Bi10Cd3O20 crystallizes in the monoclinic C2 space group. There are two inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to two equivalent O(1) and two equivalent O(3) atoms to form CdO4 tetrahedra that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids, and corners with two equivalent Bi(4)O5 square pyramids. In the second Cd site, Cd(2) is bonded to one O(1), one O(6), one O(7), one O(8), and one O(9) atom to form distorted CdO5 square pyramids that share corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(3)O5 square pyramid. There are five inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(1), one O(5), one O(7), and two equivalent O(4) atoms to form distorted BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(1)O5 square pyramid. In the second Bi site, Bi(2) is bonded to one O(1), one O(10), one O(2), one O(5), and one O(6) atom to form BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(4)O5 square pyramid. In the third Bi site, Bi(3) is bonded to one O(2), one O(3), one O(5), one O(7), and one O(9) atom to form distorted BiO5 square pyramids that share corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Cd(2)O5 square pyramid. In the fourth Bi site, Bi(4) is bonded to one O(2), one O(3), one O(4), one O(6), and one O(8) atom to form distorted BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(2)O5 square pyramid. In the fifth Bi site, Bi(5) is bonded in a 5-coordinate geometry to one O(3), one O(8), one O(9), and two equivalent O(10) atoms. There are ten inequivalent O sites. In the first O site, O(6) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(2), and one Bi(4) atom. In the second O site, O(7) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(1), and one Bi(3) atom. In the third O site, O(8) is bonded in a trigonal planar geometry to one Cd(2), one Bi(4), and one Bi(5) atom. In the fourth O site, O(9) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(3), and one Bi(5) atom. In the fifth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Bi(2) and two equivalent Bi(5) atoms. In the sixth O site, O(1) is bonded to one Cd(1), one Cd(2), one Bi(1), and one Bi(2) atom to form OCd2Bi2 tetrahedra that share  a cornercorner with one O(1)Cd2Bi2 tetrahedra and corners with two equivalent O(3)CdBi3 tetrahedra. In the seventh O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Bi(2), one Bi(3), and one Bi(4) atom. In the eighth O site, O(3) is bonded to one Cd(1), one Bi(3), one Bi(4), and one Bi(5) atom to form distorted OCdBi3 tetrahedra that share  a cornercorner with one O(3)CdBi3 tetrahedra and corners with two equivalent O(1)Cd2Bi2 tetrahedra. In the ninth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Bi(4) and two equivalent Bi(1) atoms. In the tenth O site, O(5) is bonded in a trigonal planar geometry to one Bi(1), one Bi(2), and one Bi(3) atom.
Bi10Cd3O20 crystallizes in the monoclinic C2 space group. There are two inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to two equivalent O(1) and two equivalent O(3) atoms to form CdO4 tetrahedra that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids, and corners with two equivalent Bi(4)O5 square pyramids. Both Cd(1)-O(1) bond lengths are 2.28 Å. Both Cd(1)-O(3) bond lengths are 2.29 Å. In the second Cd site, Cd(2) is bonded to one O(1), one O(6), one O(7), one O(8), and one O(9) atom to form distorted CdO5 square pyramids that share corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(3)O5 square pyramid. The Cd(2)-O(1) bond length is 2.36 Å. The Cd(2)-O(6) bond length is 2.22 Å. The Cd(2)-O(7) bond length is 2.30 Å. The Cd(2)-O(8) bond length is 2.34 Å. The Cd(2)-O(9) bond length is 2.40 Å. There are five inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one O(1), one O(5), one O(7), and two equivalent O(4) atoms to form distorted BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(1)O5 square pyramid. The Bi(1)-O(1) bond length is 2.50 Å. The Bi(1)-O(5) bond length is 2.26 Å. The Bi(1)-O(7) bond length is 2.08 Å. There is one shorter (2.29 Å) and one longer (2.55 Å) Bi(1)-O(4) bond length. In the second Bi site, Bi(2) is bonded to one O(1), one O(10), one O(2), one O(5), and one O(6) atom to form BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(4)O5 square pyramid. The Bi(2)-O(1) bond length is 2.33 Å. The Bi(2)-O(10) bond length is 2.08 Å. The Bi(2)-O(2) bond length is 2.31 Å. The Bi(2)-O(5) bond length is 2.24 Å. The Bi(2)-O(6) bond length is 2.38 Å. In the third Bi site, Bi(3) is bonded to one O(2), one O(3), one O(5), one O(7), and one O(9) atom to form distorted BiO5 square pyramids that share corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(2)O5 square pyramids, corners with two equivalent Bi(4)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Cd(2)O5 square pyramid. The Bi(3)-O(2) bond length is 2.13 Å. The Bi(3)-O(3) bond length is 2.68 Å. The Bi(3)-O(5) bond length is 2.39 Å. The Bi(3)-O(7) bond length is 2.34 Å. The Bi(3)-O(9) bond length is 2.22 Å. In the fourth Bi site, Bi(4) is bonded to one O(2), one O(3), one O(4), one O(6), and one O(8) atom to form distorted BiO5 square pyramids that share corners with two equivalent Cd(2)O5 square pyramids, corners with two equivalent Bi(1)O5 square pyramids, corners with two equivalent Bi(3)O5 square pyramids,  a cornercorner with one Cd(1)O4 tetrahedra, and  an edgeedge with one Bi(2)O5 square pyramid. The Bi(4)-O(2) bond length is 2.53 Å. The Bi(4)-O(3) bond length is 2.28 Å. The Bi(4)-O(4) bond length is 2.08 Å. The Bi(4)-O(6) bond length is 2.27 Å. The Bi(4)-O(8) bond length is 2.22 Å. In the fifth Bi site, Bi(5) is bonded in a 5-coordinate geometry to one O(3), one O(8), one O(9), and two equivalent O(10) atoms. The Bi(5)-O(3) bond length is 2.42 Å. The Bi(5)-O(8) bond length is 2.23 Å. The Bi(5)-O(9) bond length is 2.09 Å. There is one shorter (2.33 Å) and one longer (2.67 Å) Bi(5)-O(10) bond length. There are ten inequivalent O sites. In the first O site, O(6) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(2), and one Bi(4) atom. In the second O site, O(7) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(1), and one Bi(3) atom. In the third O site, O(8) is bonded in a trigonal planar geometry to one Cd(2), one Bi(4), and one Bi(5) atom. In the fourth O site, O(9) is bonded in a trigonal non-coplanar geometry to one Cd(2), one Bi(3), and one Bi(5) atom. In the fifth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Bi(2) and two equivalent Bi(5) atoms. In the sixth O site, O(1) is bonded to one Cd(1), one Cd(2), one Bi(1), and one Bi(2) atom to form OCd2Bi2 tetrahedra that share  a cornercorner with one O(1)Cd2Bi2 tetrahedra and corners with two equivalent O(3)CdBi3 tetrahedra. In the seventh O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Bi(2), one Bi(3), and one Bi(4) atom. In the eighth O site, O(3) is bonded to one Cd(1), one Bi(3), one Bi(4), and one Bi(5) atom to form distorted OCdBi3 tetrahedra that share  a cornercorner with one O(3)CdBi3 tetrahedra and corners with two equivalent O(1)Cd2Bi2 tetrahedra. In the ninth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Bi(4) and two equivalent Bi(1) atoms. In the tenth O site, O(5) is bonded in a trigonal planar geometry to one Bi(1), one Bi(2), and one Bi(3) atom.