MgV12Zn6O24 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(14), one O(18), one O(20), one O(21), one O(23), and one O(24) atom to form MgO6 octahedra that share corners with three equivalent V(10)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, edges with two equivalent V(11)O6 octahedra, edges with two equivalent V(7)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. There are twelve inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(11), one O(2), one O(3), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. In the second V site, V(2) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. In the third V site, V(3) is bonded to one O(10), one O(15), one O(16), one O(19), one O(6), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(6)O6 octahedra, and edges with two equivalent V(8)O6 octahedra. In the fourth V site, V(4) is bonded to one O(1), one O(11), one O(2), one O(4), one O(5), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. In the fifth V site, V(5) is bonded to one O(11), one O(12), one O(5), one O(6), one O(7), and one O(9) atom to form VO6 octahedra that share corners with three equivalent Zn(2)O4 tetrahedra, corners with three equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  an edgeedge with one V(8)O6 octahedra. In the sixth V site, V(6) is bonded to one O(10), one O(12), one O(13), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(3)O6 octahedra, and edges with two equivalent V(8)O6 octahedra. In the seventh V site, V(7) is bonded to one O(14), one O(17), one O(18), one O(22), one O(23), and one O(24) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(11)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. In the eighth V site, V(8) is bonded to one O(10), one O(12), one O(13), one O(16), one O(19), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(3)O6 octahedra, and edges with two equivalent V(6)O6 octahedra. In the ninth V site, V(9) is bonded to one O(14), one O(17), one O(20), one O(21), one O(22), and one O(24) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(11)O6 octahedra, and edges with two equivalent V(7)O6 octahedra. In the tenth V site, V(10) is bonded to one O(13), one O(14), one O(15), one O(18), one O(19), and one O(20) atom to form VO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. In the eleventh V site, V(11) is bonded to one O(17), one O(18), one O(20), one O(21), one O(22), and one O(23) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(7)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. In the twelfth V site, V(12) is bonded in a rectangular see-saw-like geometry to one O(21), one O(23), one O(24), and one O(8) atom. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to one O(1), one O(17), one O(3), and one O(4) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, and corners with three equivalent Zn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. In the second Zn site, Zn(2) is bonded to one O(12), one O(2), one O(6), and one O(9) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(4)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with two equivalent V(6)O6 octahedra, corners with two equivalent V(8)O6 octahedra, and corners with three equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the third Zn site, Zn(3) is bonded to one O(1), one O(21), one O(23), one O(24), one O(3), and one O(4) atom to form ZnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Zn(1)O4 tetrahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. In the fourth Zn site, Zn(4) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(14), one O(18), and one O(20) atom. In the fifth Zn site, Zn(5) is bonded to one O(11), one O(16), one O(5), and one O(7) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  a cornercorner with one V(8)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, and corners with three equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. In the sixth Zn site, Zn(6) is bonded to one O(13), one O(15), one O(19), and one O(22) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with two equivalent V(6)O6 octahedra, corners with two equivalent V(8)O6 octahedra, and corners with three equivalent V(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one V(1), one V(4), one Zn(1), and one Zn(3) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one V(1), one V(2), one V(4), and one Zn(2) atom. In the third O site, O(3) is bonded to one V(1), one V(2), one Zn(1), and one Zn(3) atom to form distorted OV2Zn2 trigonal pyramids that share  a cornercorner with one O(23)MgV3Zn square pyramid, corners with two equivalent O(8)V4 tetrahedra,  a cornercorner with one O(21)MgV3Zn trigonal bipyramid,  a cornercorner with one O(24)MgV3Zn trigonal bipyramid,  a cornercorner with one O(5)V3Zn trigonal pyramid, and corners with two equivalent O(7)V3Zn trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(2), one V(4), one Zn(1), and one Zn(3) atom. In the fifth O site, O(5) is bonded to one V(2), one V(4), one V(5), and one Zn(5) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(7)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid,  an edgeedge with one O(8)V4 tetrahedra, and  an edgeedge with one O(7)V3Zn trigonal pyramid. In the sixth O site, O(6) is bonded to one V(3), one V(5), one V(8), and one Zn(2) atom to form a mixture of distorted edge and corner-sharing OV3Zn trigonal pyramids. In the seventh O site, O(7) is bonded to one V(1), one V(2), one V(5), and one Zn(5) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(5)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid, corners with two equivalent O(3)V2Zn2 trigonal pyramids,  an edgeedge with one O(8)V4 tetrahedra, and  an edgeedge with one O(5)V3Zn trigonal pyramid. In the eighth O site, O(8) is bonded to one V(1), one V(12), one V(2), and one V(4) atom to form OV4 tetrahedra that share  a cornercorner with one O(23)MgV3Zn square pyramid,  a cornercorner with one O(21)MgV3Zn trigonal bipyramid,  a cornercorner with one O(24)MgV3Zn trigonal bipyramid, corners with two equivalent O(3)V2Zn2 trigonal pyramids,  an edgeedge with one O(5)V3Zn trigonal pyramid, and  an edgeedge with one O(7)V3Zn trigonal pyramid. In the ninth O site, O(9) is bonded to one V(3), one V(5), one V(6), and one Zn(2) atom to form a mixture of distorted edge and corner-sharing OV3Zn trigonal pyramids. In the tenth O site, O(10) is bonded to one V(3), one V(6), one V(8), and one Zn(4) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(13)V3Zn trigonal pyramids, corners with two equivalent O(15)V3Zn trigonal pyramids, corners with two equivalent O(19)V3Zn trigonal pyramids,  an edgeedge with one O(6)V3Zn trigonal pyramid, and  an edgeedge with one O(9)V3Zn trigonal pyramid. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one V(1), one V(4), one V(5), and one Zn(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one V(5), one V(6), one V(8), and one Zn(2) atom. In the thirteenth O site, O(13) is bonded to one V(10), one V(6), one V(8), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid,  an edgeedge with one O(15)V3Zn trigonal pyramid, and  an edgeedge with one O(19)V3Zn trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Mg(1), one V(10), one V(7), one V(9), and one Zn(4) atom to form OMgV3Zn square pyramids that share  a cornercorner with one O(10)V3Zn tetrahedra, corners with three equivalent O(24)MgV3Zn trigonal bipyramids,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  an edgeedge with one O(23)MgV3Zn square pyramid, edges with two equivalent O(18)MgV3Zn square pyramids, edges with two equivalent O(20)MgV3Zn square pyramids, and  an edgeedge with one O(21)MgV3Zn trigonal bipyramid. In the fifteenth O site, O(15) is bonded to one V(10), one V(3), one V(6), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid, corners with two equivalent O(9)V3Zn trigonal pyramids,  an edgeedge with one O(13)V3Zn trigonal pyramid, and  an edgeedge with one O(19)V3Zn trigonal pyramid. