NaMgCr3O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(2) atoms to form NaO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Cr(2)O6 octahedra. Mg(1) is bonded to one O(4), one O(5), and two equivalent O(2) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-78°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(4), one O(5), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-63°. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Na(1)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(3), one O(6), and two equivalent O(2) atoms to form CrO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-64°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Na(1), one Cr(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Cr(2), and one Cr(3) atom to form distorted edge-sharing ONaMgCr2 tetrahedra. In the third O site, O(3) is bonded in a distorted bent 150 degrees geometry to one Cr(2) and one Cr(3) atom. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Mg(1), one Cr(1), and one Cr(2) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Na(1), one Mg(1), and one Cr(1) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Na(1) and one Cr(3) atom.
NaMgCr3O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded to one O(5), one O(6), two equivalent O(1), and two equivalent O(2) atoms to form NaO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Cr(2)O6 octahedra. The Na(1)-O(5) bond length is 2.46 Å. The Na(1)-O(6) bond length is 2.41 Å. Both Na(1)-O(1) bond lengths are 2.34 Å. Both Na(1)-O(2) bond lengths are 2.43 Å. Mg(1) is bonded to one O(4), one O(5), and two equivalent O(2) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-78°. The Mg(1)-O(4) bond length is 2.01 Å. The Mg(1)-O(5) bond length is 2.00 Å. Both Mg(1)-O(2) bond lengths are 2.04 Å. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(4), one O(5), and two equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 44-63°. The Cr(1)-O(4) bond length is 1.81 Å. The Cr(1)-O(5) bond length is 1.70 Å. Both Cr(1)-O(1) bond lengths are 1.72 Å. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(3)O4 tetrahedra, and edges with two equivalent Na(1)O6 octahedra. The Cr(2)-O(3) bond length is 2.00 Å. The Cr(2)-O(4) bond length is 2.04 Å. Both Cr(2)-O(1) bond lengths are 2.01 Å. Both Cr(2)-O(2) bond lengths are 2.05 Å. In the third Cr site, Cr(3) is bonded to one O(3), one O(6), and two equivalent O(2) atoms to form CrO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 45-64°. The Cr(3)-O(3) bond length is 1.68 Å. The Cr(3)-O(6) bond length is 1.62 Å. Both Cr(3)-O(2) bond lengths are 1.84 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Na(1), one Cr(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Cr(2), and one Cr(3) atom to form distorted edge-sharing ONaMgCr2 tetrahedra. In the third O site, O(3) is bonded in a distorted bent 150 degrees geometry to one Cr(2) and one Cr(3) atom. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Mg(1), one Cr(1), and one Cr(2) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Na(1), one Mg(1), and one Cr(1) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Na(1) and one Cr(3) atom.