MgV12Zn6O24 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(7) atom to form MgO6 octahedra that share corners with three equivalent V(5)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. 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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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(4)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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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 Mg(1)O6 octahedra, corners with three equivalent Zn(2)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 corner-sharing octahedral tilt angles range from 3-5°. 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(4)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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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(4)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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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 Zn(4)O4 tetrahedra, 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. 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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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 to one O(21), one O(23), one O(24), and one O(8) atom to form VO4 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(11)O6 octahedra, corners with two equivalent V(7)O6 octahedra, corners with two equivalent V(9)O6 octahedra, and corners with three equivalent Zn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-63°. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 4-coordinate geometry to one O(1), one O(17), one O(3), and one O(4) atom. 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 57-60°. 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 V(12)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 1-3°. In the fourth Zn site, Zn(4) is bonded to one O(10), one O(14), one O(18), and one O(20) 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(11)O6 octahedra, corners with two equivalent V(7)O6 octahedra, corners with two equivalent V(9)O6 octahedra, and corners with three equivalent V(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. In the fifth Zn site, Zn(5) is bonded in a distorted rectangular see-saw-like geometry to one O(11), one O(16), one O(5), and one O(7) atom. 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 55-62°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one V(1), one V(4), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(11)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(5)MgV3Zn square pyramid,  an edgeedge with one O(7)MgV3Zn square pyramid, edges with two equivalent O(3)MgV2Zn2 square pyramids, edges with two equivalent O(4)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the second O site, O(2) is bonded to one V(1), one V(2), one V(4), and one Zn(2) atom to form distorted OV3Zn trigonal pyramids that share corners with two equivalent O(11)MgV3Zn square pyramids, corners with two equivalent O(5)MgV3Zn square pyramids, corners with two equivalent O(7)MgV3Zn square pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(3)MgV2Zn2 square pyramid, and  an edgeedge with one O(4)MgV2Zn2 square pyramid. In the third O site, O(3) is bonded to one Mg(1), one V(1), one V(2), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(7)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(11)MgV3Zn square pyramid,  an edgeedge with one O(5)MgV3Zn square pyramid, edges with two equivalent O(1)MgV2Zn2 square pyramids, edges with two equivalent O(4)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one V(2), one V(4), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(5)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(11)MgV3Zn square pyramid,  an edgeedge with one O(7)MgV3Zn square pyramid, edges with two equivalent O(1)MgV2Zn2 square pyramids, edges with two equivalent O(3)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the fifth O site, O(5) is bonded to one Mg(1), one V(2), one V(4), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(4)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(3)MgV2Zn2 square pyramid, edges with two equivalent O(11)MgV3Zn square pyramids, and edges with two equivalent O(7)MgV3Zn square pyramids. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one V(3), one V(5), one V(8), and one Zn(2) atom. In the seventh O site, O(7) is bonded to one Mg(1), one V(1), one V(2), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(3)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(4)MgV2Zn2 square pyramid, edges with two equivalent O(11)MgV3Zn square pyramids, and edges with two equivalent O(5)MgV3Zn square pyramids. