K4Bi2O5 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(4), two equivalent O(2), and two equivalent O(3) atoms to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(2)O6 octahedra, corners with two equivalent K(1)O5 trigonal bipyramids,  an edgeedge with one K(2)O6 octahedra, edges with four equivalent K(4)O6 octahedra, and  an edgeedge with one K(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 25°. In the second K site, K(2) is bonded to one O(1), one O(2), one O(4), and three equivalent O(5) atoms to form distorted KO6 octahedra that share corners with two equivalent K(2)O6 octahedra,  a cornercorner with one K(1)O5 trigonal bipyramid, edges with two equivalent K(2)O6 octahedra, edges with three equivalent K(4)O6 octahedra, and  an edgeedge with one K(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 13°. In the third K site, K(3) is bonded in a distorted square co-planar geometry to one O(3), one O(4), and two equivalent O(1) atoms. In the fourth K site, K(4) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form distorted KO6 octahedra that share corners with two equivalent K(4)O6 octahedra,  an edgeedge with one K(4)O6 octahedra, edges with three equivalent K(2)O6 octahedra, and edges with four equivalent K(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 14°. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a distorted trigonal non-coplanar geometry to one O(1), one O(2), and one O(5) atom. In the second Bi site, Bi(2) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(5), and two equivalent O(4) atoms. There are five inequivalent O sites. In the first O site, O(1) is bonded to one K(2), one K(4), two equivalent K(3), and one Bi(1) atom to form distorted OK4Bi trigonal bipyramids that share  a cornercorner with one O(5)K4Bi2 octahedra, corners with two equivalent O(2)K5Bi octahedra,  a cornercorner with one O(4)K3Bi2 trigonal bipyramid,  an edgeedge with one O(2)K5Bi octahedra, edges with two equivalent O(5)K4Bi2 octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles range from 17-82°. In the second O site, O(2) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Bi(1) atom to form distorted OK5Bi octahedra that share corners with two equivalent O(2)K5Bi octahedra,  a cornercorner with one O(4)K3Bi2 trigonal bipyramid, corners with two equivalent O(1)K4Bi trigonal bipyramids,  an edgeedge with one O(2)K5Bi octahedra, edges with three equivalent O(5)K4Bi2 octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 14°. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(1), two equivalent K(4), and one Bi(2) atom. In the fourth O site, O(4) is bonded to one K(1), one K(2), one K(3), and two equivalent Bi(2) atoms to form distorted OK3Bi2 trigonal bipyramids that share  a cornercorner with one O(2)K5Bi octahedra, corners with three equivalent O(5)K4Bi2 octahedra,  a cornercorner with one O(1)K4Bi trigonal bipyramid,  an edgeedge with one O(5)K4Bi2 octahedra,  an edgeedge with one O(2)K5Bi octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles range from 13-79°. In the fifth O site, O(5) is bonded to one K(4), three equivalent K(2), one Bi(1), and one Bi(2) atom to form distorted OK4Bi2 octahedra that share corners with two equivalent O(5)K4Bi2 octahedra,  a cornercorner with one O(1)K4Bi trigonal bipyramid, corners with three equivalent O(4)K3Bi2 trigonal bipyramids, edges with two equivalent O(5)K4Bi2 octahedra, edges with three equivalent O(2)K5Bi octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and edges with two equivalent O(1)K4Bi trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°.
