Mg2W9O13 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to one O(3), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form distorted MgO6 octahedra that share corners with two equivalent W(5)O6 octahedra, corners with two equivalent W(2)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent W(5)O6 octahedra, and edges with two equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 14-15°. There are five inequivalent W sites. In the first W site, W(1) is bonded in a linear geometry to two equivalent O(7) atoms. In the second W site, W(2) is bonded to one O(4), two equivalent O(1), and two equivalent O(3) atoms to form distorted WO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent W(2)O5 square pyramids, and edges with three equivalent W(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 56-57°. In the third W site, W(3) is bonded to one O(5), two equivalent O(6), and two equivalent O(7) atoms to form WO5 square pyramids that share corners with two equivalent W(5)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent W(5)O6 octahedra, and edges with two equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles are 13°. In the fourth W site, W(4) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms. In the fifth W site, W(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form WO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent W(3)O5 square pyramids, edges with two equivalent W(5)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, and edges with three equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 14-15°. There are seven inequivalent O sites. In the first O site, O(1) is bonded to two equivalent W(4) and four equivalent W(2) atoms to form OW6 octahedra that share corners with two equivalent O(2)Mg2W2 tetrahedra, corners with eight equivalent O(3)MgW4 trigonal bipyramids, edges with two equivalent O(1)W6 octahedra, and edges with two equivalent O(3)MgW4 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one W(4), and one W(5) atom to form OMg2W2 tetrahedra that share  a cornercorner with one O(1)W6 octahedra, corners with four equivalent O(5)Mg2W3 square pyramids,  a cornercorner with one O(7)W4 tetrahedra, corners with two equivalent O(2)Mg2W2 tetrahedra,  an edgeedge with one O(5)Mg2W3 square pyramid, edges with two equivalent O(6)MgW4 square pyramids, and edges with two equivalent O(3)MgW4 trigonal bipyramids. The corner-sharing octahedral tilt angles are 18°. In the third O site, O(3) is bonded to one Mg(1), two equivalent W(2), and two equivalent W(4) atoms to form distorted OMgW4 trigonal bipyramids that share corners with four equivalent O(1)W6 octahedra,  a cornercorner with one O(6)MgW4 square pyramid, corners with two equivalent O(5)Mg2W3 square pyramids,  an edgeedge with one O(1)W6 octahedra, edges with two equivalent O(2)Mg2W2 tetrahedra, and edges with two equivalent O(3)MgW4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 16-67°. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one W(2) and two equivalent W(4) atoms. In the fifth O site, O(5) is bonded to two equivalent Mg(1), one W(3), and two equivalent W(5) atoms to form OMg2W3 square pyramids that share corners with two equivalent O(6)MgW4 square pyramids, corners with four equivalent O(2)Mg2W2 tetrahedra, corners with two equivalent O(3)MgW4 trigonal bipyramids, edges with two equivalent O(5)Mg2W3 square pyramids, edges with three equivalent O(6)MgW4 square pyramids,  an edgeedge with one O(2)Mg2W2 tetrahedra, and edges with two equivalent O(7)W4 tetrahedra. In the sixth O site, O(6) is bonded to one Mg(1), two equivalent W(3), and two equivalent W(5) atoms to form OMgW4 square pyramids that share corners with two equivalent O(5)Mg2W3 square pyramids, corners with four equivalent O(7)W4 tetrahedra,  a cornercorner with one O(3)MgW4 trigonal bipyramid, edges with two equivalent O(6)MgW4 square pyramids, edges with three equivalent O(5)Mg2W3 square pyramids,  an edgeedge with one O(7)W4 tetrahedra, and edges with two equivalent O(2)Mg2W2 tetrahedra. In the seventh O site, O(7) is bonded to one W(1), one W(5), and two equivalent W(3) atoms to form OW4 tetrahedra that share corners with four equivalent O(6)MgW4 square pyramids,  a cornercorner with one O(2)Mg2W2 tetrahedra, corners with three equivalent O(7)W4 tetrahedra,  an edgeedge with one O(6)MgW4 square pyramid, and edges with two equivalent O(5)Mg2W3 square pyramids.
