Bi2MgO4 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form MgO5 trigonal bipyramids that share corners with two equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(1)O4 trigonal pyramids, corners with five equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Bi(1)O4 trigonal pyramid. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form BiO4 trigonal pyramids that share corners with two equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(1)O4 trigonal pyramids, corners with three equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. In the second Bi site, Bi(2) is bonded to one O(1), one O(4), and two equivalent O(2) atoms to form BiO4 trigonal pyramids that share corners with five equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(2)O4 trigonal pyramids, and corners with three equivalent Bi(1)O4 trigonal pyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Mg(1), one Bi(1), and one Bi(2) atom. In the second O site, O(2) is bonded to one Mg(1), one Bi(1), and two equivalent Bi(2) atoms to form corner-sharing OMgBi3 tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to two equivalent Mg(1) and one Bi(2) atom.
Bi2MgO4 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form MgO5 trigonal bipyramids that share corners with two equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(1)O4 trigonal pyramids, corners with five equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Bi(1)O4 trigonal pyramid. The Mg(1)-O(1) bond length is 2.09 Å. The Mg(1)-O(2) bond length is 2.15 Å. The Mg(1)-O(3) bond length is 2.12 Å. Both Mg(1)-O(4) bond lengths are 2.09 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form BiO4 trigonal pyramids that share corners with two equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(1)O4 trigonal pyramids, corners with three equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Mg(1)O5 trigonal bipyramid. The Bi(1)-O(1) bond length is 2.10 Å. The Bi(1)-O(2) bond length is 2.39 Å. Both Bi(1)-O(3) bond lengths are 2.25 Å. In the second Bi site, Bi(2) is bonded to one O(1), one O(4), and two equivalent O(2) atoms to form BiO4 trigonal pyramids that share corners with five equivalent Mg(1)O5 trigonal bipyramids, corners with two equivalent Bi(2)O4 trigonal pyramids, and corners with three equivalent Bi(1)O4 trigonal pyramids. The Bi(2)-O(1) bond length is 2.33 Å. The Bi(2)-O(4) bond length is 2.12 Å. Both Bi(2)-O(2) bond lengths are 2.32 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Mg(1), one Bi(1), and one Bi(2) atom. In the second O site, O(2) is bonded to one Mg(1), one Bi(1), and two equivalent Bi(2) atoms to form corner-sharing OMgBi3 tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Bi(1) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to two equivalent Mg(1) and one Bi(2) atom.