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one V(3), one V(6), one V(8), and one Zn(5) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one V(11), one V(7), one V(9), and one Zn(1) atom. In the eighteenth O site, O(18) is bonded to one Mg(1), one V(10), one V(11), one V(7), and one Zn(4) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(23)MgV3Zn square pyramids,  a cornercorner with one O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid, edges with two equivalent O(14)MgV3Zn square pyramids, edges with two equivalent O(20)MgV3Zn square pyramids,  an edgeedge with one O(21)MgV3Zn trigonal bipyramid, and  an edgeedge with one O(24)MgV3Zn trigonal bipyramid. In the nineteenth O site, O(19) is bonded to one V(10), one V(3), one V(8), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid, corners with two equivalent O(6)V3Zn trigonal pyramids,  an edgeedge with one O(13)V3Zn trigonal pyramid, and  an edgeedge with one O(15)V3Zn trigonal pyramid. In the twentieth O site, O(20) is bonded to one Mg(1), one V(10), one V(11), one V(9), and one Zn(4) atom to form OMgV3Zn square pyramids that share  a cornercorner with one O(10)V3Zn tetrahedra, corners with three equivalent O(21)MgV3Zn trigonal bipyramids,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  an edgeedge with one O(23)MgV3Zn square pyramid, edges with two equivalent O(14)MgV3Zn square pyramids, edges with two equivalent O(18)MgV3Zn square pyramids, and  an edgeedge with one O(24)MgV3Zn trigonal bipyramid. In the twenty-first O site, O(21) is bonded to one Mg(1), one V(11), one V(12), one V(9), and one Zn(3) atom to form OMgV3Zn trigonal bipyramids that share corners with three equivalent O(20)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(14)MgV3Zn square pyramid,  an edgeedge with one O(18)MgV3Zn square pyramid, edges with two equivalent O(23)MgV3Zn square pyramids, and edges with two equivalent O(24)MgV3Zn trigonal bipyramids. In the twenty-second O site, O(22) is bonded in a distorted rectangular see-saw-like geometry to one V(11), one V(7), one V(9), and one Zn(6) atom. In the twenty-third O site, O(23) is bonded to one Mg(1), one V(11), one V(12), one V(7), and one Zn(3) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(18)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(14)MgV3Zn square pyramid,  an edgeedge with one O(20)MgV3Zn square pyramid, edges with two equivalent O(21)MgV3Zn trigonal bipyramids, and edges with two equivalent O(24)MgV3Zn trigonal bipyramids. In the twenty-fourth O site, O(24) is bonded to one Mg(1), one V(12), one V(7), one V(9), and one Zn(3) atom to form OMgV3Zn trigonal bipyramids that share corners with three equivalent O(14)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(18)MgV3Zn square pyramid,  an edgeedge with one O(20)MgV3Zn square pyramid, edges with two equivalent O(23)MgV3Zn square pyramids, and edges with two equivalent O(21)MgV3Zn trigonal bipyramids.
MgV12Zn6O24 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(14), one O(18), one O(20), one O(21), one O(23), and one O(24) atom to form MgO6 octahedra that share corners with three equivalent V(10)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, edges with two equivalent V(11)O6 octahedra, edges with two equivalent V(7)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. The Mg(1)-O(14) bond length is 2.10 Å. The Mg(1)-O(18) bond length is 2.17 Å. The Mg(1)-O(20) bond length is 2.10 Å. The Mg(1)-O(21) bond length is 2.10 Å. The Mg(1)-O(23) bond length is 2.09 Å. The Mg(1)-O(24) bond length is 2.12 Å. There are twelve inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(11), one