W4Bi6O21 crystallizes in the triclinic P1 space group. There are four inequivalent W sites. In the first W site, W(1) is bonded to one O(1), one O(14), one O(16), one O(5), and one O(7) atom to form distorted WO5 trigonal bipyramids that share  a cornercorner with one Bi(4)O5 square pyramid. In the second W site, W(2) is bonded to one O(11), one O(13), one O(15), one O(2), one O(20), and one O(9) atom to form distorted edge-sharing WO6 octahedra. In the third W site, W(3) is bonded to one O(10), one O(12), one O(19), one O(3), one O(4), and one O(8) atom to form WO6 octahedra that share corners with four equivalent Bi(4)O5 square pyramids. In the fourth W site, W(4) is bonded to one O(15), one O(17), one O(20), one O(21), and one O(6) atom to form distorted edge-sharing WO5 trigonal bipyramids. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 3-coordinate geometry to one O(1), one O(11), and one O(13) atom. In the second Bi site, Bi(2) is bonded in a distorted pentagonal planar geometry to one O(12), one O(14), one O(16), one O(4), and one O(5) atom. In the third Bi site, Bi(3) is bonded in a 5-coordinate geometry to one O(10), one O(18), one O(19), one O(3), and one O(6) atom. In the fourth Bi site, Bi(4) is bonded to one O(12), one O(19), one O(3), one O(4), and one O(5) atom to form distorted BiO5 square pyramids that share corners with four equivalent W(3)O6 octahedra and  a cornercorner with one W(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 41-57°. In the fifth Bi site, Bi(5) is bonded in a 5-coordinate geometry to one O(13), one O(15), one O(2), one O(20), and one O(9) atom. In the sixth Bi site, Bi(6) is bonded in a 5-coordinate geometry to one O(10), one O(17), one O(18), one O(6), and one O(8) atom. There are twenty-one inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one W(2) and one Bi(5) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(3), and one Bi(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one W(3), one Bi(2), and one Bi(4) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one W(1), one Bi(2), and one Bi(4) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one W(4), one Bi(3), and one Bi(6) atom. In the seventh O site, O(7) is bonded in a distorted single-bond geometry to one W(1) atom. In the eighth O site, O(8) is bonded in a distorted water-like geometry to one W(3) and one Bi(6) atom. In the ninth O site, O(9) is bonded in a distorted water-like geometry to one W(2) and one Bi(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one W(3), one Bi(3), and one Bi(6) atom. In the eleventh O site, O(11) is bonded in a bent 120 degrees geometry to one W(2) and one Bi(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(2), and one Bi(4) atom. In the thirteenth O site, O(13) is bonded in a trigonal non-coplanar geometry to one W(2), one Bi(1), and one Bi(5) atom. In the fourteenth O site, O(14) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(2) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one W(2), one W(4), and one Bi(5) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(2) atom. In the seventeenth O site, O(17) is bonded in a distorted bent 150 degrees geometry to one W(4) and one Bi(6) atom. In the eighteenth O site, O(18) is bonded in a bent 120 degrees geometry to one Bi(3) and one Bi(6) atom. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(3), and one Bi(4) atom. In the twentieth O site, O(20) is bonded in a distorted T-shaped geometry to one W(2), one W(4), and one Bi(5) atom. In the twenty-first O site, O(21) is bonded in a single-bond geometry to one W(4) atom.
W4Bi6O21 crystallizes in the triclinic P1 space group. There are four inequivalent W sites. In the first W site, W(1) is bonded to one O(1), one O(14), one O(16), one O(5), and one O(7) atom to form distorted WO5 trigonal bipyramids that share  a cornercorner with one Bi(4)O5 square pyramid. The W(1)-O(1) bond length is 1.88 Å. The W(1)-O(14) bond length is 1.87 Å. The W(1)-O(16) bond length is 1.84 Å. The W(1)-O(5) bond length is 2.23 Å. The W(1)-O(7) bond length is 1.81 Å. In the second W site, W(2) is bonded to one O(11), one O(13), one O(15), one O(2), one O(20), and one O(9) atom to form distorted edge-sharing WO6 octahedra. The W(2)-O(11) bond length is 1.87 Å. The W(2)-O(13) bond length is 2.18 Å. The W(2)-O(15) bond length is 1.98 Å. The W(2)-O(2) bond length is 1.83 Å. The W(2)-O(20) bond length is 2.20 Å. The W(2)-O(9) bond length is 1.86 Å. In the third W site, W(3) is bonded to one O(10), one O(12), one O(19), one O(3), one O(4), and one O(8) atom to form WO6 octahedra that share corners with