The crystal structure described by Bi3Pb4Sb5O21 crystallizes in the triclinic P1 space group. There are four inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), one O(7), one O(8), and one O(9) atom to form PbO8 hexagonal bipyramids that share edges with two equivalent Sb(3)O6 octahedra, edges with two equivalent Sb(4)O6 octahedra, and edges with two equivalent Sb(5)O6 octahedra. In the second Pb site, Pb(2) is bonded in a 7-coordinate geometry to one O(1), one O(13), one O(16), one O(17), one O(21), one O(5), and one O(6) atom. In the third Pb site, Pb(3) is bonded in a 6-coordinate geometry to one O(13), one O(15), one O(17), one O(2), one O(4), and one O(6) atom. In the fourth Pb site, Pb(4) is bonded in a 7-coordinate geometry to one O(14), one O(19), one O(2), one O(20), one O(21), one O(3), and one O(4) atom. There are three inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(13), one O(21), one O(3), one O(4), and one O(5) atom. In the second Bi site, Bi(2) is bonded in a 5-coordinate geometry to one O(1), one O(14), one O(21), one O(3), and one O(5) atom. In the third Bi site, Bi(3) is bonded in a 5-coordinate geometry to one O(1), one O(14), one O(2), one O(21), and one O(6) atom. There are five inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one O(1), one O(18), one O(19), one O(2), one O(20), and one O(3) atom to form corner-sharing SbO6 octahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the second Sb site, Sb(2) is bonded to one O(15), one O(16), one O(17), one O(4), one O(5), and one O(6) atom to form corner-sharing SbO6 octahedra. The corner-sharing octahedral tilt angles range from 43-45°. In the third Sb site, Sb(3) is bonded to one O(11), one O(12), one O(15), one O(18), one O(8), and one O(9) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(4)O6 octahedra, corners with two equivalent Sb(5)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-46°. In the fourth Sb site, Sb(4) is bonded to one O(10), one O(12), one O(16), one O(19), one O(7), and one O(9) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(3)O6 octahedra, corners with two equivalent Sb(5)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-45°. In the fifth Sb site, Sb(5) is bonded to one O(10), one O(11), one O(17), one O(20), one O(7), and one O(8) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(3)O6 octahedra, corners with two equivalent Sb(4)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 43-45°. There are twenty-one inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Pb(2), one Bi(2), one Bi(3), and one Sb(1) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Pb(3), one Pb(4), one Bi(3), and one Sb(1) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Pb(4), one Bi(1), one Bi(2), and one Sb(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Pb(3), one Pb(4), one Bi(1), and one Sb(2) atom. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Pb(2), one Bi(1), one Bi(2), and one Sb(2) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Pb(2), one Pb(3), one Bi(3), and one Sb(2) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(4), and one Sb(5) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Pb(1), one Sb(3), and one Sb(5) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(3), and one Sb(4) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(4), and one Sb(5) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Pb(1), one Sb(3), and one Sb(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(3), and one Sb(4) atom. In the thirteenth O site, O(13) is bonded to one Pb(1), one Pb(2), one Pb(3), and one Bi(1) atom to form corner-sharing OBiPb3 tetrahedra. In the fourteenth O site, O(14) is bonded to one Pb(1), one Pb(4), one Bi(2), and one Bi(3) atom to form distorted corner-sharing OBi2Pb2 tetrahedra. In the fifteenth O site, O(15) is bonded in a 2-coordinate geometry to one Pb(3), one Sb(2), and one Sb(3) atom. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one Pb(2), one Sb(2), and one Sb(4) atom. In the seventeenth O site, O(17) is bonded in a distorted bent 150 degrees geometry to one Pb(2), one Pb(3), one Sb(2), and one Sb(5) atom. In the eighteenth O site, O(18) is bonded in a distorted bent 120 degrees geometry to one Sb(1) and one Sb(3) atom. In the nineteenth O site, O(19) is bonded in a 2-coordinate geometry to one Pb(4), one Sb(1), and one Sb(4) atom. In the twentieth O site, O(20) is bonded in a 2-coordinate geometry to one Pb(4), one Sb(1), and one Sb(5) atom. In the twenty-first O site, O(21) is bonded in a 3-coordinate geometry to one Pb(2), one Pb(4), one Bi(1), one Bi(2), and one Bi(3) atom. is represented by the CIF card [CIF]
