The crystal structure described by HfZn22 crystallizes in the cubic Fd-3m space group. Hf(1) is bonded in a 16-coordinate geometry to four equivalent Zn(3) and twelve equivalent Zn(2) atoms. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Zn(4), four equivalent Zn(1), and six equivalent Zn(2) atoms to form distorted ZnZn12 cuboctahedra that share corners with two equivalent Zn(1)Zn12 cuboctahedra, corners with sixteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(4)Zn12 cuboctahedra, faces with two equivalent Zn(4)Zn12 cuboctahedra, faces with nine equivalent Zn(1)Zn12 cuboctahedra, and faces with fourteen equivalent Zn(2)HfZn11 cuboctahedra. In the second Zn site, Zn(3) is bonded in a 14-coordinate geometry to two equivalent Hf(1) and twelve equivalent Zn(2) atoms. In the third Zn site, Zn(4) is bonded to six equivalent Zn(1) and six equivalent Zn(2) atoms to form ZnZn12 cuboctahedra that share corners with six equivalent Zn(4)Zn12 cuboctahedra, edges with six equivalent Zn(1)Zn12 cuboctahedra, edges with eighteen equivalent Zn(2)HfZn11 cuboctahedra, faces with six equivalent Zn(2)HfZn11 cuboctahedra, and faces with six equivalent Zn(1)Zn12 cuboctahedra. In the fourth Zn site, Zn(2) is bonded to one Hf(1), one Zn(4), two equivalent Zn(3), three equivalent Zn(1), and five equivalent Zn(2) atoms to form ZnHfZn11 cuboctahedra that share corners with eight equivalent Zn(1)Zn12 cuboctahedra, corners with fifteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(2)HfZn11 cuboctahedra, edges with three equivalent Zn(4)Zn12 cuboctahedra,  a faceface with one Zn(4)Zn12 cuboctahedra, faces with seven equivalent Zn(1)Zn12 cuboctahedra, and faces with fifteen equivalent Zn(2)HfZn11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfZn22
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.836
_cell_length_b   9.836
_cell_length_c   9.836
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   672.893
_cell_formula_units_Z   2
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  0.500  0.500  0.500  1.0
  Hf  Hf1  1  0.750  0.750  0.750  1.0
  Zn  Zn2  1  0.860  0.860  0.140  1.0
  Zn  Zn3  1  0.140  0.140  0.860  1.0
  Zn  Zn4  1  0.860  0.140  0.860  1.0
  Zn  Zn5  1  0.140  0.860  0.140  1.0
  Zn  Zn6  1  0.140  0.860  0.860  1.0
  Zn  Zn7  1  0.860  0.140  0.140  1.0
  Zn  Zn8  1  0.390  0.390  0.110  1.0
  Zn  Zn9  1  0.110  0.110  0.390  1.0
  Zn  Zn10  1  0.390  0.110  0.390  1.0
  Zn  Zn11  1  0.110  0.390  0.110  1.0
  Zn  Zn12  1  0.110  0.390  0.390  1.0
  Zn  Zn13  1  0.390  0.110  0.110  1.0
  Zn  Zn14  1  0.567  0.306  0.306  1.0
  Zn  Zn15  1  0.306  0.567  0.820  1.0
  Zn  Zn16  1  0.306  0.820  0.567  1.0
  Zn  Zn17  1  0.820  0.306  0.306  1.0
  Zn  Zn18  1  0.306  0.306  0.567  1.0
  Zn  Zn19  1  0.567  0.820  0.306  1.0
  Zn  Zn20  1  0.820  0.567  0.306  1.0
  Zn  Zn21  1  0.306  0.306  0.820  1.0
  Zn  Zn22  1  0.306  0.567  0.306  1.0
  Zn  Zn23  1  0.820  0.306  0.567  1.0
  Zn  Zn24  1  0.567  0.306  0.820  1.0
  Zn  Zn25  1  0.306  0.820  0.306  1.0
  Zn  Zn26  1  0.683  0.944  0.944  1.0
  Zn  Zn27  1  0.944  0.683  0.430  1.0
  Zn  Zn28  1  0.944  0.430  0.683  1.0
  Zn  Zn29  1  0.430  0.944  0.944  1.0
  Zn  Zn30  1  0.944  0.944  0.683  1.0
  Zn  Zn31  1  0.683  0.430  0.944  1.0
  Zn  Zn32  1  0.430  0.683  0.944  1.0
  Zn  Zn33  1  0.944  0.944  0.430  1.0
  Zn  Zn34  1  0.944  0.683  0.944  1.0
  Zn  Zn35  1  0.430  0.944  0.683  1.0
  Zn  Zn36  1  0.683  0.944  0.430  1.0
  Zn  Zn37  1  0.944  0.430  0.944  1.0
  Zn  Zn38  1  0.125  0.625  0.625  1.0
  Zn  Zn39  1  0.625  0.125  0.625  1.0
  Zn  Zn40  1  0.625  0.625  0.125  1.0
  Zn  Zn41  1  0.625  0.625  0.625  1.0
  Zn  Zn42  1  0.625  0.125  0.125  1.0
  Zn  Zn43  1  0.125  0.625  0.125  1.0
  Zn  Zn44  1  0.125  0.125  0.625  1.0
  Zn  Zn45  1  0.125  0.125  0.125  1.0
[/CIF]
.
