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.
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°. The Mg(1)-O(3) bond length is 1.98 Å. The Mg(1)-O(6) bond length is 2.00 Å. The Mg(1)-O(7) bond length is 2.01 Å. The Mg(1)-O(8) bond length is 1.98 Å. 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. The Co(1)-O(1) bond length is 2.26 Å. The Co(1)-O(2) bond length is 2.10 Å. The Co(1)-O(4) bond length is 2.11 Å. The Co(1)-O(5) bond length is 2.12 Å. The Co(1)-O(6) bond length is 2.13 Å. The Co(1)-O(7) bond length is 2.11 Å. 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°. The Co(2)-O(1) bond length is 1.96 Å. The Co(2)-O(2) bond length is 1.98 Å. The Co(2)-O(3) bond length is 2.08 Å. The Co(2)-O(4) bond length is 1.89 Å. The Co(2)-O(8) bond length is 2.01 Å. 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. The Co(3)-O(1) bond length is 1.89 Å. The Co(3)-O(5) bond length is 1.86 Å. The Co(3)-O(6) bond length is 1.84 Å. The Co(3)-O(7) bond length is 1.88 Å. 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. The Co(4)-O(2) bond length is 2.08 Å. The Co(4)-O(3) bond length is 2.07 Å. The Co(4)-O(4) bond length is 2.14 Å. The Co(4)-O(5) bond length is 2.17 Å. The Co(4)-O(7) bond length is 2.42 Å. The Co(4)-O(8) bond length is 2.02 Å. 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. The Hg(1)-O(2) bond length is 2.02 Å. The Hg(1)-O(3) bond length is 2.03 Å. 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. The Hg(2)-O(1) bond length is 2.38 Å. The Hg(2)-O(4) bond length is 2.32 Å. The Hg(2)-O(5) bond length is 2.38 Å. The Hg(2)-O(8) bond length is 2.34 Å. 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.