O(2), one O(3), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The V(1)-O(1) bond length is 2.08 Å. The V(1)-O(11) bond length is 2.08 Å. The V(1)-O(2) bond length is 2.04 Å. The V(1)-O(3) bond length is 2.07 Å. The V(1)-O(7) bond length is 2.07 Å. The V(1)-O(8) bond length is 2.02 Å. In the second V site, V(2) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The V(2)-O(2) bond length is 2.04 Å. The V(2)-O(3) bond length is 2.07 Å. The V(2)-O(4) bond length is 2.07 Å. The V(2)-O(5) bond length is 2.07 Å. The V(2)-O(7) bond length is 2.07 Å. The V(2)-O(8) bond length is 2.03 Å. In the third V site, V(3) is bonded to one O(10), one O(15), one O(16), one O(19), one O(6), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(6)O6 octahedra, and edges with two equivalent V(8)O6 octahedra. The V(3)-O(10) bond length is 2.03 Å. The V(3)-O(15) bond length is 2.05 Å. The V(3)-O(16) bond length is 2.02 Å. The V(3)-O(19) bond length is 2.12 Å. The V(3)-O(6) bond length is 2.10 Å. The V(3)-O(9) bond length is 2.04 Å. In the fourth V site, V(4) is bonded to one O(1), one O(11), one O(2), one O(4), one O(5), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Zn(2)O4 tetrahedra, corners with two equivalent Zn(1)O4 tetrahedra, corners with two equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, and edges with two equivalent V(2)O6 octahedra. The V(4)-O(1) bond length is 2.07 Å. The V(4)-O(11) bond length is 2.10 Å. The V(4)-O(2) bond length is 2.03 Å. The V(4)-O(4) bond length is 2.09 Å. The V(4)-O(5) bond length is 2.11 Å. The V(4)-O(8) bond length is 1.98 Å. In the fifth V site, V(5) is bonded to one O(11), one O(12), one O(5), one O(6), one O(7), and one O(9) atom to form VO6 octahedra that share corners with three equivalent Zn(2)O4 tetrahedra, corners with three equivalent Zn(5)O4 tetrahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and  an edgeedge with one V(8)O6 octahedra. The V(5)-O(11) bond length is 2.03 Å. The V(5)-O(12) bond length is 2.06 Å. The V(5)-O(5) bond length is 2.04 Å. The V(5)-O(6) bond length is 2.05 Å. The V(5)-O(7) bond length is 2.08 Å. The V(5)-O(9) bond length is 2.10 Å. In the sixth V site, V(6) is bonded to one O(10), one O(12), one O(13), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(3)O6 octahedra, and edges with two equivalent V(8)O6 octahedra. The V(6)-O(10) bond length is 2.04 Å. The V(6)-O(12) bond length is 2.04 Å. The V(6)-O(13) bond length is 2.05 Å. The V(6)-O(15) bond length is 2.10 Å. The V(6)-O(16) bond length is 2.05 Å. The V(6)-O(9) bond length is 2.06 Å. In the seventh V site, V(7) is bonded to one O(14), one O(17), one O(18), one O(22), one O(23), and one O(24) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(11)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. The V(7)-O(14) bond length is 2.12 Å. The V(7)-O(17) bond length is 2.03 Å. The V(7)-O(18) bond length is 2.13 Å. The V(7)-O(22) bond length is 2.05 Å. The V(7)-O(23) bond length is 2.11 Å. The V(7)-O(24) bond length is 2.04 Å. In the eighth V site, V(8) is bonded to one O(10), one O(12), one O(13), one O(16), one O(19), and one O(6) atom to form VO6 octahedra that share  a cornercorner with one Zn(5)O4 tetrahedra, corners with two equivalent Zn(2)O4 tetrahedra, corners with two equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, edges with two equivalent V(3)O6 octahedra, and edges with two equivalent V(6)O6 octahedra. The V(8)-O(10) bond length is 2.02 Å. The V(8)-O(12) bond length is 2.10 Å. The V(8)-O(13) bond length is 2.13 Å. The V(8)-O(16) bond length is 2.01 Å. The V(8)-O(19) bond length is 2.04 Å. The V(8)-O(6) bond length is 2.05 Å. In the ninth V site, V(9) is bonded to one O(14), one O(17), one O(20), one O(21), one O(22), and one O(24) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(11)O6 octahedra, and edges with two