data_Bi3Sb5Pb4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.432
_cell_length_b   7.459
_cell_length_c   10.180
_cell_angle_alpha   89.691
_cell_angle_beta   89.646
_cell_angle_gamma   60.553
_symmetry_Int_Tables_number   1
_cell_volume   491.392
_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  0.138  0.712  0.355  1.0
  Bi  Bi1  1  0.298  0.850  0.643  1.0
  Bi  Bi2  1  0.846  0.295  0.639  1.0
  Sb  Sb3  1  0.336  0.334  0.702  1.0
  Sb  Sb4  1  0.669  0.663  0.302  1.0
  Sb  Sb5  1  0.500  0.501  0.000  1.0
  Sb  Sb6  1  0.001  0.500  1.000  1.0
  Sb  Sb7  1  0.500  0.999  0.001  1.0
  Pb  Pb8  1  0.001  1.000  0.001  1.0
  Pb  Pb9  1  0.161  0.172  0.333  1.0
  Pb  Pb10  1  0.657  0.173  0.329  1.0
  Pb  Pb11  1  0.827  0.833  0.665  1.0
  O  O12  1  0.206  0.201  0.596  1.0
  O  O13  1  0.601  0.203  0.595  1.0
  O  O14  1  0.211  0.593  0.592  1.0
  O  O15  1  0.803  0.794  0.407  1.0
  O  O16  1  0.410  0.789  0.411  1.0
  O  O17  1  0.799  0.402  0.411  1.0
  O  O18  1  0.203  0.202  0.044  1.0
  O  O19  1  0.594  0.203  0.044  1.0
  O  O20  1  0.203  0.596  0.043  1.0
  O  O21  1  0.798  0.797  0.957  1.0
  O  O22  1  0.403  0.798  0.958  1.0
  O  O23  1  0.798  0.404  0.959  1.0
  O  O24  1  0.997  0.999  0.244  1.0
  O  O25  1  0.000  0.004  0.758  1.0
  O  O26  1  0.533  0.533  0.194  1.0
  O  O27  1  0.934  0.534  0.194  1.0
  O  O28  1  0.537  0.926  0.193  1.0
  O  O29  1  0.470  0.468  0.806  1.0
  O  O30  1  0.070  0.466  0.807  1.0
  O  O31  1  0.466  0.070  0.809  1.0
  O  O32  1  0.027  0.986  0.507  1.0
[/CIF]
.
The crystal structure described by Bi3Pb4Sb5O21 crystallizes in the triclinic P1 space group. There are four inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), one O(7), one O(8), and one O(9) atom to form PbO8 hexagonal bipyramids that share edges with two equivalent Sb(3)O6 octahedra, edges with two equivalent Sb(4)O6 octahedra, and edges with two equivalent Sb(5)O6 octahedra. In the second Pb site, Pb(2) is bonded in a 7-coordinate geometry to one O(1), one O(13), one O(16), one O(17), one O(21), one O(5), and one O(6) atom. In the third Pb site, Pb(3) is bonded in a 6-coordinate geometry to one O(13), one O(15), one O(17), one O(2), one O(4), and one O(6) atom. In the fourth Pb site, Pb(4) is bonded in a 7-coordinate geometry to one O(14), one O(19), one O(2), one O(20), one O(21), one O(3), and one O(4) atom. There are three inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 5-coordinate geometry to one O(13), one O(21), one O(3), one O(4), and one O(5) atom. In the second Bi site, Bi(2) is bonded in a 5-coordinate geometry to one O(1), one O(14), one O(21), one O(3), and one O(5) atom. In the third Bi site, Bi(3) is bonded in a 5-coordinate geometry to one O(1), one O(14), one O(2), one O(21), and one O(6) atom. There are five inequivalent Sb sites. In the first Sb site, Sb(1) is bonded to one O(1), one O(18), one O(19), one O(2), one O(20), and one O(3) atom to form corner-sharing SbO6 octahedra. The corner-sharing octahedral tilt angles range from 45-46°. In the second Sb site, Sb(2) is bonded to one O(15), one O(16), one O(17), one O(4), one O(5), and one O(6) atom to form corner-sharing SbO6 octahedra. The corner-sharing octahedral tilt angles range from 43-45°. In the third Sb site, Sb(3) is bonded to one O(11), one O(12), one O(15), one O(18), one O(8), and one O(9) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(4)O6 octahedra, corners with two equivalent Sb(5)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-46°. In the fourth Sb site, Sb(4) is bonded to one O(10), one O(12), one O(16), one O(19), one O(7), and one O(9) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(3)O6 octahedra, corners with two equivalent Sb(5)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 44-45°. In the fifth Sb site, Sb(5) is