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 4-coordinate geometry to one O(2), one O(4), one O(5), and one O(6) atom. In the second Na site, Na(2) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form NaO4 tetrahedra that share corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Na(4)O4 trigonal pyramid, corners with two equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Na(4)O4 trigonal pyramid. In the third Na site, Na(3) is bonded in a 4-coordinate geometry to one O(1), one O(3), one O(4), and one O(5) atom. In the fourth Na site, Na(4) is bonded to one O(2), one O(3), one O(5), and one O(6) atom to form distorted NaO4 trigonal pyramids that share  a cornercorner with one Na(2)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Na(2)O4 tetrahedra. 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, corners with two equivalent Na(4)O4 trigonal pyramids, and corners with three equivalent Bi(2)O4 trigonal pyramids. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a distorted trigonal non-coplanar geometry to one O(2), one O(4), one O(5), and one O(6) atom. In the second Bi site, Bi(2) is bonded to one O(1), one O(3), one O(4), and one O(6) atom to form distorted BiO4 trigonal pyramids that share corners with two equivalent Na(2)O4 tetrahedra, corners with three equivalent Mg(1)O4 tetrahedra, and corners with two equivalent Na(4)O4 trigonal pyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Na(2), one Na(3), one Mg(1), and one Bi(2) atom. In the second O site, O(2) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), and one Bi(1) atom to form distorted ONa3MgBi trigonal bipyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(5)Na4Bi square pyramid, and  an edgeedge with one O(6)Na3Bi2 trigonal bipyramid. In the third O site, O(3) is bonded to one Na(3), one Na(4), one Mg(1), and one Bi(2) atom to form distorted ONa2MgBi trigonal pyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, and corners with two equivalent O(2)Na3MgBi trigonal bipyramids. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Na(1), one Na(3), one Mg(1), one Bi(1), and one Bi(2) atom. In the fifth O site, O(5) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), and one Bi(1) atom to form ONa4Bi square pyramids that share corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, corners with two equivalent O(2)Na3MgBi trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(6)Na3Bi2 trigonal bipyramid, and  an edgeedge with one O(2)Na3MgBi trigonal bipyramid. In the sixth O site, O(6) is bonded to one Na(1), one Na(2), one Na(4), one Bi(1), and one Bi(2) atom to form distorted ONa3Bi2 trigonal bipyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(2)Na3MgBi trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(5)Na4Bi square pyramid, and  an edgeedge with one O(2)Na3MgBi trigonal bipyramid.
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 4-coordinate geometry to one O(2), one O(4), one O(5), and one O(6) atom. The Na(1)-O(2) bond length is 2.41 Å. The Na(1)-O(4) bond length is 2.55 Å. The Na(1)-O(5) bond length is 2.28 Å. The Na(1)-O(6) bond length is 2.28 Å. In the second Na site, Na(2) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form NaO4 tetrahedra that share corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Na(4)O4 trigonal pyramid, corners with two equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Na(4)O4 trigonal pyramid. The Na(2)-O(1) bond length is 2.38 Å. The Na(2)-O(2) bond length is 2.41 Å. The Na(2)-O(5) bond length is 2.50 Å. The Na(2)-O(6) bond length is 2.33 Å. In the third Na site, Na(3) is bonded in a 4-coordinate geometry to one O(1), one O(3), one O(4), and one O(5) atom. The Na(3)-O(1) bond length is 2.41 Å. The Na(3)-O(3) bond length is 2.43 Å. The Na(3)-O(4) bond length is 2.95 Å. The Na(3)-O(5) bond length is 2.40 Å. In the fourth Na site, Na(4) is bonded to one O(2), one O(3), one O(5), and one O(6) atom to form distorted NaO4 trigonal pyramids that share  a cornercorner with one Na(2)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Bi(2)O4 trigonal pyramids, and  an edgeedge with one Na(2)O4 tetrahedra. The Na(4)-O(2) bond length is 2.33 Å. The Na(4)-O(3) bond length is 2.32 Å. The Na(4)-O(5) bond length is 2.35 Å. The Na(4)-O(6) bond length is 2.47 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, corners with two equivalent Na(4)O4 trigonal pyramids, and corners with three equivalent Bi(2)O4 trigonal pyramids. The Mg(1)-O(1) bond length is 2.01 Å. The Mg(1)-O(2) bond length is 2.02 Å. The Mg(1)-O(3) bond length is 2.00 Å. The Mg(1)-O(4) bond length is 1.96 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a distorted trigonal non-coplanar geometry to one O(2), one O(4), one O(5), and one O(6) atom. The Bi(1)-O(2) bond length is 2.21 Å. The Bi(1)-O(4) bond length is 2.87 Å. The Bi(1)-O(5) bond length is 2.15 Å. The Bi(1)-O(6) bond length is 2.11 Å. In the second Bi site, Bi(2) is bonded to one O(1), one O(3), one O(4), and one O(6) atom to form distorted BiO4 trigonal pyramids that share corners with two equivalent Na(2)O4 tetrahedra, corners with three equivalent Mg(1)O4 tetrahedra, and corners with two equivalent Na(4)O4 trigonal pyramids. The Bi(2)-O(1) bond length is 2.22 Å. The Bi(2)-O(3) bond length is 2.16 Å. The Bi(2)-O(4) bond length is 2.14 Å. The Bi(2)-O(6) bond length is 2.65 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Na(2), one Na(3), one Mg(1), and one Bi(2) atom. In the second O site, O(2) is bonded to one Na(1), one Na(2), one Na(4), one Mg(1), and one Bi(1) atom to form distorted ONa3MgBi trigonal bipyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(5)Na4Bi square pyramid, and  an edgeedge with one O(6)Na3Bi2 trigonal bipyramid. In the third O site, O(3) is bonded to one Na(3), one Na(4), one Mg(1), and one Bi(2) atom to form distorted ONa2MgBi trigonal pyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, and corners with two equivalent O(2)Na3MgBi trigonal bipyramids. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Na(1), one Na(3), one Mg(1), one Bi(1), and one Bi(2) atom. In the fifth O site, O(5) is bonded to one Na(1), one Na(2), one Na(3), one Na(4), and one Bi(1) atom to form ONa4Bi square pyramids that share corners with two equivalent O(6)Na3Bi2 trigonal bipyramids, corners with two equivalent O(2)Na3MgBi trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(6)Na3Bi2 trigonal bipyramid, and  an edgeedge with one O(2)Na3MgBi trigonal bipyramid. In the sixth O site, O(6) is bonded to one Na(1), one Na(2), one Na(4), one Bi(1), and one Bi(2) atom to form distorted ONa3Bi2 trigonal bipyramids that share corners with two equivalent O(5)Na4Bi square pyramids, corners with two equivalent O(2)Na3MgBi trigonal bipyramids, corners with two equivalent O(3)Na2MgBi trigonal pyramids,  an edgeedge with one O(5)Na4Bi square pyramid, and  an edgeedge with one O(2)Na3MgBi trigonal bipyramid.