Mg9V10O24 crystallizes in the monoclinic C2/m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3), one O(8), and two equivalent O(1) atoms to form MgO4 tetrahedra that share  a cornercorner with one V(5)O6 octahedra, corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with three equivalent V(4)O6 octahedra, and corners with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. In the second Mg site, Mg(2) is bonded to one O(2), one O(4), and two equivalent O(5) atoms to form MgO4 tetrahedra that share corners with three equivalent V(2)O6 octahedra, corners with three equivalent V(3)O6 octahedra, and corners with six equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the third Mg site, Mg(3) is bonded to one O(6), one O(9), and two equivalent O(7) atoms to form distorted MgO4 trigonal pyramids that share  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with three equivalent V(4)O6 octahedra, corners with four equivalent Mg(5)O6 octahedra, and  a faceface with one Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-68°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(9) and four equivalent O(7) atoms to form MgO6 octahedra that share corners with six equivalent V(4)O6 octahedra, edges with two equivalent V(5)O6 octahedra, edges with four equivalent Mg(5)O6 octahedra, and faces with two equivalent Mg(3)O4 trigonal pyramids. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth Mg site, Mg(5) is bonded to two equivalent O(7), two equivalent O(8), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with four equivalent Mg(3)O4 trigonal pyramids, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. There are five inequivalent V sites. In the first V site, V(1) 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 VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 trigonal pyramid,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. In the second V site, V(2) is bonded to two equivalent O(4) and four equivalent O(5) atoms to form VO6 octahedra that share corners with six equivalent Mg(2)O4 tetrahedra, edges with two equivalent V(3)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. In the third V site, V(3) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(5) atoms to form VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 trigonal pyramid,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. In the fourth V site, V(4) is bonded to one O(3), one O(9), two equivalent O(1), and two equivalent O(7) atoms to form VO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(3)O4 trigonal pyramids,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth V site, V(5) is bonded to two equivalent O(8) and four equivalent O(7) atoms to form VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with four equivalent Mg(3)O4 trigonal pyramids, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with four equivalent Mg(5)O6 octahedra. There are nine inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one V(1), one V(3), and one V(4) atom to form distorted OMgV3 trigonal pyramids that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(6)MgV3 tetrahedra,  a cornercorner with one O(8)Mg3V trigonal pyramid,  a cornercorner with one O(1)MgV3 trigonal pyramid,  a cornercorner with one O(3)MgV3 trigonal pyramid,  a cornercorner with one O(4)MgV3 trigonal pyramid, corners with three equivalent O(5)MgV3 trigonal pyramids,  an edgeedge with one O(1)MgV3 trigonal pyramid, and  an edgeedge with one O(3)MgV3 trigonal pyramid. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2), one V(3), and two equivalent V(1) atoms. In the third O site, O(3) is bonded to one Mg(1), one V(4), and two equivalent V(1) atoms to form distorted OMgV3 trigonal pyramids that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(6)MgV3 tetrahedra,  a cornercorner with one O(8)Mg3V trigonal pyramid, corners with two equivalent O(1)MgV3 trigonal pyramids, corners with two equivalent O(4)MgV3 trigonal pyramids, corners with two equivalent O(5)MgV3 trigonal pyramids, and edges with two equivalent O(1)MgV3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one V(2), and two equivalent V(1) atoms to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(2), one V(1), one V(2), and one V(3) atom to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(3), one V(3), and two equivalent V(1) atoms to form distorted OMgV3 tetrahedra that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(3)MgV3 trigonal pyramids, corners with four equivalent O(1)MgV3 trigonal pyramids,  an edgeedge with one O(4)MgV3 trigonal pyramid, and edges with two equivalent O(5)MgV3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(3), one