BaMgMn4O8 crystallizes in the monoclinic Cm space group. Ba(1) is bonded in a 9-coordinate geometry to one O(2), one O(5), one O(8), two equivalent O(1), two equivalent O(6), and two equivalent O(7) atoms. Mg(1) is bonded in a 5-coordinate geometry to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(8), two equivalent O(4), and two equivalent O(7) atoms to form MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Mn site, Mn(2) is bonded to one O(5), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form distorted MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the third Mn site, Mn(3) is bonded to one O(1), one O(2), two equivalent O(6), and two equivalent O(8) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Mn site, Mn(4) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form MnO4 tetrahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(3)O6 octahedra, and corners with two equivalent Mn(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-70°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), and one Mn(3) atom. In the second O site, O(2) is bonded to one Ba(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted OBaMn3 trigonal pyramids that share corners with two equivalent O(3)Mg2Mn3 square pyramids, corners with two equivalent O(2)BaMn3 trigonal pyramids,  an edgeedge with one O(3)Mg2Mn3 square pyramid, and edges with two equivalent O(7)Ba2Mn3 square pyramids. In the third O site, O(3) is bonded to two equivalent Mg(1), one Mn(1), and two equivalent Mn(2) atoms to form OMg2Mn3 square pyramids that share corners with two equivalent O(2)BaMn3 trigonal pyramids, edges with two equivalent O(7)Ba2Mn3 square pyramids, edges with two equivalent O(3)Mg2Mn3 square pyramids,  an edgeedge with one O(2)BaMn3 trigonal pyramid, and edges with two equivalent O(4)MgMn3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mn(4), and two equivalent Mn(1) atoms to form OMgMn3 trigonal pyramids that share corners with two equivalent O(7)Ba2Mn3 square pyramids, corners with two equivalent O(4)MgMn3 trigonal pyramids,  an edgeedge with one O(7)Ba2Mn3 square pyramid, and edges with two equivalent O(3)Mg2Mn3 square pyramids. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ba(1), one Mg(1), one Mn(2), and two equivalent Mn(4) atoms. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Mn(4), and two equivalent Mn(3) atoms. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Mn(2), and two equivalent Mn(1) atoms to form distorted OBa2Mn3 square pyramids that share corners with two equivalent O(4)MgMn3 trigonal pyramids, edges with two equivalent O(7)Ba2Mn3 square pyramids, edges with two equivalent O(3)Mg2Mn3 square pyramids,  an edgeedge with one O(4)MgMn3 trigonal pyramid, and edges with two equivalent O(2)BaMn3 trigonal pyramids. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Ba(1), one Mn(1), and two equivalent Mn(3) atoms.
BaMgMn4O8 crystallizes in the monoclinic Cm space group. Ba(1) is bonded in a 9-coordinate geometry to one O(2), one O(5), one O(8), two equivalent O(1), two equivalent O(6), and two equivalent O(7) atoms. The Ba(1)-O(2) bond length is 2.90 Å. The Ba(1)-O(5) bond length is 2.74 Å. The Ba(1)-O(8) bond length is 2.95 Å. Both Ba(1)-O(1) bond lengths are 2.83 Å. Both Ba(1)-O(6) bond lengths are 2.93 Å. Both Ba(1)-O(7) bond lengths are 2.58 Å. Mg(1) is bonded in a 5-coordinate geometry to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms. The Mg(1)-O(4) bond length is 2.08 Å. The Mg(1)-O(5) bond length is 2.72 Å. Both Mg(1)-O(1) bond lengths are 2.07 Å. Both Mg(1)-O(3) bond lengths are 2.18 Å. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(8), two equivalent O(4), and two equivalent O(7) atoms to form MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. The Mn(1)-O(3) bond length is 1.96 Å. The Mn(1)-O(8) bond length is 1.96 Å. Both Mn(1)-O(4) bond lengths are 2.06 Å. Both Mn(1)-O(7) bond lengths are 2.05 Å. In the second Mn site, Mn(2) is bonded to one O(5), one O(7), two equivalent O(2), and two equivalent O(3) atoms to form distorted MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, edges with two equivalent Mn(1)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. The Mn(2)-O(5) bond length is 2.17 Å. The Mn(2)-O(7) bond length is 2.13 Å. Both Mn(2)-O(2) bond lengths are 2.03 Å. Both Mn(2)-O(3) bond lengths are 2.22 Å. In the third Mn site, Mn(3) is bonded to one O(1), one O(2), two equivalent O(6), and two equivalent O(8) atoms to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O4 tetrahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Mn(3)-O(1) bond length is 2.01 Å. The Mn(3)-O(2) bond length is 2.04 Å. Both Mn(3)-O(6) bond lengths are 2.15 Å. Both Mn(3)-O(8) bond lengths are 2.04 Å. In the fourth Mn site, Mn(4) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form MnO4 tetrahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(3)O6 octahedra, and corners with two equivalent Mn(4)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-70°. The Mn(4)-O(4) bond length is 1.96 Å. The Mn(4)-O(6) bond length is 2.07 Å. Both Mn(4)-O(5) bond lengths are 1.99 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), and one Mn(3) atom. In the second O site, O(2) is bonded to one Ba(1), one Mn(3), and two equivalent Mn(2) atoms to form distorted OBaMn3 trigonal pyramids that share corners with two equivalent O(3)Mg2Mn3 square pyramids, corners with two equivalent O(2)BaMn3 trigonal pyramids,  an edgeedge with one O(3)Mg2Mn3 square pyramid, and edges with two equivalent O(7)Ba2Mn3 square pyramids. In the third O site, O(3) is bonded to two equivalent Mg(1), one Mn(1), and two equivalent Mn(2) atoms to form OMg2Mn3 square pyramids that share corners with two equivalent O(2)BaMn3 trigonal pyramids, edges with two equivalent O(7)Ba2Mn3 square pyramids, edges with two equivalent O(3)Mg2Mn3 square pyramids,  an edgeedge with one O(2)BaMn3 trigonal pyramid, and edges with two equivalent O(4)MgMn3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mn(4), and two equivalent Mn(1) atoms to form OMgMn3 trigonal pyramids that share corners with two equivalent O(7)Ba2Mn3 square pyramids, corners with two equivalent O(4)MgMn3 trigonal pyramids,  an edgeedge with one O(7)Ba2Mn3 square pyramid, and edges with two equivalent O(3)Mg2Mn3 square pyramids. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Ba(1), one Mg(1), one Mn(2), and two equivalent Mn(4) atoms. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to two equivalent Ba(1), one Mn(4), and two equivalent Mn(3) atoms. In the seventh O site, O(7) is bonded to two equivalent Ba(1), one Mn(2), and two equivalent Mn(1) atoms to form distorted OBa2Mn3 square pyramids that share corners with two equivalent O(4)MgMn3 trigonal pyramids, edges with two equivalent O(7)Ba2Mn3 square pyramids, edges with two equivalent O(3)Mg2Mn3 square pyramids,  an edgeedge with one O(4)MgMn3 trigonal pyramid, and edges with two equivalent O(2)BaMn3 trigonal pyramids. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Ba(1), one Mn(1), and two equivalent Mn(3) atoms.