MgFe4(CoO4)2 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(3), and two equivalent O(2) atoms. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CoO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the second Co site, Co(2) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CoO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Fe(1), two equivalent Fe(2), and one Co(1) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra, corners with four equivalent O(1)MgFe3Co trigonal bipyramids, edges with six equivalent O(2)MgFe2Co2 square pyramids, and  an edgeedge with one O(3)Fe3Co tetrahedra. In the second O site, O(2) is bonded to one Mg(1), one Fe(1), one Fe(2), one Co(1), and one Co(2) atom to form OMgFe2Co2 square pyramids that share corners with five equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(1)MgFe3Co trigonal bipyramid, edges with three equivalent O(2)MgFe2Co2 square pyramids,  an edgeedge with one O(3)Fe3Co tetrahedra, and edges with three equivalent O(1)MgFe3Co trigonal bipyramids. In the third O site, O(3) is bonded to one Fe(1), two equivalent Fe(2), and one Co(2) atom to form distorted OFe3Co tetrahedra that share corners with six equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra, corners with three equivalent O(1)MgFe3Co trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 square pyramids, and  an edgeedge with one O(1)MgFe3Co trigonal bipyramid.
MgFe4(CoO4)2 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. Both Mg(1)-O(1) bond lengths are 2.10 Å. All Mg(1)-O(2) bond lengths are 2.14 Å. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(3), and two equivalent O(2) atoms. The Fe(1)-O(1) bond length is 2.12 Å. The Fe(1)-O(3) bond length is 1.90 Å. Both Fe(1)-O(2) bond lengths are 2.12 Å. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form FeO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. Both Fe(2)-O(1) bond lengths are 2.13 Å. Both Fe(2)-O(2) bond lengths are 2.08 Å. Both Fe(2)-O(3) bond lengths are 1.97 Å. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1) and four equivalent O(2) atoms to form CoO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. Both Co(1)-O(1) bond lengths are 2.27 Å. All Co(1)-O(2) bond lengths are 2.23 Å. In the second Co site, Co(2) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CoO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. Both Co(2)-O(3) bond lengths are 2.02 Å. All Co(2)-O(2) bond lengths are 2.15 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Fe(1), two equivalent Fe(2), and one Co(1) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra, corners with four equivalent O(1)MgFe3Co trigonal bipyramids, edges with six equivalent O(2)MgFe2Co2 square pyramids, and  an edgeedge with one O(3)Fe3Co tetrahedra. In the second O site, O(2) is bonded to one Mg(1), one Fe(1), one Fe(2), one Co(1), and one Co(2) atom to form OMgFe2Co2 square pyramids that share corners with five equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(1)MgFe3Co trigonal bipyramid, edges with three equivalent O(2)MgFe2Co2 square pyramids,  an edgeedge with one O(3)Fe3Co tetrahedra, and edges with three equivalent O(1)MgFe3Co trigonal bipyramids. In the third O site, O(3) is bonded to one Fe(1), two equivalent Fe(2), and one Co(2) atom to form distorted OFe3Co tetrahedra that share corners with six equivalent O(2)MgFe2Co2 square pyramids, corners with three equivalent O(3)Fe3Co tetrahedra, corners with three equivalent O(1)MgFe3Co trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 square pyramids, and  an edgeedge with one O(1)MgFe3Co trigonal bipyramid.