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one V(1), one V(12), one V(2), and one V(4) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one V(3), one V(5), one V(6), and one Zn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one V(3), one V(6), one V(8), and one Zn(4) atom. In the eleventh O site, O(11) is bonded to one Mg(1), one V(1), one V(4), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(1)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(3)MgV2Zn2 square pyramid,  an edgeedge with one O(4)MgV2Zn2 square pyramid, edges with two equivalent O(5)MgV3Zn square pyramids, and edges with two equivalent O(7)MgV3Zn square pyramids. 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 in a rectangular see-saw-like geometry to one V(10), one V(6), one V(8), and one Zn(6) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one V(10), one V(7), one V(9), and one Zn(4) atom. 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 a mixture of distorted corner and edge-sharing OV3Zn trigonal pyramids. In the sixteenth O site, O(16) is bonded to one V(3), one V(6), one V(8), and one Zn(5) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(11)MgV3Zn square pyramid,  a cornercorner with one O(5)MgV3Zn square pyramid,  a cornercorner with one O(7)MgV3Zn square pyramid, and  an edgeedge with one O(15)V3Zn trigonal pyramid. In the seventeenth O site, O(17) is bonded to one V(11), one V(7), one V(9), and one Zn(1) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(1)MgV2Zn2 square pyramid,  a cornercorner with one O(3)MgV2Zn2 square pyramid,  a cornercorner with one O(4)MgV2Zn2 square pyramid, and corners with three equivalent O(22)V3Zn trigonal pyramids. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one V(10), one V(11), one V(7), and one Zn(4) atom. In the nineteenth O site, O(19) is bonded in a rectangular see-saw-like geometry to one V(10), one V(3), one V(8), and one Zn(6) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one V(10), one V(11), one V(9), and one Zn(4) atom. In the twenty-first O site, O(21) is bonded in a rectangular see-saw-like geometry to one V(11), one V(12), one V(9), and one Zn(3) atom. In the twenty-second O site, O(22) is bonded to one V(11), one V(7), one V(9), and one Zn(6) atom to form distorted corner-sharing OV3Zn trigonal pyramids. In the twenty-third O site, O(23) is bonded in a rectangular see-saw-like geometry to one V(11), one V(12), one V(7), and one Zn(3) atom. In the twenty-fourth O site, O(24) is bonded in a rectangular see-saw-like geometry to one V(12), one V(7), one V(9), and one Zn(3) atom.
MgV12Zn6O24 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(7) atom to form MgO6 octahedra that share corners with three equivalent V(5)O6 octahedra, corners with three equivalent Zn(3)O6 octahedra, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(2)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-5°. The Mg(1)-O(1) bond length is 2.14 Å. The Mg(1)-O(11) bond length is 2.17 Å. The Mg(1)-O(3) bond length is 2.10 Å. The Mg(1)-O(4) bond length is 2.11 Å. The Mg(1)-O(5) bond length is 2.13 Å. The Mg(1)-O(7) bond length is 2.13 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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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 2.11 Å. The V(1)-O(11) bond length is 2.13 Å. The V(1)-O(2) bond length is 2.07 Å. The V(1)-O(3) bond length is 2.14 Å. The V(1)-O(7) bond length is 2.15 Å. The V(1)-O(8) bond length is 2.12 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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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 2.01 Å. The V(2)-O(3) bond length is 2.09 Å. The V(2)-O(4) bond length is 2.09 Å. The V(2)-O(5) bond length is 2.09 Å. The V(2)-O(7) bond length is 2.09 Å. The V(2)-O(8) bond length is 2.11 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(4)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 2.10 Å. The V(3)-O(16) bond length is 2.02 Å. The V(3)-O(19) bond length is 2.07 Å. The V(3)-O(6) bond length is 2.10 Å. The V(3)-O(9) bond length is 2.14 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 V(12)O4 tetrahedra,  a cornercorner with one Zn(2)O4 tetrahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one Zn(3)O6 octahedra, edges with two equivalent Mg(1)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 2.12 Å. The V(4)-O(11) bond length is 2.14 Å. The V(4)-O(2) bond length is 2.09 Å. The V(4)-O(4) bond length is 2.14 Å. The V(4)-O(5) bond length is 2.15 Å. The V(4)-O(8) bond length is 2.13 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 Mg(1)O6 octahedra, corners with three equivalent Zn(2)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 corner-sharing octahedral tilt angles range from 3-5°. The V(5)-O(11) bond length is 2.16 Å. The V(5)-O(12) bond length is 2.03 Å. The V(5)-O(5) bond length is 2.18 Å. The V(5)-O(6) bond length is 2.02 Å. The V(5)-O(7) bond length is 2.21 Å. The V(5)-O(9) bond length is 2.06 