The structure described by Hf8PbO24 crystallizes in the monoclinic C2/m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one O(1), one O(2), one O(3), one O(7), one O(8), and one O(9) atom to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Hf(2)O6 octahedra, and  a faceface with one Pb(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second Hf site, Hf(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Hf(2)O6 octahedra, and  a faceface with one Pb(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-11°. Pb(1) is bonded to two equivalent O(3), two equivalent O(4), four equivalent O(2), and four equivalent O(7) atoms to form PbO12 cuboctahedra that share faces with four equivalent Hf(1)O6 octahedra and faces with four equivalent Hf(2)O6 octahedra. There are nine inequivalent O sites. In the first O site, O(9) is bonded in a linear geometry to two equivalent Hf(1) atoms. In the second O site, O(1) is bonded in a linear geometry to two equivalent Hf(1) atoms. In the third O site, O(2) is bonded in a distorted linear geometry to one Hf(1), one Hf(2), and one Pb(1) atom. In the fourth O site, O(3) is bonded in a distorted linear geometry to two equivalent Hf(1) and one Pb(1) atom. In the fifth O site, O(4) is bonded in a linear geometry to two equivalent Hf(2) and one Pb(1) atom. In the sixth O site, O(5) is bonded in a linear geometry to two equivalent Hf(2) atoms. In the seventh O site, O(6) is bonded in a linear geometry to two equivalent Hf(2) atoms. In the eighth O site, O(7) is bonded in a distorted linear geometry to one Hf(1), one Hf(2), and one Pb(1) atom. In the ninth O site, O(8) is bonded in a linear geometry to one Hf(1) and one Hf(2) atom. is represented by the CIF file [CIF]
data_Hf8PbO24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.251
_cell_length_b   9.251
_cell_length_c   9.240
_cell_angle_alpha   66.598
_cell_angle_beta   66.598
_cell_angle_gamma   53.104
_symmetry_Int_Tables_number   1
_cell_volume   566.687
_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
  Hf  Hf0  1  0.818  0.309  0.754  1.0
  Hf  Hf1  1  0.691  0.182  0.246  1.0
  Hf  Hf2  1  0.309  0.818  0.754  1.0
  Hf  Hf3  1  0.055  0.564  0.754  1.0
  Hf  Hf4  1  0.182  0.691  0.246  1.0
  Hf  Hf5  1  0.945  0.436  0.246  1.0
  Hf  Hf6  1  0.564  0.055  0.754  1.0
  Hf  Hf7  1  0.436  0.945  0.246  1.0
  Pb  Pb8  1  0.500  0.500  0.500  1.0
  O  O9  1  0.748  0.252  0.000  1.0
  O  O10  1  0.678  0.203  0.737  1.0
  O  O11  1  0.797  0.322  0.263  1.0
  O  O12  1  0.559  0.559  0.737  1.0
  O  O13  1  0.322  0.322  0.738  1.0
  O  O14  1  0.441  0.441  0.263  1.0
  O  O15  1  0.186  0.186  0.252  1.0
  O  O16  1  0.252  0.748  0.000  1.0
  O  O17  1  0.203  0.678  0.737  1.0
  O  O18  1  0.000  0.500  0.000  1.0
  O  O19  1  0.144  0.619  0.500  1.0
  O  O20  1  0.322  0.797  0.263  1.0
  O  O21  1  0.938  0.438  0.747  1.0
  O  O22  1  0.856  0.381  0.500  1.0
  O  O23  1  0.062  0.562  0.253  1.0
  O  O24  1  0.814  0.814  0.748  1.0
  O  O25  1  0.938  0.938  0.251  1.0
  O  O26  1  0.678  0.678  0.262  1.0
  O  O27  1  0.062  0.062  0.749  1.0
  O  O28  1  0.500  0.000  0.000  1.0
  O  O29  1  0.438  0.938  0.747  1.0
  O  O30  1  0.562  0.062  0.253  1.0
  O  O31  1  0.381  0.856  0.500  1.0
  O  O32  1  0.619  0.144  0.500  1.0
[/CIF]
.