Mg(4), one Mg(5), one V(4), and one V(5) atom to form OMg3V2 square pyramids that share corners with three equivalent O(7)Mg3V2 square pyramids,  a cornercorner with one O(6)MgV3 tetrahedra,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(8)Mg3V trigonal pyramids, corners with two equivalent O(1)MgV3 trigonal pyramids, edges with three equivalent O(7)Mg3V2 square pyramids, edges with three equivalent O(9)Mg4V square pyramids, and  an edgeedge with one O(8)Mg3V trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), two equivalent Mg(5), and one V(5) atom to form distorted OMg3V trigonal pyramids that share corners with two equivalent O(9)Mg4V square pyramids, corners with four equivalent O(7)Mg3V2 square pyramids,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(1)MgV3 trigonal pyramids, corners with three equivalent O(8)Mg3V trigonal pyramids,  an edgeedge with one O(9)Mg4V square pyramid, and edges with two equivalent O(7)Mg3V2 square pyramids. In the ninth O site, O(9) is bonded to one Mg(3), one Mg(4), two equivalent Mg(5), and one V(4) atom to form OMg4V square pyramids that share corners with three equivalent O(9)Mg4V square pyramids,  a cornercorner with one O(6)MgV3 tetrahedra,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(8)Mg3V trigonal pyramids, corners with two equivalent O(1)MgV3 trigonal pyramids, edges with six equivalent O(7)Mg3V2 square pyramids, and  an edgeedge with one O(8)Mg3V trigonal pyramid.
Mg9V10O24 crystallizes in the monoclinic C2/m space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3), one O(8), and two equivalent O(1) atoms to form MgO4 tetrahedra that share  a cornercorner with one V(5)O6 octahedra, corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with three equivalent V(4)O6 octahedra, and corners with four equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. The Mg(1)-O(3) bond length is 2.05 Å. The Mg(1)-O(8) bond length is 2.00 Å. Both Mg(1)-O(1) bond lengths are 2.04 Å. In the second Mg site, Mg(2) is bonded to one O(2), one O(4), and two equivalent O(5) atoms to form MgO4 tetrahedra that share corners with three equivalent V(2)O6 octahedra, corners with three equivalent V(3)O6 octahedra, and corners with six equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. The Mg(2)-O(2) bond length is 2.05 Å. The Mg(2)-O(4) bond length is 1.97 Å. Both Mg(2)-O(5) bond lengths are 1.97 Å. In the third Mg site, Mg(3) is bonded to one O(6), one O(9), and two equivalent O(7) atoms to form distorted MgO4 trigonal pyramids that share  a cornercorner with one V(3)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(5)O6 octahedra, corners with three equivalent V(4)O6 octahedra, corners with four equivalent Mg(5)O6 octahedra, and  a faceface with one Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-68°. The Mg(3)-O(6) bond length is 1.86 Å. The Mg(3)-O(9) bond length is 2.02 Å. Both Mg(3)-O(7) bond lengths are 2.05 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent O(9) and four equivalent O(7) atoms to form MgO6 octahedra that share corners with six equivalent V(4)O6 octahedra, edges with two equivalent V(5)O6 octahedra, edges with four equivalent Mg(5)O6 octahedra, and faces with two equivalent Mg(3)O4 trigonal pyramids. The corner-sharing octahedral tilt angles range from 0-2°. Both Mg(4)-O(9) bond lengths are 2.18 Å. All Mg(4)-O(7) bond lengths are 2.13 Å. In the fifth Mg site, Mg(5) is bonded to two equivalent O(7), two equivalent O(8), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with four equivalent Mg(3)O4 trigonal pyramids, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. Both Mg(5)-O(7) bond lengths are 2.15 Å. Both Mg(5)-O(8) bond lengths are 2.06 Å. Both Mg(5)-O(9) bond lengths are 2.15 Å. There are five inequivalent V sites. In the first V site, V(1) 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 VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 trigonal pyramid,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. The V(1)-O(1) bond length is 2.07 Å. The V(1)-O(2) bond length is 2.03 Å. The V(1)-O(3) bond length is 2.10 Å. The V(1)-O(4) bond length is 2.07 Å. The V(1)-O(5) bond length is 2.07 Å. The V(1)-O(6) bond length is 2.01 Å. In the second V site, V(2) is bonded to two equivalent O(4) and four equivalent O(5) atoms to form VO6 octahedra that share corners with six equivalent Mg(2)O4 tetrahedra, edges with two equivalent V(3)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. Both V(2)-O(4) bond lengths are 2.05 Å. All V(2)-O(5) bond lengths are 2.05 Å. In the third V site, V(3) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(5) atoms