Ba3MgMn3O9 is Krennerite-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 11-coordinate geometry to one O(6), two equivalent O(1), two equivalent O(4), two equivalent O(5), and four equivalent O(3) atoms. In the second Ba site, Ba(2) is bonded in a 3-coordinate geometry to one O(2), one O(4), and two equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(6), two equivalent O(2), two equivalent O(3), and four equivalent O(1) atoms. Mg(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(5) atoms to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Mn(3)O6 octahedra and  a faceface with one Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 38°. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded in a 5-coordinate geometry to one O(2), two equivalent O(1), and two equivalent O(5) atoms. In the second Mn site, Mn(2) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form MnO6 octahedra that share  a faceface with one Mn(3)O6 octahedra and  a faceface with one Mg(1)O5 trigonal bipyramid. In the third Mn site, Mn(3) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Mg(1)O5 trigonal bipyramids and  a faceface with one Mn(2)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Ba(1), two equivalent Ba(3), one Mg(1), one Mn(1), and one Mn(2) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), two equivalent Ba(3), one Mg(1), one Mn(1), and one Mn(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Ba(2), two equivalent Ba(1), one Mn(2), and one Mn(3) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Ba(1), one Mg(1), one Mn(1), and one Mn(3) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(3), and one Mn(3) atom.
Ba3MgMn3O9 is Krennerite-derived structured and crystallizes in the monoclinic Cm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 11-coordinate geometry to one O(6), two equivalent O(1), two equivalent O(4), two equivalent O(5), and four equivalent O(3) atoms. The Ba(1)-O(6) bond length is 2.79 Å. Both Ba(1)-O(1) bond lengths are 2.93 Å. Both Ba(1)-O(4) bond lengths are 2.88 Å. Both Ba(1)-O(5) bond lengths are 2.94 Å. There are two shorter (2.96 Å) and two longer (3.04 Å) Ba(1)-O(3) bond lengths. In the second Ba site, Ba(2) is bonded in a 3-coordinate geometry to one O(2), one O(4), and two equivalent O(3) atoms. The Ba(2)-O(2) bond length is 2.88 Å. The Ba(2)-O(4) bond length is 2.51 Å. Both Ba(2)-O(3) bond lengths are 2.66 Å. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(6), two equivalent O(2), two equivalent O(3), and four equivalent O(1) atoms. The Ba(3)-O(6) bond length is 2.92 Å. Both Ba(3)-O(2) bond lengths are 2.94 Å. Both Ba(3)-O(3) bond lengths are 2.83 Å. There are two shorter (2.97 Å) and two longer (3.01 Å) Ba(3)-O(1) bond lengths. Mg(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(5) atoms to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Mn(3)O6 octahedra and  a faceface with one Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 38°. The Mg(1)-O(2) bond length is 2.16 Å. Both Mg(1)-O(1) bond lengths are 2.07 Å. Both Mg(1)-O(5) bond lengths are 2.03 Å. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded in a 5-coordinate geometry to one O(2), two equivalent O(1), and two equivalent O(5) atoms. The Mn(1)-O(2) bond length is 2.28 Å. Both Mn(1)-O(1) bond lengths are 2.03 Å. Both Mn(1)-O(5) bond lengths are 2.22 Å. In the second Mn site, Mn(2) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form MnO6 octahedra that share  a faceface with one Mn(3)O6 octahedra and  a faceface with one Mg(1)O5 trigonal bipyramid. The Mn(2)-O(2) bond length is 2.15 Å. The Mn(2)-O(4) bond length is 1.89 Å. Both Mn(2)-O(1) bond lengths are 1.96 Å. Both Mn(2)-O(3) bond lengths are 1.96 Å. In the third Mn site, Mn(3) is bonded to one O(4), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form MnO6 octahedra that share corners with two equivalent Mg(1)O5 trigonal bipyramids and  a faceface with one Mn(2)O6 octahedra. The Mn(3)-O(4) bond length is 2.03 Å. The Mn(3)-O(6) bond length is 1.84 Å. Both Mn(3)-O(3) bond lengths are 2.05 Å. Both Mn(3)-O(5) bond lengths are 1.93 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Ba(1), two equivalent Ba(3), one Mg(1), one Mn(1), and one Mn(2) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), two equivalent Ba(3), one Mg(1), one Mn(1), and one Mn(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Ba(2), two equivalent Ba(1), one Mn(2), and one Mn(3) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Ba(1), one Mg(1), one Mn(1), and one Mn(3) atom. In the sixth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(3), and one Mn(3) atom.