Mg2W9O13 crystallizes in the triclinic P-1 space group. Mg(1) is bonded to one O(3), one O(6), two equivalent O(2), and two equivalent O(5) atoms to form distorted MgO6 octahedra that share corners with two equivalent W(5)O6 octahedra, corners with two equivalent W(2)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent W(5)O6 octahedra, and edges with two equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 14-15°. The Mg(1)-O(3) bond length is 2.25 Å. The Mg(1)-O(6) bond length is 2.22 Å. There is one shorter (2.03 Å) and one longer (2.04 Å) Mg(1)-O(2) bond length. There is one shorter (2.30 Å) and one longer (2.42 Å) Mg(1)-O(5) bond length. There are five inequivalent W sites. In the first W site, W(1) is bonded in a linear geometry to two equivalent O(7) atoms. Both W(1)-O(7) bond lengths are 2.20 Å. In the second W site, W(2) is bonded to one O(4), two equivalent O(1), and two equivalent O(3) atoms to form distorted WO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent W(2)O5 square pyramids, and edges with three equivalent W(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 56-57°. The W(2)-O(4) bond length is 2.10 Å. There is one shorter (2.31 Å) and one longer (2.35 Å) W(2)-O(1) bond length. Both W(2)-O(3) bond lengths are 2.23 Å. In the third W site, W(3) is bonded to one O(5), two equivalent O(6), and two equivalent O(7) atoms to form WO5 square pyramids that share corners with two equivalent W(5)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent W(5)O6 octahedra, and edges with two equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles are 13°. The W(3)-O(5) bond length is 2.27 Å. There is one shorter (2.27 Å) and one longer (2.31 Å) W(3)-O(6) bond length. There is one shorter (2.15 Å) and one longer (2.16 Å) W(3)-O(7) bond length. In the fourth W site, W(4) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms. The W(4)-O(1) bond length is 2.66 Å. The W(4)-O(2) bond length is 2.08 Å. There is one shorter (2.26 Å) and one longer (2.29 Å) W(4)-O(3) bond length. There is one shorter (2.07 Å) and one longer (2.08 Å) W(4)-O(4) bond length. In the fifth W site, W(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form WO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent W(3)O5 square pyramids, edges with two equivalent W(5)O6 octahedra, edges with three equivalent Mg(1)O6 octahedra, and edges with three equivalent W(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 14-15°. The W(5)-O(2) bond length is 2.14 Å. The W(5)-O(7) bond length is 2.20 Å. Both W(5)-O(5) bond lengths are 2.21 Å. There is one shorter (2.26 Å) and one longer (2.27 Å) W(5)-O(6) bond length. There are seven inequivalent O sites. In the first O site, O(1) is bonded to two equivalent W(4) and four equivalent W(2) atoms to form OW6 octahedra that share corners with two equivalent O(2)Mg2W2 tetrahedra, corners with eight equivalent O(3)MgW4 trigonal bipyramids, edges with two equivalent O(1)W6 octahedra, and edges with two equivalent O(3)MgW4 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one W(4), and one W(5) atom to form OMg2W2 tetrahedra that share  a cornercorner with one O(1)W6 octahedra, corners with four equivalent O(5)Mg2W3 square pyramids,  a cornercorner with one O(7)W4 tetrahedra, corners with two equivalent O(2)Mg2W2 tetrahedra,  an edgeedge with one O(5)Mg2W3 square pyramid, edges with two equivalent O(6)MgW4 square pyramids, and edges with two equivalent O(3)MgW4 trigonal bipyramids. The corner-sharing octahedral tilt angles are 18°. In the third O site, O(3) is bonded to one Mg(1), two equivalent W(2), and two equivalent W(4) atoms to form distorted OMgW4 trigonal bipyramids that share corners with four equivalent O(1)W6 octahedra,  a cornercorner with one O(6)MgW4 square pyramid, corners with two equivalent O(5)Mg2W3 square pyramids,  an edgeedge with one O(1)W6 octahedra, edges with two equivalent O(2)Mg2W2 tetrahedra, and edges with two equivalent O(3)MgW4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 16-67°. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one W(2) and two equivalent W(4) atoms. In the fifth O site, O(5) is bonded to two equivalent Mg(1), one W(3), and two equivalent W(5) atoms to form OMg2W3 square pyramids that share corners with two equivalent O(6)MgW4 square pyramids, corners with four equivalent O(2)Mg2W2 tetrahedra, corners with two equivalent O(3)MgW4 trigonal bipyramids, edges with two equivalent O(5)Mg2W3 square pyramids, edges with three equivalent O(6)MgW4 square pyramids,  an edgeedge with one O(2)Mg2W2 tetrahedra, and edges with two equivalent O(7)W4 tetrahedra. In the sixth O site, O(6) is bonded to one Mg(1), two equivalent W(3), and two equivalent W(5) atoms to form OMgW4 square pyramids that share corners with two equivalent O(5)Mg2W3 square pyramids, corners with four equivalent O(7)W4 tetrahedra,  a cornercorner with one O(3)MgW4 trigonal bipyramid, edges with two equivalent O(6)MgW4 square pyramids, edges with three equivalent O(5)Mg2W3 square pyramids,  an edgeedge with one O(7)W4 tetrahedra, and edges with two equivalent O(2)Mg2W2 tetrahedra. In the seventh O site, O(7) is bonded to one W(1), one W(5), and two equivalent W(3) atoms to form OW4 tetrahedra that share corners with four equivalent O(6)MgW4 square pyramids,  a cornercorner with one O(2)Mg2W2 tetrahedra, corners with three equivalent O(7)W4 tetrahedra,  an edgeedge with one O(6)MgW4 square pyramid, and edges with two equivalent O(5)Mg2W3 square pyramids.