four equivalent Bi(4)O5 square pyramids. The W(3)-O(10) bond length is 2.09 Å. The W(3)-O(12) bond length is 1.88 Å. The W(3)-O(19) bond length is 1.96 Å. The W(3)-O(3) bond length is 1.99 Å. The W(3)-O(4) bond length is 2.04 Å. The W(3)-O(8) bond length is 1.89 Å. In the fourth W site, W(4) is bonded to one O(15), one O(17), one O(20), one O(21), and one O(6) atom to form distorted edge-sharing WO5 trigonal bipyramids. The W(4)-O(15) bond length is 2.22 Å. The W(4)-O(17) bond length is 1.82 Å. The W(4)-O(20) bond length is 1.93 Å. The W(4)-O(21) bond length is 1.80 Å. The W(4)-O(6) bond length is 1.85 Å. There are six inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 3-coordinate geometry to one O(1), one O(11), and one O(13) atom. The Bi(1)-O(1) bond length is 2.20 Å. The Bi(1)-O(11) bond length is 2.18 Å. The Bi(1)-O(13) bond length is 2.17 Å. In the second Bi site, Bi(2) is bonded in a distorted pentagonal planar geometry to one O(12), one O(14), one O(16), one O(4), and one O(5) atom. The Bi(2)-O(12) bond length is 2.49 Å. The Bi(2)-O(14) bond length is 2.35 Å. The Bi(2)-O(16) bond length is 2.46 Å. The Bi(2)-O(4) bond length is 2.34 Å. The Bi(2)-O(5) bond length is 2.06 Å. In the third Bi site, Bi(3) is bonded in a 5-coordinate geometry to one O(10), one O(18), one O(19), one O(3), and one O(6) atom. The Bi(3)-O(10) bond length is 2.22 Å. The Bi(3)-O(18) bond length is 2.14 Å. The Bi(3)-O(19) bond length is 2.26 Å. The Bi(3)-O(3) bond length is 2.56 Å. The Bi(3)-O(6) bond length is 2.54 Å. In the fourth Bi site, Bi(4) is bonded to one O(12), one O(19), one O(3), one O(4), and one O(5) atom to form distorted BiO5 square pyramids that share corners with four equivalent W(3)O6 octahedra and  a cornercorner with one W(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 41-57°. The Bi(4)-O(12) bond length is 2.56 Å. The Bi(4)-O(19) bond length is 2.39 Å. The Bi(4)-O(3) bond length is 2.13 Å. The Bi(4)-O(4) bond length is 2.32 Å. The Bi(4)-O(5) bond length is 2.24 Å. In the fifth Bi site, Bi(5) is bonded in a 5-coordinate geometry to one O(13), one O(15), one O(2), one O(20), and one O(9) atom. The Bi(5)-O(13) bond length is 2.20 Å. The Bi(5)-O(15) bond length is 2.33 Å. The Bi(5)-O(2) bond length is 2.39 Å. The Bi(5)-O(20) bond length is 2.34 Å. The Bi(5)-O(9) bond length is 2.27 Å. In the sixth Bi site, Bi(6) is bonded in a 5-coordinate geometry to one O(10), one O(17), one O(18), one O(6), and one O(8) atom. The Bi(6)-O(10) bond length is 2.26 Å. The Bi(6)-O(17) bond length is 2.57 Å. The Bi(6)-O(18) bond length is 2.08 Å. The Bi(6)-O(6) bond length is 2.76 Å. The Bi(6)-O(8) bond length is 2.35 Å. There are twenty-one inequivalent O sites. In the first O site, O(1) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one W(2) and one Bi(5) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(3), and one Bi(4) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one W(3), one Bi(2), and one Bi(4) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one W(1), one Bi(2), and one Bi(4) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one W(4), one Bi(3), and one Bi(6) atom. In the seventh O site, O(7) is bonded in a distorted single-bond geometry to one W(1) atom. In the eighth O site, O(8) is bonded in a distorted water-like geometry to one W(3) and one Bi(6) atom. In the ninth O site, O(9) is bonded in a distorted water-like geometry to one W(2) and one Bi(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one W(3), one Bi(3), and one Bi(6) atom. In the eleventh O site, O(11) is bonded in a bent 120 degrees geometry to one W(2) and one Bi(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(2), and one Bi(4) atom. In the thirteenth O site, O(13) is bonded in a trigonal non-coplanar geometry to one W(2), one Bi(1), and one Bi(5) atom. In the fourteenth O site, O(14) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(2) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one W(2), one W(4), and one Bi(5) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one W(1) and one Bi(2) atom. In the seventeenth O site, O(17) is bonded in a distorted bent 150 degrees geometry to one W(4) and one Bi(6) atom. In the eighteenth O site, O(18) is bonded in a bent 120 degrees geometry to one Bi(3) and one Bi(6) atom. In the nineteenth O site, O(19) is bonded in a distorted trigonal planar geometry to one W(3), one Bi(3), and one Bi(4) atom. In the twentieth O site, O(20) is bonded in a distorted T-shaped geometry to one W(2), one W(4), and one Bi(5) atom. In the twenty-first O site, O(21) is bonded in a single-bond geometry to one W(4) atom.