bonded to one O(10), one O(11), one O(17), one O(20), one O(7), and one O(8) atom to form SbO6 octahedra that share  a cornercorner with one Sb(1)O6 octahedra,  a cornercorner with one Sb(2)O6 octahedra, corners with two equivalent Sb(3)O6 octahedra, corners with two equivalent Sb(4)O6 octahedra, and edges with two equivalent Pb(1)O8 hexagonal bipyramids. The corner-sharing octahedral tilt angles range from 43-45°. There are twenty-one inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Pb(2), one Bi(2), one Bi(3), and one Sb(1) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Pb(3), one Pb(4), one Bi(3), and one Sb(1) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Pb(4), one Bi(1), one Bi(2), and one Sb(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Pb(3), one Pb(4), one Bi(1), and one Sb(2) atom. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Pb(2), one Bi(1), one Bi(2), and one Sb(2) atom. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Pb(2), one Pb(3), one Bi(3), and one Sb(2) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(4), and one Sb(5) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Pb(1), one Sb(3), and one Sb(5) atom. In the ninth O site, O(9) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(3), and one Sb(4) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(4), and one Sb(5) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Pb(1), one Sb(3), and one Sb(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Pb(1), one Sb(3), and one Sb(4) atom. In the thirteenth O site, O(13) is bonded to one Pb(1), one Pb(2), one Pb(3), and one Bi(1) atom to form corner-sharing OBiPb3 tetrahedra. In the fourteenth O site, O(14) is bonded to one Pb(1), one Pb(4), one Bi(2), and one Bi(3) atom to form distorted corner-sharing OBi2Pb2 tetrahedra. In the fifteenth O site, O(15) is bonded in a 2-coordinate geometry to one Pb(3), one Sb(2), and one Sb(3) atom. In the sixteenth O site, O(16) is bonded in a 2-coordinate geometry to one Pb(2), one Sb(2), and one Sb(4) atom. In the seventeenth O site, O(17) is bonded in a distorted bent 150 degrees geometry to one Pb(2), one Pb(3), one Sb(2), and one Sb(5) atom. In the eighteenth O site, O(18) is bonded in a distorted bent 120 degrees geometry to one Sb(1) and one Sb(3) atom. In the nineteenth O site, O(19) is bonded in a 2-coordinate geometry to one Pb(4), one Sb(1), and one Sb(4) atom. In the twentieth O site, O(20) is bonded in a 2-coordinate geometry to one Pb(4), one Sb(1), and one Sb(5) atom. In the twenty-first O site, O(21) is bonded in a 3-coordinate geometry to one Pb(2), one Pb(4), one Bi(1), one Bi(2), and one Bi(3) atom. is represented by the CIF card [CIF]
data_Bi3Sb5Pb4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.432
_cell_length_b   7.459
_cell_length_c   10.180
_cell_angle_alpha   89.691
_cell_angle_beta   89.646
_cell_angle_gamma   60.553
_symmetry_Int_Tables_number   1
_cell_volume   491.392
_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  0.138  0.712  0.355  1.0
  Bi  Bi1  1  0.298  0.850  0.643  1.0
  Bi  Bi2  1  0.846  0.295  0.639  1.0
  Sb  Sb3  1  0.336  0.334  0.702  1.0
  Sb  Sb4  1  0.669  0.663  0.302  1.0
  Sb  Sb5  1  0.500  0.501  0.000  1.0
  Sb  Sb6  1  0.001  0.500  1.000  1.0
  Sb  Sb7  1  0.500  0.999  0.001  1.0
  Pb  Pb8  1  0.001  1.000  0.001  1.0
  Pb  Pb9  1  0.161  0.172  0.333  1.0
  Pb  Pb10  1  0.657  0.173  0.329  1.0
  Pb  Pb11  1  0.827  0.833  0.665  1.0
  O  O12  1  0.206  0.201  0.596  1.0
  O  O13  1  0.601  0.203  0.595  1.0
  O  O14  1  0.211  0.593  0.592  1.0
  O  O15  1  0.803  0.794  0.407  1.0
  O  O16  1  0.410  0.789  0.411  1.0
  O  O17  1  0.799  0.402  0.411  1.0
  O  O18  1  0.203  0.202  0.044  1.0
  O  O19  1  0.594  0.203  0.044  1.0
  O  O20  1  0.203  0.596  0.043  1.0
  O  O21  1  0.798  0.797  0.957  1.0
  O  O22  1  0.403  0.798  0.958  1.0
  O  O23  1  0.798  0.404  0.959  1.0
  O  O24  1  0.997  0.999  0.244  1.0
  O  O25  1  0.000  0.004  0.758  1.0
  O  O26  1  0.533  0.533  0.194  1.0
  O  O27  1  0.934  0.534  0.194  1.0
  O  O28  1  0.537  0.926  0.193  1.0
  O  O29  1  0.470  0.468  0.806  1.0
  O  O30  1  0.070  0.466  0.807  1.0
  O  O31  1  0.466  0.070  0.809  1.0
  O  O32  1  0.027  0.986  0.507  1.0
[/CIF]
.