Na4Mg(BiO3)2 crystallizes in the triclinic P1 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(2), one O(3), and one O(4) atom. In the second Na site, Na(2) is bonded to one O(2), one O(4), one O(5), and one O(6) atom to form distorted NaO4 tetrahedra that share corners with two equivalent Na(3)O4 tetrahedra and corners with two equivalent Mg(1)O4 tetrahedra. In the third Na site, Na(3) is bonded to one O(1), one O(3), one O(5), and one O(6) atom to form distorted NaO4 tetrahedra that share corners with two equivalent Na(2)O4 tetrahedra and corners with two equivalent Mg(1)O4 tetrahedra. In the fourth Na site, Na(4) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(5) atom. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form MgO4 tetrahedra that share corners with two equivalent Na(2)O4 tetrahedra and corners with two equivalent Na(3)O4 tetrahedra. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(5), and one O(6) atom. In the second Bi site, Bi(2) is bonded in a 4-coordinate geometry to one O(3), one O(4), one O(5), and one O(6) atom. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), and one Bi(1) atom to form distorted ONa3MgBi trigonal bipyramids that share corners with three equivalent O(5)Na3Bi2 trigonal bipyramids,  a cornercorner with one O(3)Na2MgBi trigonal pyramid, and  an edgeedge with one O(3)Na2MgBi trigonal pyramid. In the second O site, O(2) is bonded in a distorted see-saw-like geometry to one Na(1), one Na(2), one Mg(1), and one Bi(1) atom. In the third O site, O(3) is bonded to one Na(1), one Na(3), one Mg(1), and one Bi(2) atom to form ONa2MgBi trigonal pyramids that share  a cornercorner with one O(1)Na3MgBi trigonal bipyramid, corners with two equivalent O(5)Na3Bi2 trigonal bipyramids, and  an edgeedge with one O(1)Na3MgBi trigonal bipyramid. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Na(1), one Na(2), one Na(4), one Mg(1), one Bi(1), and one Bi(2) atom. In the fifth O site, O(5) is bonded to one Na(2), one Na(3), one Na(4), one Bi(1), and one Bi(2) atom to form distorted ONa3Bi2 trigonal bipyramids that share corners with three equivalent O(1)Na3MgBi trigonal bipyramids and corners with two equivalent O(3)Na2MgBi trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(3), one Bi(1), and one Bi(2) atom.
Na4Mg(BiO3)2 crystallizes in the triclinic P1 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a rectangular see-saw-like geometry to one O(1), one O(2), one O(3), and one O(4) atom. The Na(1)-O(1) bond length is 2.61 Å. The Na(1)-O(2) bond length is 2.38 Å. The Na(1)-O(3) bond length is 2.36 Å. The Na(1)-O(4) bond length is 2.62 Å. In the second Na site, Na(2) is bonded to one O(2), one O(4), one O(5), and one O(6) atom to form distorted NaO4 tetrahedra that share corners with two equivalent Na(3)O4 tetrahedra and corners with two equivalent Mg(1)O4 tetrahedra. The Na(2)-O(2) bond length is 2.39 Å. The Na(2)-O(4) bond length is 2.36 Å. The Na(2)-O(5) bond length is 2.38 Å. The Na(2)-O(6) bond length is 2.58 Å. In the third Na site, Na(3) is bonded to one O(1), one O(3), one O(5), and one O(6) atom to form distorted NaO4 tetrahedra that share corners with two equivalent Na(2)O4 tetrahedra and corners with two equivalent Mg(1)O4 tetrahedra. The Na(3)-O(1) bond length is 2.42 Å. The Na(3)-O(3) bond length is 2.39 Å. The Na(3)-O(5) bond length is 2.41 Å. The Na(3)-O(6) bond length is 2.43 Å. In the fourth Na site, Na(4) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(5) atom. The Na(4)-O(1) bond length is 2.26 Å. The Na(4)-O(4) bond length is 2.24 Å. The Na(4)-O(5) bond length is 2.29 Å. Mg(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form MgO4 tetrahedra that share corners with two equivalent Na(2)O4 tetrahedra and corners with two equivalent Na(3)O4 tetrahedra. The Mg(1)-O(1) bond length is 2.07 Å. The Mg(1)-O(2) bond length is 1.99 Å. The Mg(1)-O(3) bond length is 1.97 Å. The Mg(1)-O(4) bond length is 2.02 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(5), and one O(6) atom. The Bi(1)-O(1) bond length is 2.21 Å. The Bi(1)-O(2) bond length is 2.23 Å. The Bi(1)-O(4) bond length is 2.71 Å. The Bi(1)-O(5) bond length is 2.66 Å. The Bi(1)-O(6) bond length is 2.23 Å. In the second Bi site, Bi(2) is bonded in a 4-coordinate geometry to one O(3), one O(4), one O(5), and one O(6) atom. The Bi(2)-O(3) bond length is 2.14 Å. The Bi(2)-O(4) bond length is 2.60 Å. The Bi(2)-O(5) bond length is 2.21 Å. The Bi(2)-O(6) bond length is 2.22 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Na(3), one Na(4), one Mg(1), and one Bi(1) atom to form distorted ONa3MgBi trigonal bipyramids that share corners with three equivalent O(5)Na3Bi2 trigonal bipyramids,  a cornercorner with one O(3)Na2MgBi trigonal pyramid, and  an edgeedge with one O(3)Na2MgBi trigonal pyramid. In the second O site, O(2) is bonded in a distorted see-saw-like geometry to one Na(1), one Na(2), one Mg(1), and one Bi(1) atom. In the third O site, O(3) is bonded to one Na(1), one Na(3), one Mg(1), and one Bi(2) atom to form ONa2MgBi trigonal pyramids that share  a cornercorner with one O(1)Na3MgBi trigonal bipyramid, corners with two equivalent O(5)Na3Bi2 trigonal bipyramids, and  an edgeedge with one O(1)Na3MgBi trigonal bipyramid. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Na(1), one Na(2), one Na(4), one Mg(1), one Bi(1), and one Bi(2) atom. In the fifth O site, O(5) is bonded to one Na(2), one Na(3), one Na(4), one Bi(1), and one Bi(2) atom to form distorted ONa3Bi2 trigonal bipyramids that share corners with three equivalent O(1)Na3MgBi trigonal bipyramids and corners with two equivalent O(3)Na2MgBi trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Na(2), one Na(3), one Bi(1), and one Bi(2) atom.