NaMgMn4O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded to one O(3), one O(4), two equivalent O(2), and two equivalent O(5) atoms to form NaO6 octahedra that share edges with two equivalent Mn(1)O6 octahedra and edges with four equivalent Mn(2)O6 octahedra. Mg(1) is bonded in a rectangular see-saw-like geometry to one O(3), one O(6), and two equivalent O(2) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form MnO6 octahedra that share edges with two equivalent Na(1)O6 octahedra and edges with four equivalent Mn(2)O6 octahedra. In the second Mn site, Mn(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted MnO6 octahedra that share edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. In the third Mn site, Mn(3) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(2), and two equivalent O(5) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(1) and two equivalent Mn(2) atoms. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mn(1), one Mn(2), and one Mn(3) atom to form distorted ONaMgMn3 trigonal bipyramids that share  a cornercorner with one O(6)MgMn3 tetrahedra,  a cornercorner with one O(4)NaMn3 trigonal pyramid,  an edgeedge with one O(6)MgMn3 tetrahedra, edges with two equivalent O(2)NaMgMn3 trigonal bipyramids, and  an edgeedge with one O(4)NaMn3 trigonal pyramid. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Na(1), one Mg(1), one Mn(3), and two equivalent Mn(2) atoms. In the fourth O site, O(4) is bonded to one Na(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted ONaMn3 trigonal pyramids that share corners with two equivalent O(6)MgMn3 tetrahedra, corners with two equivalent O(2)NaMgMn3 trigonal bipyramids, and edges with two equivalent O(2)NaMgMn3 trigonal bipyramids. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Na(1), one Mn(1), one Mn(2), and one Mn(3) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Mn(1), and two equivalent Mn(2) atoms to form OMgMn3 tetrahedra that share corners with two equivalent O(2)NaMgMn3 trigonal bipyramids, corners with two equivalent O(4)NaMn3 trigonal pyramids, and edges with two equivalent O(2)NaMgMn3 trigonal bipyramids.
NaMgMn4O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded to one O(3), one O(4), two equivalent O(2), and two equivalent O(5) atoms to form NaO6 octahedra that share edges with two equivalent Mn(1)O6 octahedra and edges with four equivalent Mn(2)O6 octahedra. The Na(1)-O(3) bond length is 2.34 Å. The Na(1)-O(4) bond length is 2.28 Å. Both Na(1)-O(2) bond lengths are 2.40 Å. Both Na(1)-O(5) bond lengths are 2.34 Å. Mg(1) is bonded in a rectangular see-saw-like geometry to one O(3), one O(6), and two equivalent O(2) atoms. The Mg(1)-O(3) bond length is 2.03 Å. The Mg(1)-O(6) bond length is 2.02 Å. Both Mg(1)-O(2) bond lengths are 2.12 Å. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form MnO6 octahedra that share edges with two equivalent Na(1)O6 octahedra and edges with four equivalent Mn(2)O6 octahedra. The Mn(1)-O(1) bond length is 1.92 Å. The Mn(1)-O(6) bond length is 2.07 Å. Both Mn(1)-O(2) bond lengths are 1.99 Å. Both Mn(1)-O(5) bond lengths are 1.92 Å. In the second Mn site, Mn(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted MnO6 octahedra that share edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The Mn(2)-O(1) bond length is 1.97 Å. The Mn(2)-O(2) bond length is 2.38 Å. The Mn(2)-O(3) bond length is 1.95 Å. The Mn(2)-O(4) bond length is 1.92 Å. The Mn(2)-O(5) bond length is 2.28 Å. The Mn(2)-O(6) bond length is 2.04 Å. In the third Mn site, Mn(3) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(2), and two equivalent O(5) atoms. The Mn(3)-O(3) bond length is 2.55 Å. The Mn(3)-O(4) bond length is 2.10 Å. Both Mn(3)-O(2) bond lengths are 2.02 Å. Both Mn(3)-O(5) bond lengths are 1.92 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(1) and two equivalent Mn(2) atoms. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mn(1), one Mn(2), and one Mn(3) atom to form distorted ONaMgMn3 trigonal bipyramids that share  a cornercorner with one O(6)MgMn3 tetrahedra,  a cornercorner with one O(4)NaMn3 trigonal pyramid,  an edgeedge with one O(6)MgMn3 tetrahedra, edges with two equivalent O(2)NaMgMn3 trigonal bipyramids, and  an edgeedge with one O(4)NaMn3 trigonal pyramid. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Na(1), one Mg(1), one Mn(3), and two equivalent Mn(2) atoms. In the fourth O site, O(4) is bonded to one Na(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted ONaMn3 trigonal pyramids that share corners with two equivalent O(6)MgMn3 tetrahedra, corners with two equivalent O(2)NaMgMn3 trigonal bipyramids, and edges with two equivalent O(2)NaMgMn3 trigonal bipyramids. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Na(1), one Mn(1), one Mn(2), and one Mn(3) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Mn(1), and two equivalent Mn(2) atoms to form OMgMn3 tetrahedra that share corners with two equivalent O(2)NaMgMn3 trigonal bipyramids, corners with two equivalent O(4)NaMn3 trigonal pyramids, and edges with two equivalent O(2)NaMgMn3 trigonal bipyramids.