K4Bi2O5 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(4), two equivalent O(2), and two equivalent O(3) atoms to form distorted KO5 trigonal bipyramids that share  a cornercorner with one K(2)O6 octahedra, corners with two equivalent K(1)O5 trigonal bipyramids,  an edgeedge with one K(2)O6 octahedra, edges with four equivalent K(4)O6 octahedra, and  an edgeedge with one K(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 25°. The K(1)-O(4) bond length is 2.70 Å. There is one shorter (2.69 Å) and one longer (2.74 Å) K(1)-O(2) bond length. There is one shorter (2.85 Å) and one longer (2.91 Å) K(1)-O(3) bond length. In the second K site, K(2) is bonded to one O(1), one O(2), one O(4), and three equivalent O(5) atoms to form distorted KO6 octahedra that share corners with two equivalent K(2)O6 octahedra,  a cornercorner with one K(1)O5 trigonal bipyramid, edges with two equivalent K(2)O6 octahedra, edges with three equivalent K(4)O6 octahedra, and  an edgeedge with one K(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 13°. The K(2)-O(1) bond length is 2.68 Å. The K(2)-O(2) bond length is 2.70 Å. The K(2)-O(4) bond length is 2.81 Å. There are a spread of K(2)-O(5) bond distances ranging from 2.81-2.90 Å. In the third K site, K(3) is bonded in a distorted square co-planar geometry to one O(3), one O(4), and two equivalent O(1) atoms. The K(3)-O(3) bond length is 2.69 Å. The K(3)-O(4) bond length is 2.68 Å. There is one shorter (2.63 Å) and one longer (2.65 Å) K(3)-O(1) bond length. In the fourth K site, K(4) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form distorted KO6 octahedra that share corners with two equivalent K(4)O6 octahedra,  an edgeedge with one K(4)O6 octahedra, edges with three equivalent K(2)O6 octahedra, and edges with four equivalent K(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 14°. The K(4)-O(1) bond length is 2.66 Å. The K(4)-O(5) bond length is 2.94 Å. There is one shorter (2.84 Å) and one longer (2.87 Å) K(4)-O(2) bond length. There is one shorter (2.67 Å) and one longer (3.06 Å) K(4)-O(3) bond length. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a distorted trigonal non-coplanar geometry to one O(1), one O(2), and one O(5) atom. The Bi(1)-O(1) bond length is 2.05 Å. The Bi(1)-O(2) bond length is 2.07 Å. The Bi(1)-O(5) bond length is 2.14 Å. In the second Bi site, Bi(2) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(5), and two equivalent O(4) atoms. The Bi(2)-O(3) bond length is 2.06 Å. The Bi(2)-O(5) bond length is 2.40 Å. There is one shorter (2.10 Å) and one longer (2.41 Å) Bi(2)-O(4) bond length. There are five inequivalent O sites. In the first O site, O(1) is bonded to one K(2), one K(4), two equivalent K(3), and one Bi(1) atom to form distorted OK4Bi trigonal bipyramids that share  a cornercorner with one O(5)K4Bi2 octahedra, corners with two equivalent O(2)K5Bi octahedra,  a cornercorner with one O(4)K3Bi2 trigonal bipyramid,  an edgeedge with one O(2)K5Bi octahedra, edges with two equivalent O(5)K4Bi2 octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles range from 17-82°. In the second O site, O(2) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Bi(1) atom to form distorted OK5Bi octahedra that share corners with two equivalent O(2)K5Bi octahedra,  a cornercorner with one O(4)K3Bi2 trigonal bipyramid, corners with two equivalent O(1)K4Bi trigonal bipyramids,  an edgeedge with one O(2)K5Bi octahedra, edges with three equivalent O(5)K4Bi2 octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles are 14°. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(1), two equivalent K(4), and one Bi(2) atom. In the fourth O site, O(4) is bonded to one K(1), one K(2), one K(3), and two equivalent Bi(2) atoms to form distorted OK3Bi2 trigonal bipyramids that share  a cornercorner with one O(2)K5Bi octahedra, corners with three equivalent O(5)K4Bi2 octahedra,  a cornercorner with one O(1)K4Bi trigonal bipyramid,  an edgeedge with one O(5)K4Bi2 octahedra,  an edgeedge with one O(2)K5Bi octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and  an edgeedge with one O(1)K4Bi trigonal bipyramid. The corner-sharing octahedral tilt angles range from 13-79°. In the fifth O site, O(5) is bonded to one K(4), three equivalent K(2), one Bi(1), and one Bi(2) atom to form distorted OK4Bi2 octahedra that share corners with two equivalent O(5)K4Bi2 octahedra,  a cornercorner with one O(1)K4Bi trigonal bipyramid, corners with three equivalent O(4)K3Bi2 trigonal bipyramids, edges with two equivalent O(5)K4Bi2 octahedra, edges with three equivalent O(2)K5Bi octahedra,  an edgeedge with one O(4)K3Bi2 trigonal bipyramid, and edges with two equivalent O(1)K4Bi trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°.