The crystal structure described by HfZn22 crystallizes in the cubic Fd-3m space group. Hf(1) is bonded in a 16-coordinate geometry to four equivalent Zn(3) and twelve equivalent Zn(2) atoms. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Zn(4), four equivalent Zn(1), and six equivalent Zn(2) atoms to form distorted ZnZn12 cuboctahedra that share corners with two equivalent Zn(1)Zn12 cuboctahedra, corners with sixteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(4)Zn12 cuboctahedra, faces with two equivalent Zn(4)Zn12 cuboctahedra, faces with nine equivalent Zn(1)Zn12 cuboctahedra, and faces with fourteen equivalent Zn(2)HfZn11 cuboctahedra. In the second Zn site, Zn(3) is bonded in a 14-coordinate geometry to two equivalent Hf(1) and twelve equivalent Zn(2) atoms. In the third Zn site, Zn(4) is bonded to six equivalent Zn(1) and six equivalent Zn(2) atoms to form ZnZn12 cuboctahedra that share corners with six equivalent Zn(4)Zn12 cuboctahedra, edges with six equivalent Zn(1)Zn12 cuboctahedra, edges with eighteen equivalent Zn(2)HfZn11 cuboctahedra, faces with six equivalent Zn(2)HfZn11 cuboctahedra, and faces with six equivalent Zn(1)Zn12 cuboctahedra. In the fourth Zn site, Zn(2) is bonded to one Hf(1), one Zn(4), two equivalent Zn(3), three equivalent Zn(1), and five equivalent Zn(2) atoms to form ZnHfZn11 cuboctahedra that share corners with eight equivalent Zn(1)Zn12 cuboctahedra, corners with fifteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(2)HfZn11 cuboctahedra, edges with three equivalent Zn(4)Zn12 cuboctahedra,  a faceface with one Zn(4)Zn12 cuboctahedra, faces with seven equivalent Zn(1)Zn12 cuboctahedra, and faces with fifteen equivalent Zn(2)HfZn11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfZn22
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.836
_cell_length_b   9.836
_cell_length_c   9.836
_cell_angle_alpha   60.000
_cell_angle_beta   60.000
_cell_angle_gamma   60.000
_symmetry_Int_Tables_number   1
_cell_volume   672.893
_cell_formula_units_Z   2
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  0.500  0.500  0.500  1.0
  Hf  Hf1  1  0.750  0.750  0.750  1.0
  Zn  Zn2  1  0.860  0.860  0.140  1.0
  Zn  Zn3  1  0.140  0.140  0.860  1.0
  Zn  Zn4  1  0.860  0.140  0.860  1.0
  Zn  Zn5  1  0.140  0.860  0.140  1.0
  Zn  Zn6  1  0.140  0.860  0.860  1.0
  Zn  Zn7  1  0.860  0.140  0.140  1.0
  Zn  Zn8  1  0.390  0.390  0.110  1.0
  Zn  Zn9  1  0.110  0.110  0.390  1.0
  Zn  Zn10  1  0.390  0.110  0.390  1.0
  Zn  Zn11  1  0.110  0.390  0.110  1.0
  Zn  Zn12  1  0.110  0.390  0.390  1.0
  Zn  Zn13  1  0.390  0.110  0.110  1.0
  Zn  Zn14  1  0.567  0.306  0.306  1.0
  Zn  Zn15  1  0.306  0.567  0.820  1.0
  Zn  Zn16  1  0.306  0.820  0.567  1.0
  Zn  Zn17  1  0.820  0.306  0.306  1.0
  Zn  Zn18  1  0.306  0.306  0.567  1.0
  Zn  Zn19  1  0.567  0.820  0.306  1.0
  Zn  Zn20  1  0.820  0.567  0.306  1.0
  Zn  Zn21  1  0.306  0.306  0.820  1.0
  Zn  Zn22  1  0.306  0.567  0.306  1.0
  Zn  Zn23  1  0.820  0.306  0.567  1.0
  Zn  Zn24  1  0.567  0.306  0.820  1.0
  Zn  Zn25  1  0.306  0.820  0.306  1.0
  Zn  Zn26  1  0.683  0.944  0.944  1.0
  Zn  Zn27  1  0.944  0.683  0.430  1.0
  Zn  Zn28  1  0.944  0.430  0.683  1.0
  Zn  Zn29  1  0.430  0.944  0.944  1.0
  Zn  Zn30  1  0.944  0.944  0.683  1.0
  Zn  Zn31  1  0.683  0.430  0.944  1.0
  Zn  Zn32  1  0.430  0.683  0.944  1.0
  Zn  Zn33  1  0.944  0.944  0.430  1.0
  Zn  Zn34  1  0.944  0.683  0.944  1.0
  Zn  Zn35  1  0.430  0.944  0.683  1.0
  Zn  Zn36  1  0.683  0.944  0.430  1.0
  Zn  Zn37  1  0.944  0.430  0.944  1.0
  Zn  Zn38  1  0.125  0.625  0.625  1.0
  Zn  Zn39  1  0.625  0.125  0.625  1.0
  Zn  Zn40  1  0.625  0.625  0.125  1.0
  Zn  Zn41  1  0.625  0.625  0.625  1.0
  Zn  Zn42  1  0.625  0.125  0.125  1.0
  Zn  Zn43  1  0.125  0.625  0.125  1.0
  Zn  Zn44  1  0.125  0.125  0.625  1.0
  Zn  Zn45  1  0.125  0.125  0.125  1.0
[/CIF]
.