The structure described by Hf8PbO24 crystallizes in the monoclinic C2/m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one O(1), one O(2), one O(3), one O(7), one O(8), and one O(9) atom to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Hf(2)O6 octahedra, and  a faceface with one Pb(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-11°. In the second Hf site, Hf(2) is bonded to one O(2), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Hf(2)O6 octahedra, and  a faceface with one Pb(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-11°. Pb(1) is bonded to two equivalent O(3), two equivalent O(4), four equivalent O(2), and four equivalent O(7) atoms to form PbO12 cuboctahedra that share faces with four equivalent Hf(1)O6 octahedra and faces with four equivalent Hf(2)O6 octahedra. There are nine inequivalent O sites. In the first O site, O(9) is bonded in a linear geometry to two equivalent Hf(1) atoms. In the second O site, O(1) is bonded in a linear geometry to two equivalent Hf(1) atoms. In the third O site, O(2) is bonded in a distorted linear geometry to one Hf(1), one Hf(2), and one Pb(1) atom. In the fourth O site, O(3) is bonded in a distorted linear geometry to two equivalent Hf(1) and one Pb(1) atom. In the fifth O site, O(4) is bonded in a linear geometry to two equivalent Hf(2) and one Pb(1) atom. In the sixth O site, O(5) is bonded in a linear geometry to two equivalent Hf(2) atoms. In the seventh O site, O(6) is bonded in a linear geometry to two equivalent Hf(2) atoms. In the eighth O site, O(7) is bonded in a distorted linear geometry to one Hf(1), one Hf(2), and one Pb(1) atom. In the ninth O site, O(8) is bonded in a linear geometry to one Hf(1) and one Hf(2) atom. is represented by the CIF file [CIF]
data_Hf8PbO24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.251
_cell_length_b   9.251
_cell_length_c   9.240
_cell_angle_alpha   66.598
_cell_angle_beta   66.598
_cell_angle_gamma   53.104
_symmetry_Int_Tables_number   1
_cell_volume   566.687
_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
  Hf  Hf0  1  0.818  0.309  0.754  1.0
  Hf  Hf1  1  0.691  0.182  0.246  1.0
  Hf  Hf2  1  0.309  0.818  0.754  1.0
  Hf  Hf3  1  0.055  0.564  0.754  1.0
  Hf  Hf4  1  0.182  0.691  0.246  1.0
  Hf  Hf5  1  0.945  0.436  0.246  1.0
  Hf  Hf6  1  0.564  0.055  0.754  1.0
  Hf  Hf7  1  0.436  0.945  0.246  1.0
  Pb  Pb8  1  0.500  0.500  0.500  1.0
  O  O9  1  0.748  0.252  0.000  1.0
  O  O10  1  0.678  0.203  0.737  1.0
  O  O11  1  0.797  0.322  0.263  1.0
  O  O12  1  0.559  0.559  0.737  1.0
  O  O13  1  0.322  0.322  0.738  1.0
  O  O14  1  0.441  0.441  0.263  1.0
  O  O15  1  0.186  0.186  0.252  1.0
  O  O16  1  0.252  0.748  0.000  1.0
  O  O17  1  0.203  0.678  0.737  1.0
  O  O18  1  0.000  0.500  0.000  1.0
  O  O19  1  0.144  0.619  0.500  1.0
  O  O20  1  0.322  0.797  0.263  1.0
  O  O21  1  0.938  0.438  0.747  1.0
  O  O22  1  0.856  0.381  0.500  1.0
  O  O23  1  0.062  0.562  0.253  1.0
  O  O24  1  0.814  0.814  0.748  1.0
  O  O25  1  0.938  0.938  0.251  1.0
  O  O26  1  0.678  0.678  0.262  1.0
  O  O27  1  0.062  0.062  0.749  1.0
  O  O28  1  0.500  0.000  0.000  1.0
  O  O29  1  0.438  0.938  0.747  1.0
  O  O30  1  0.562  0.062  0.253  1.0
  O  O31  1  0.381  0.856  0.500  1.0
  O  O32  1  0.619  0.144  0.500  1.0
[/CIF]
.