  1  0.406  0.787  0.411  1.0
  O  O12  1  0.432  0.343  0.786  1.0
  O  O13  1  0.890  0.767  0.772  1.0
  O  O14  1  0.334  0.802  0.872  1.0
[/CIF]
.