The structure described by 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. is represented by the Crystallographic Information File (CIF) [CIF]
data_Bi6W4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.058
_cell_length_b   5.101
_cell_length_c   18.620
_cell_angle_alpha   87.456
_cell_angle_beta   86.265
_cell_angle_gamma   85.121
_symmetry_Int_Tables_number   1
_cell_volume   477.237
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Bi  Bi0  1  0.542  0.454  0.921  1.0
  Bi  Bi1  1  0.452  0.499  0.692  1.0
  Bi  Bi2  1  0.956  0.006  0.406  1.0
  Bi  Bi3  1  0.924  0.992  0.599  1.0
  Bi  Bi4  1  0.697  0.563  0.101  1.0
  Bi  Bi5  1  0.555  0.537  0.323  1.0
  W  W6  1  0.952  0.965  0.787  1.0
  W  W7  1  0.078  0.035  0.025  1.0
  W  W8  1  0.450  0.507  0.506  1.0
  W  W9  1  0.124  0.083  0.202  1.0
  O  O10  1  0.723  0.122  0.859  1.0
  O  O11  1  0.381  0.813  0.029  1.0
  O  O12  1  0.196  0.825  0.517  1.0
  O  O13  1  0.661  0.648  0.584  1.0
  O  O14  1  0.167  0.813  0.687  1.0
  O  O15  1  0.118  0.855  0.282  1.0
  O  O16  1  0.177  0.744  0.837  1.0
  O  O17  1  0.268  0.444  0.424  1.0
  O  O18  1  0.879  0.765  0.001  1.0
  O  O19  1  0.702  0.672  0.426  1.0
  O  O20  1  0.192  0.233  0.943  1.0
  O  O21  1  0.272  0.331  0.583  1.0
  O  O22  1  0.697  0.266  0.018  1.0
  O  O23  1  0.682  0.821  0.742  1.0
  O  O24  1  0.099  0.305  0.096  1.0
  O  O25  1  0.073  0.271  0.746  1.0
  O  O26  1  0.947  0.382  0.236  1.0
  O  O27  1  0.628  0.134  0.343  1.0
  O  O28  1  0.714  0.203  0.498  1.0
  O  O29  1  0.992  0.861  0.133  1.0
  O  O30  1  0.475  0.117  0.188  1.0
[/CIF]
.
The structure described by 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. is represented by the Crystallographic Information File (CIF) [CIF]
data_Bi6W4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.058
_cell_length_b   5.101
_cell_length_c   18.620
_cell_angle_alpha   87.456
_cell_angle_beta   86.265
_cell_angle_gamma   85.121
_symmetry_Int_Tables_number   1
_cell_volume   477.237
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Bi  Bi0  1  0.542  0.454  0.921  1.0
  Bi  Bi1  1  0.452  0.499  0.692  1.0
  Bi  Bi2  1  0.956  0.006  0.406  1.0
  Bi  Bi3  1  0.924  0.992  0.599  1.0
  Bi  Bi4  1  0.697  0.563  0.101  1.0
  Bi  Bi5  1  0.555  0.537  0.323  1.0
  W  W6  1  0.952  0.965  0.787  1.0
  W  W7  1  0.078  0.035  0.025  1.0
  W  W8  1  0.450  0.507  0.506  1.0
  W  W9  1  0.124  0.083  0.202  1.0
  O  O10  1  0.723  0.122  0.859  1.0
  O  O11  1  0.381  0.813  0.029  1.0
  O  O12  1  0.196  0.825  0.517  1.0
  O  O13  1  0.661  0.648  0.584  1.0
  O  O14  1  0.167  0.813  0.687  1.0
  O  O15  1  0.118  0.855  0.282  1.0
  O  O16  1  0.177  0.744  0.837  1.0
  O  O17  1  0.268  0.444  0.424  1.0
  O  O18  1  0.879  0.765  0.001  1.0
  O  O19  1  0.702  0.672  0.426  1.0
  O  O20  1  0.192  0.233  0.943  1.0
  O  O21  1  0.272  0.331  0.583  1.0
  O  O22  1  0.697  0.266  0.018  1.0
  O  O23  1  0.682  0.821  0.742  1.0
  O  O24  1  0.099  0.305  0.096  1.0
  O  O25  1  0.073  0.271  0.746  1.0
  O  O26  1  0.947  0.382  0.236  1.0
  O  O27  1  0.628  0.134  0.343  1.0
  O  O28  1  0.714  0.203  0.498  1.0
  O  O29  1  0.992  0.861  0.133  1.0
  O  O30  1  0.475  0.117  0.188  1.0
[/CIF]
.