equivalent V(7)O6 octahedra. The V(9)-O(14) bond length is 2.12 Å. The V(9)-O(17) bond length is 2.15 Å. The V(9)-O(20) bond length is 2.12 Å. The V(9)-O(21) bond length is 2.12 Å. The V(9)-O(22) bond length is 2.12 Å. The V(9)-O(24) bond length is 2.11 Å. In the tenth V site, V(10) is bonded to one O(13), one O(14), one O(15), one O(18), one O(19), and one O(20) atom to form VO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Zn(6)O4 tetrahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. The V(10)-O(13) bond length is 2.09 Å. The V(10)-O(14) bond length is 2.13 Å. The V(10)-O(15) bond length is 2.13 Å. The V(10)-O(18) bond length is 2.27 Å. The V(10)-O(19) bond length is 2.09 Å. The V(10)-O(20) bond length is 2.13 Å. In the eleventh V site, V(11) is bonded to one O(17), one O(18), one O(20), one O(21), one O(22), and one O(23) atom to form VO6 octahedra that share  a cornercorner with one Zn(1)O4 tetrahedra,  a cornercorner with one Zn(6)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent V(7)O6 octahedra, and edges with two equivalent V(9)O6 octahedra. The V(11)-O(17) bond length is 2.03 Å. The V(11)-O(18) bond length is 2.11 Å. The V(11)-O(20) bond length is 2.13 Å. The V(11)-O(21) bond length is 2.07 Å. The V(11)-O(22) bond length is 2.04 Å. The V(11)-O(23) bond length is 2.08 Å. In the twelfth V site, V(12) is bonded in a rectangular see-saw-like geometry to one O(21), one O(23), one O(24), and one O(8) atom. The V(12)-O(21) bond length is 2.14 Å. The V(12)-O(23) bond length is 2.18 Å. The V(12)-O(24) bond length is 2.13 Å. The V(12)-O(8) bond length is 1.93 Å. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to one O(1), one O(17), one O(3), and one O(4) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, and corners with three equivalent Zn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. The Zn(1)-O(1) bond length is 2.02 Å. The Zn(1)-O(17) bond length is 2.17 Å. The Zn(1)-O(3) bond length is 1.99 Å. The Zn(1)-O(4) bond length is 2.01 Å. In the second Zn site, Zn(2) is bonded to one O(12), one O(2), one O(6), and one O(9) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(4)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with two equivalent V(6)O6 octahedra, corners with two equivalent V(8)O6 octahedra, and corners with three equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. The Zn(2)-O(12) bond length is 2.00 Å. The Zn(2)-O(2) bond length is 2.02 Å. The Zn(2)-O(6) bond length is 2.00 Å. The Zn(2)-O(9) bond length is 1.99 Å. In the third Zn site, Zn(3) is bonded to one O(1), one O(21), one O(23), one O(24), one O(3), and one O(4) atom to form ZnO6 octahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Zn(1)O4 tetrahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-8°. The Zn(3)-O(1) bond length is 2.11 Å. The Zn(3)-O(21) bond length is 2.23 Å. The Zn(3)-O(23) bond length is 2.31 Å. The Zn(3)-O(24) bond length is 2.32 Å. The Zn(3)-O(3) bond length is 2.16 Å. The Zn(3)-O(4) bond length is 2.11 Å. In the fourth Zn site, Zn(4) is bonded in a distorted rectangular see-saw-like geometry to one O(10), one O(14), one O(18), and one O(20) atom. The Zn(4)-O(10) bond length is 1.83 Å. The Zn(4)-O(14) bond length is 2.18 Å. The Zn(4)-O(18) bond length is 2.04 Å. The Zn(4)-O(20) bond length is 2.10 Å. In the fifth Zn site, Zn(5) is bonded to one O(11), one O(16), one O(5), and one O(7) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  a cornercorner with one V(8)O6 octahedra, corners with two equivalent V(1)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, and corners with three equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. The Zn(5)-O(11) bond length is 1.99 Å. The Zn(5)-O(16) bond length is 2.05 Å. The Zn(5)-O(5) bond length is 1.99 Å. The Zn(5)-O(7) bond length is 1.98 Å. In the sixth Zn site, Zn(6) is bonded to one O(13), one O(15), one O(19), and one O(22) atom to form ZnO4 tetrahedra that share  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with two equivalent V(6)O6 octahedra, corners with two equivalent V(8)O6 octahedra, and corners with three equivalent V(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. The Zn(6)-O(13) bond length is 2.03 Å. The Zn(6)-O(15) bond length is 2.03 Å. The Zn(6)-O(19) bond length is 2.03 Å. The Zn(6)-O(22) bond length is 2.07 Å. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one V(1), one V(4), one Zn(1), and one Zn(3) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one V(1), one V(2), one V(4), and one Zn(2) atom. In the third O site, O(3) is bonded to one V(1), one V(2), one Zn(1), and one Zn(3) atom to form distorted OV2Zn2 trigonal pyramids that share  a cornercorner with one O(23)MgV3Zn square pyramid, corners with two equivalent O(8)V4 tetrahedra,  a cornercorner with one O(21)MgV3Zn trigonal bipyramid,  a cornercorner with one O(24)MgV3Zn trigonal bipyramid,  a cornercorner with one O(5)V3Zn trigonal pyramid, and corners with two equivalent O(7)V3Zn trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one V(2), one V(4), one Zn(1), and one Zn(3) atom. In the fifth O site, O(5) is bonded to one V(2), one V(4), one V(5), and one Zn(5) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(7)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid,  an edgeedge with one O(8)V4 tetrahedra, and  an edgeedge with one O(7)V3Zn trigonal pyramid. In the sixth O site, O(6) is bonded to one V(3), one V(5), one V(8), and one Zn(2) atom to form a mixture of distorted edge and corner-sharing OV3Zn trigonal pyramids. In the seventh O site, O(7) is bonded to one V(1), one V(2), one V(5), and one Zn(5) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(5)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid, corners with two equivalent O(3)V2Zn2 trigonal pyramids,  an edgeedge with one O(8)V4 tetrahedra, and  an edgeedge with one O(5)V3Zn trigonal pyramid. In the eighth O site, O(8) is bonded to one V(1), one V(12), one V(2), and one V(4) atom to form OV4 tetrahedra that share  a cornercorner with one O(23)MgV3Zn square pyramid,  a cornercorner with one O(21)MgV3Zn trigonal bipyramid,  a cornercorner with one O(24)MgV3Zn trigonal bipyramid, corners with two equivalent O(3)V2Zn2 trigonal pyramids,  an edgeedge with one O(5)V3Zn trigonal pyramid, and  an edgeedge with one O(7)V3Zn trigonal pyramid. In the ninth O site, O(9) is bonded to one V(3), one V(5), one V(6), and one Zn(2) atom to form a mixture of distorted edge and corner-sharing OV3Zn trigonal pyramids. In the tenth O site, O(10) is bonded to one V(3), one V(6), one V(8), and one Zn(4) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(13)V3Zn trigonal pyramids, corners with two equivalent O(15)V3Zn trigonal pyramids, corners with two equivalent O(19)V3Zn trigonal pyramids,  an edgeedge with one O(6)V3Zn trigonal pyramid, and  an edgeedge with one O(9)V3Zn trigonal pyramid. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one V(1), one V(4), one V(5), and one Zn(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one V(5), one V(6), one V(8), and one Zn(2) atom. In the thirteenth O site, O(13) is bonded to one V(10), one V(6), one V(8), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid,  an edgeedge with one O(15)V3Zn trigonal pyramid, and  an edgeedge with one O(19)V3Zn trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Mg(1), one V(10), one V(7), one V(9), and one Zn(4) atom to form OMgV3Zn square pyramids that share  a cornercorner with one O(10)V3Zn tetrahedra, corners with three equivalent O(24)MgV3Zn trigonal bipyramids,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  an edgeedge with one O(23)MgV3Zn square pyramid, edges with two equivalent O(18)MgV3Zn square pyramids, edges with two equivalent O(20)MgV3Zn square pyramids, and  an edgeedge with one O(21)MgV3Zn trigonal bipyramid. In the fifteenth O site, O(15) is bonded to one V(10), one V(3), one V(6), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  a cornercorner with one O(6)V3Zn trigonal pyramid, corners with two equivalent O(9)V3Zn trigonal pyramids,  an edgeedge with one O(13)V3Zn trigonal pyramid, and  an edgeedge with one O(19)V3Zn trigonal pyramid. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one V(3), one V(6), one V(8), and one Zn(5) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one V(11), one V(7), one V(9), and one Zn(1) atom. In the eighteenth O site, O(18) is bonded to one Mg(1), one V(10), one V(11), one V(7), and one Zn(4) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(23)MgV3Zn square pyramids,  a cornercorner with one O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid, edges with two equivalent O(14)MgV3Zn square pyramids, edges with two equivalent O(20)MgV3Zn square pyramids,  an edgeedge with one O(21)MgV3Zn trigonal bipyramid, and  an edgeedge with one O(24)MgV3Zn trigonal bipyramid. In the nineteenth O site, O(19) is bonded to one V(10), one V(3), one V(8), and one Zn(6) atom to form distorted OV3Zn trigonal pyramids that share  a cornercorner with one O(14)MgV3Zn square pyramid,  a cornercorner with one O(18)MgV3Zn square pyramid,  a cornercorner with one O(20)MgV3Zn square pyramid, corners with two equivalent O(10)V3Zn tetrahedra,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(9)V3Zn trigonal pyramid, corners with two equivalent O(6)V3Zn trigonal pyramids,  an edgeedge with one O(13)V3Zn trigonal pyramid, and  an edgeedge with one O(15)V3Zn trigonal pyramid. In the twentieth O site, O(20) is bonded to one Mg(1), one V(10), one V(11), one V(9), and one Zn(4) atom to form OMgV3Zn square pyramids that share  a cornercorner with one O(10)V3Zn tetrahedra, corners with three equivalent O(21)MgV3Zn trigonal bipyramids,  a cornercorner with one O(13)V3Zn trigonal pyramid,  a cornercorner with one O(15)V3Zn trigonal pyramid,  a cornercorner with one O(19)V3Zn trigonal pyramid,  an edgeedge with one O(23)MgV3Zn square pyramid, edges with two equivalent O(14)MgV3Zn square pyramids, edges with two equivalent O(18)MgV3Zn square pyramids, and  an edgeedge with one O(24)MgV3Zn trigonal bipyramid. In the twenty-first O site, O(21) is bonded to one Mg(1), one V(11), one V(12), one V(9), and one Zn(3) atom to form OMgV3Zn trigonal bipyramids that share corners with three equivalent O(20)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(14)MgV3Zn square pyramid,  an edgeedge with one O(18)MgV3Zn square pyramid, edges with two equivalent O(23)MgV3Zn square pyramids, and edges with two equivalent O(24)MgV3Zn trigonal bipyramids. In the twenty-second O site, O(22) is bonded in a distorted rectangular see-saw-like geometry to one V(11), one V(7), one V(9), and one Zn(6) atom. In the twenty-third O site, O(23) is bonded to one Mg(1), one V(11), one V(12), one V(7), and one Zn(3) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(18)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(14)MgV3Zn square pyramid,  an edgeedge with one O(20)MgV3Zn square pyramid, edges with two equivalent O(21)MgV3Zn trigonal bipyramids, and edges with two equivalent O(24)MgV3Zn trigonal bipyramids. In the twenty-fourth O site, O(24) is bonded to one Mg(1), one V(12), one V(7), one V(9), and one Zn(3) atom to form OMgV3Zn trigonal bipyramids that share corners with three equivalent O(14)MgV3Zn square pyramids,  a cornercorner with one O(8)V4 tetrahedra,  a cornercorner with one O(3)V2Zn2 trigonal pyramid,  an edgeedge with one O(18)MgV3Zn square pyramid,  an edgeedge with one O(20)MgV3Zn square pyramid, edges with two equivalent O(23)MgV3Zn square pyramids, and edges with two equivalent O(21)MgV3Zn trigonal bipyramids.