K4V2O9 crystallizes in the orthorhombic Cmcm space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(4), and four equivalent O(2) atoms to form KO7 pentagonal bipyramids that share corners with two equivalent V(1)O4 tetrahedra, edges with two equivalent K(1)O7 pentagonal bipyramids, and edges with two equivalent V(1)O4 tetrahedra. In the second K site, K(2) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(4), and four equivalent O(1) atoms. In the third K site, K(3) is bonded in a 9-coordinate geometry to one O(3), two equivalent O(2), two equivalent O(4), and four equivalent O(1) atoms. V(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form VO4 tetrahedra that share  a cornercorner with one K(1)O7 pentagonal bipyramid,  a cornercorner with one V(1)O4 tetrahedra, and  an edgeedge with one K(1)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(2) is bonded in a distorted single-bond geometry to two equivalent K(1), two equivalent K(3), and one V(1) atom. In the second O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), two equivalent K(3), and two equivalent V(1) atoms. In the third O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), and two equivalent K(3) atoms. In the fourth O site, O(1) is bonded in a distorted single-bond geometry to one K(2), two equivalent K(3), and one V(1) atom.
K4V2O9 crystallizes in the orthorhombic Cmcm space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(4), and four equivalent O(2) atoms to form KO7 pentagonal bipyramids that share corners with two equivalent V(1)O4 tetrahedra, edges with two equivalent K(1)O7 pentagonal bipyramids, and edges with two equivalent V(1)O4 tetrahedra. The K(1)-O(3) bond length is 2.91 Å. Both K(1)-O(4) bond lengths are 3.03 Å. There are two shorter (2.79 Å) and two longer (2.85 Å) K(1)-O(2) bond lengths. In the second K site, K(2) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(4), and four equivalent O(1) atoms. The K(2)-O(3) bond length is 3.08 Å. Both K(2)-O(4) bond lengths are 2.70 Å. All K(2)-O(1) bond lengths are 2.87 Å. In the third K site, K(3) is bonded in a 9-coordinate geometry to one O(3), two equivalent O(2), two equivalent O(4), and four equivalent O(1) atoms. The K(3)-O(3) bond length is 3.13 Å. Both K(3)-O(2) bond lengths are 3.02 Å. There is one shorter (2.94 Å) and one longer (3.37 Å) K(3)-O(4) bond length. There are two shorter (2.79 Å) and two longer (2.89 Å) K(3)-O(1) bond lengths. V(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form VO4 tetrahedra that share  a cornercorner with one K(1)O7 pentagonal bipyramid,  a cornercorner with one V(1)O4 tetrahedra, and  an edgeedge with one K(1)O7 pentagonal bipyramid. The V(1)-O(2) bond length is 1.70 Å. The V(1)-O(3) bond length is 1.84 Å. Both V(1)-O(1) bond lengths are 1.72 Å. There are four inequivalent O sites. In the first O site, O(2) is bonded in a distorted single-bond geometry to two equivalent K(1), two equivalent K(3), and one V(1) atom. In the second O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), two equivalent K(3), and two equivalent V(1) atoms. In the third O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), and two equivalent K(3) atoms. In the fourth O site, O(1) is bonded in a distorted single-bond geometry to one K(2), two equivalent K(3), and one V(1) atom.