to form VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 trigonal pyramid,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra, and edges with four equivalent V(1)O6 octahedra. The V(3)-O(2) bond length is 2.02 Å. The V(3)-O(6) bond length is 2.01 Å. Both V(3)-O(1) bond lengths are 2.10 Å. Both V(3)-O(5) bond lengths are 2.07 Å. In the fourth V site, V(4) is bonded to one O(3), one O(9), two equivalent O(1), and two equivalent O(7) atoms to form VO6 octahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(3)O4 trigonal pyramids,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, and edges with two equivalent V(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. The V(4)-O(3) bond length is 2.08 Å. The V(4)-O(9) bond length is 2.07 Å. Both V(4)-O(1) bond lengths are 2.09 Å. Both V(4)-O(7) bond lengths are 2.17 Å. In the fifth V site, V(5) is bonded to two equivalent O(8) and four equivalent O(7) atoms to form VO6 octahedra that share corners with two equivalent Mg(1)O4 tetrahedra, corners with four equivalent Mg(3)O4 trigonal pyramids, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with four equivalent Mg(5)O6 octahedra. Both V(5)-O(8) bond lengths are 1.98 Å. All V(5)-O(7) bond lengths are 2.12 Å. There are nine inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one V(1), one V(3), and one V(4) atom to form distorted OMgV3 trigonal pyramids that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(6)MgV3 tetrahedra,  a cornercorner with one O(8)Mg3V trigonal pyramid,  a cornercorner with one O(1)MgV3 trigonal pyramid,  a cornercorner with one O(3)MgV3 trigonal pyramid,  a cornercorner with one O(4)MgV3 trigonal pyramid, corners with three equivalent O(5)MgV3 trigonal pyramids,  an edgeedge with one O(1)MgV3 trigonal pyramid, and  an edgeedge with one O(3)MgV3 trigonal pyramid. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2), one V(3), and two equivalent V(1) atoms. In the third O site, O(3) is bonded to one Mg(1), one V(4), and two equivalent V(1) atoms to form distorted OMgV3 trigonal pyramids that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(6)MgV3 tetrahedra,  a cornercorner with one O(8)Mg3V trigonal pyramid, corners with two equivalent O(1)MgV3 trigonal pyramids, corners with two equivalent O(4)MgV3 trigonal pyramids, corners with two equivalent O(5)MgV3 trigonal pyramids, and edges with two equivalent O(1)MgV3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one V(2), and two equivalent V(1) atoms to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(2), one V(1), one V(2), and one V(3) atom to form a mixture of distorted corner and edge-sharing OMgV3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(3), one V(3), and two equivalent V(1) atoms to form distorted OMgV3 tetrahedra that share  a cornercorner with one O(9)Mg4V square pyramid, corners with two equivalent O(7)Mg3V2 square pyramids, corners with two equivalent O(3)MgV3 trigonal pyramids, corners with four equivalent O(1)MgV3 trigonal pyramids,  an edgeedge with one O(4)MgV3 trigonal pyramid, and edges with two equivalent O(5)MgV3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(3), one Mg(4), one Mg(5), one V(4), and one V(5) atom to form OMg3V2 square pyramids that share corners with three equivalent O(7)Mg3V2 square pyramids,  a cornercorner with one O(6)MgV3 tetrahedra,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(8)Mg3V trigonal pyramids, corners with two equivalent O(1)MgV3 trigonal pyramids, edges with three equivalent O(7)Mg3V2 square pyramids, edges with three equivalent O(9)Mg4V square pyramids, and  an edgeedge with one O(8)Mg3V trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), two equivalent Mg(5), and one V(5) atom to form distorted OMg3V trigonal pyramids that share corners with two equivalent O(9)Mg4V square pyramids, corners with four equivalent O(7)Mg3V2 square pyramids,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(1)MgV3 trigonal pyramids, corners with three equivalent O(8)Mg3V trigonal pyramids,  an edgeedge with one O(9)Mg4V square pyramid, and edges with two equivalent O(7)Mg3V2 square pyramids. In the ninth O site, O(9) is bonded to one Mg(3), one Mg(4), two equivalent Mg(5), and one V(4) atom to form OMg4V square pyramids that share corners with three equivalent O(9)Mg4V square pyramids,  a cornercorner with one O(6)MgV3 tetrahedra,  a cornercorner with one O(3)MgV3 trigonal pyramid, corners with two equivalent O(8)Mg3V trigonal pyramids, corners with two equivalent O(1)MgV3 trigonal pyramids, edges with six equivalent O(7)Mg3V2 square pyramids, and  an edgeedge with one O(8)Mg3V trigonal pyramid.