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(4)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 2.03 Å. The V(6)-O(12) bond length is 2.08 Å. The V(6)-O(13) bond length is 2.06 Å. The V(6)-O(15) bond length is 2.05 Å. The V(6)-O(16) bond length is 2.02 Å. The V(6)-O(9) bond length is 2.08 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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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 2.02 Å. The V(7)-O(17) bond length is 2.03 Å. The V(7)-O(18) bond length is 2.08 Å. The V(7)-O(22) bond length is 2.02 Å. The V(7)-O(23) bond length is 2.15 Å. The V(7)-O(24) bond length is 2.06 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(4)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 2.05 Å. The V(8)-O(12) bond length is 2.15 Å. The V(8)-O(13) bond length is 2.13 Å. The V(8)-O(16) bond length is 2.04 Å. The V(8)-O(19) bond length is 2.09 Å. The V(8)-O(6) bond length is 2.12 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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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 2.06 Å. The V(9)-O(17) bond length is 2.03 Å. The V(9)-O(20) bond length is 2.03 Å. The V(9)-O(21) bond length is 2.07 Å. The V(9)-O(22) bond length is 2.02 Å. The V(9)-O(24) bond length is 2.13 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 Zn(4)O4 tetrahedra, 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 V(10)-O(13) bond length is 2.01 Å. The V(10)-O(14) bond length is 2.09 Å. The V(10)-O(15) bond length is 2.06 Å. The V(10)-O(18) bond length is 2.09 Å. The V(10)-O(19) bond length is 2.03 Å. The V(10)-O(20) bond length is 2.07 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(6)O4 tetrahedra, corners with two equivalent V(12)O4 tetrahedra, corners with two equivalent Zn(4)O4 tetrahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one Zn(3)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 2.02 Å. The V(11)-O(20) bond length is 2.09 Å. The V(11)-O(21) bond length is 2.14 Å. The V(11)-O(22) bond length is 2.02 Å. The V(11)-O(23) bond length is 2.07 Å. In the twelfth V site, V(12) is bonded to one O(21), one O(23), one O(24), and one O(8) atom to form VO4 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(11)O6 octahedra, corners with two equivalent V(7)O6 octahedra, corners with two equivalent V(9)O6 octahedra, and corners with three equivalent Zn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-63°. The V(12)-O(21) bond length is 1.98 Å. The V(12)-O(23) bond length is 1.98 Å. The V(12)-O(24) bond length is 1.98 Å. The V(12)-O(8) bond length is 1.97 Å. There are six inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 4-coordinate geometry to one O(1), one O(17), one O(3), and one O(4) atom. The Zn(1)-O(1) bond length is 2.05 Å. The Zn(1)-O(17) bond length is 1.85 Å. The Zn(1)-O(3) bond length is 2.08 Å. The Zn(1)-O(4) bond length is 2.09 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 57-60°. The Zn(2)-O(12) bond length is 2.02 Å. The Zn(2)-O(2) bond length is 2.07 Å. The Zn(2)-O(6) bond length is 2.03 Å. The Zn(2)-O(9) bond length is 2.01 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 V(12)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 1-3°. The Zn(3)-O(1) bond length is 2.20 Å. The Zn(3)-O(21) bond length is 2.16 Å. The Zn(3)-O(23) bond length is 2.17 Å. The Zn(3)-O(24) bond length is 2.19 Å. The Zn(3)-O(3) bond length is 2.20 Å. The Zn(3)-O(4) bond length is 2.19 Å. In the fourth Zn site, Zn(4) is bonded to one O(10), one O(14), one O(18), and one O(20) 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(11)O6 octahedra, corners with two equivalent V(7)O6 octahedra, corners with two equivalent V(9)O6 octahedra, and corners with three equivalent V(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. The Zn(4)-O(10) bond length is 1.98 Å. The Zn(4)-O(14) bond length is 2.02 Å. The Zn(4)-O(18) bond length is 2.00 Å. The Zn(4)-O(20) bond length is 2.01 Å. In the fifth Zn site, Zn(5) is bonded in a distorted rectangular see-saw-like geometry to one O(11), one O(16), one O(5), and one O(7) atom. The Zn(5)-O(11) bond length is 2.09 Å. The Zn(5)-O(16) bond length is 1.82 Å. The Zn(5)-O(5) bond length is 2.14 Å. The Zn(5)-O(7) bond length is 2.09 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 55-62°. The Zn(6)-O(13) bond length is 1.98 Å. The Zn(6)-O(15) bond length is 1.96 Å. The Zn(6)-O(19) bond length is 1.98 Å. The Zn(6)-O(22) bond length is 2.08 Å. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one V(1), one V(4), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(11)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(5)MgV3Zn square pyramid,  an edgeedge with one O(7)MgV3Zn square pyramid, edges with two equivalent O(3)MgV2Zn2 square pyramids, edges with two equivalent O(4)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the second O site, O(2) is bonded to one V(1), one V(2), one V(4), and one Zn(2) atom to form distorted OV3Zn trigonal pyramids that share corners with two equivalent O(11)MgV3Zn square pyramids, corners with two equivalent O(5)MgV3Zn square pyramids, corners with two equivalent O(7)MgV3Zn square pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(3)MgV2Zn2 square pyramid, and  an edgeedge with one O(4)MgV2Zn2 square pyramid. In the third O site, O(3) is bonded to one Mg(1), one V(1), one V(2), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(7)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(11)MgV3Zn square pyramid,  an edgeedge with one O(5)MgV3Zn square pyramid, edges with two equivalent O(1)MgV2Zn2 square pyramids, edges with two equivalent O(4)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the fourth O site, O(4) is bonded to one Mg(1), one V(2), one V(4), one Zn(1), and one Zn(3) atom to form OMgV2Zn2 square pyramids that share corners with three equivalent O(5)MgV3Zn square pyramids,  a cornercorner with one O(17)V3Zn tetrahedra,  an edgeedge with one O(11)MgV3Zn square pyramid,  an edgeedge with one O(7)MgV3Zn square pyramid, edges with two equivalent O(1)MgV2Zn2 square pyramids, edges with two equivalent O(3)MgV2Zn2 square pyramids, and  an edgeedge with one O(2)V3Zn trigonal pyramid. In the fifth O site, O(5) is bonded to one Mg(1), one V(2), one V(4), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(4)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(3)MgV2Zn2 square pyramid, edges with two equivalent O(11)MgV3Zn square pyramids, and edges with two equivalent O(7)MgV3Zn square pyramids. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one V(3), one V(5), one V(8), and one Zn(2) atom. In the seventh O site, O(7) is bonded to one Mg(1), one V(1), one V(2), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(3)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(1)MgV2Zn2 square pyramid,  an edgeedge with one O(4)MgV2Zn2 square pyramid, edges with two equivalent O(11)MgV3Zn square pyramids, and edges with two equivalent O(5)MgV3Zn square pyramids. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one V(1), one V(12), one V(2), and one V(4) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one V(3), one V(5), one V(6), and one Zn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one V(3), one V(6), one V(8), and one Zn(4) atom. In the eleventh O site, O(11) is bonded to one Mg(1), one V(1), one V(4), one V(5), and one Zn(5) atom to form OMgV3Zn square pyramids that share corners with three equivalent O(1)MgV2Zn2 square pyramids,  a cornercorner with one O(16)V3Zn tetrahedra, corners with two equivalent O(2)V3Zn trigonal pyramids,  an edgeedge with one O(3)MgV2Zn2 square pyramid,  an edgeedge with one O(4)MgV2Zn2 square pyramid, edges with two equivalent O(5)MgV3Zn square pyramids, and edges with two equivalent O(7)MgV3Zn square pyramids. 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 in a rectangular see-saw-like geometry to one V(10), one V(6), one V(8), and one Zn(6) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one V(10), one V(7), one V(9), and one Zn(4) atom. 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 a mixture of distorted corner and edge-sharing OV3Zn trigonal pyramids. In the sixteenth O site, O(16) is bonded to one V(3), one V(6), one V(8), and one Zn(5) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(11)MgV3Zn square pyramid,  a cornercorner with one O(5)MgV3Zn square pyramid,  a cornercorner with one O(7)MgV3Zn square pyramid, and  an edgeedge with one O(15)V3Zn trigonal pyramid. In the seventeenth O site, O(17) is bonded to one V(11), one V(7), one V(9), and one Zn(1) atom to form distorted OV3Zn tetrahedra that share  a cornercorner with one O(1)MgV2Zn2 square pyramid,  a cornercorner with one O(3)MgV2Zn2 square pyramid,  a cornercorner with one O(4)MgV2Zn2 square pyramid, and corners with three equivalent O(22)V3Zn trigonal pyramids. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one V(10), one V(11), one V(7), and one Zn(4) atom. In the nineteenth O site, O(19) is bonded in a rectangular see-saw-like geometry to one V(10), one V(3), one V(8), and one Zn(6) atom. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one V(10), one V(11), one V(9), and one Zn(4) atom. In the twenty-first O site, O(21) is bonded in a rectangular see-saw-like geometry to one V(11), one V(12), one V(9), and one Zn(3) atom. In the twenty-second O site, O(22) is bonded to one V(11), one V(7), one V(9), and one Zn(6) atom to form distorted corner-sharing OV3Zn trigonal pyramids. In the twenty-third O site, O(23) is bonded in a rectangular see-saw-like geometry to one V(11), one V(12), one V(7), and one Zn(3) atom. In the twenty-fourth O site, O(24) is bonded in a rectangular see-saw-like geometry to one V(12), one V(7), one V(9), and one Zn(3) atom.