The material structure described by Pr3Zn22 crystallizes in the tetragonal I4_1/amd space group. There are two inequivalent Pr sites. In the first Pr site, Pr(1) is bonded in a 18-coordinate geometry to two equivalent Zn(3), two equivalent Zn(4), six equivalent Zn(2), and eight equivalent Zn(1) atoms. In the second Pr site, Pr(2) is bonded in a 20-coordinate geometry to four equivalent Zn(3), four equivalent Zn(4), four equivalent Zn(5), and eight equivalent Zn(1) atoms. There are five inequivalent Zn sites. In the first Zn site, Zn(3) is bonded to one Pr(1), one Pr(2), one Zn(3), one Zn(5), two equivalent Zn(2), two equivalent Zn(4), and four equivalent Zn(1) atoms to form distorted ZnPr2Zn10 cuboctahedra that share  a cornercorner with one Zn(5)Pr2Zn10 cuboctahedra, corners with two equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with two equivalent Zn(5)Pr2Zn10 cuboctahedra, edges with two equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with three equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with ten equivalent Zn(1)Pr3Zn9 cuboctahedra. In the second Zn site, Zn(1) is bonded to one Pr(2), two equivalent Pr(1), one Zn(5), two equivalent Zn(1), two equivalent Zn(2), two equivalent Zn(3), and two equivalent Zn(4) atoms to form distorted ZnPr3Zn9 cuboctahedra that share corners with two equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eleven equivalent Zn(1)Pr3Zn9 cuboctahedra,  an edgeedge with one Zn(3)Pr2Zn10 cuboctahedra,  an edgeedge with one Zn(4)Pr2Zn10 cuboctahedra,  an edgeedge with one Zn(5)Pr2Zn10 cuboctahedra, edges with five equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with six equivalent Zn(1)Pr3Zn9 cuboctahedra. In the third Zn site, Zn(4) is bonded to one Pr(1), one Pr(2), one Zn(2), one Zn(4), two equivalent Zn(3), two equivalent Zn(5), and four equivalent Zn(1) atoms to form distorted ZnPr2Zn10 cuboctahedra that share corners with two equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with five equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with two equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with three equivalent Zn(4)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(3)Pr2Zn10 cuboctahedra, and faces with ten equivalent Zn(1)Pr3Zn9 cuboctahedra. In the fourth Zn site, Zn(5) is bonded to two equivalent Pr(2), two equivalent Zn(3), four equivalent Zn(1), and four equivalent Zn(4) atoms to form ZnPr2Zn10 cuboctahedra that share corners with two equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with four equivalent Zn(3)Pr2Zn10 cuboctahedra, edges with four equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with four equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with four equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with eight equivalent Zn(1)Pr3Zn9 cuboctahedra. In the fifth Zn site, Zn(2) is bonded in a 12-coordinate geometry to three equivalent Pr(1), one Zn(4), two equivalent Zn(2), two equivalent Zn(3), and four equivalent Zn(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Pr3Zn22
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.807
_cell_length_b   8.807
_cell_length_c   12.247
_cell_angle_alpha   111.074
_cell_angle_beta   111.074
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   817.932
_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
  Pr  Pr0  1  0.496  0.746  0.993  1.0
  Pr  Pr1  1  0.746  0.496  0.493  1.0
  Pr  Pr2  1  0.504  0.254  0.007  1.0
  Pr  Pr3  1  0.254  0.504  0.507  1.0
  Pr  Pr4  1  0.125  0.875  0.250  1.0
  Pr  Pr5  1  0.875  0.125  0.750  1.0
  Zn  Zn6  1  0.422  0.195  0.377  1.0
  Zn  Zn7  1  0.422  0.682  0.377  1.0
  Zn  Zn8  1  0.195  0.422  0.877  1.0
  Zn  Zn9  1  0.195  0.956  0.877  1.0
  Zn  Zn10  1  0.956  0.195  0.377  1.0
  Zn  Zn11  1  0.956  0.682  0.377  1.0
  Zn  Zn12  1  0.682  0.422  0.877  1.0
  Zn  Zn13  1  0.682  0.956  0.877  1.0
  Zn  Zn14  1  0.578  0.805  0.623  1.0
  Zn  Zn15  1  0.578  0.318  0.623  1.0
  Zn  Zn16  1  0.805  0.578  0.123  1.0
  Zn  Zn17  1  0.805  0.044  0.123  1.0
  Zn  Zn18  1  0.044  0.805  0.623  1.0
  Zn  Zn19  1  0.044  0.318  0.623  1.0
  Zn  Zn20  1  0.318  0.578  0.123  1.0
  Zn  Zn21  1  0.318  0.044  0.123  1.0
  Zn  Zn22  1  0.147  0.623  0.746  1.0
  Zn  Zn23  1  0.623  0.147  0.246  1.0
  Zn  Zn24  1  0.623  0.599  0.246  1.0
  Zn  Zn25  1  0.599  0.623  0.746  1.0
  Zn  Zn26  1  0.853  0.377  0.254  1.0
  Zn  Zn27  1  0.377  0.853  0.754  1.0
  Zn  Zn28  1  0.377  0.401  0.754  1.0
  Zn  Zn29  1  0.401  0.377  0.254  1.0
  Zn  Zn30  1  0.487  0.884  0.268  1.0
  Zn  Zn31  1  0.884  0.487  0.768  1.0
  Zn  Zn32  1  0.884  0.780  0.768  1.0
  Zn  Zn33  1  0.780  0.884  0.268  1.0
  Zn  Zn34  1  0.513  0.116  0.732  1.0
  Zn  Zn35  1  0.116  0.513  0.232  1.0
  Zn  Zn36  1  0.116  0.220  0.232  1.0
  Zn  Zn37  1  0.220  0.116  0.732  1.0
  Zn  Zn38  1  0.835  0.736  0.972  1.0
  Zn  Zn39  1  0.736  0.835  0.472  1.0
  Zn  Zn40  1  0.736  0.136  0.472  1.0
  Zn  Zn41  1  0.136  0.736  0.972  1.0
  Zn  Zn42  1  0.165  0.264  0.028  1.0
  Zn  Zn43  1  0.264  0.165  0.528  1.0
  Zn  Zn44  1  0.264  0.864  0.528  1.0
  Zn  Zn45  1  0.864  0.264  0.028  1.0
  Zn  Zn46  1  0.500  0.000  0.500  1.0
  Zn  Zn47  1  0.000  0.500  0.000  1.0
  Zn  Zn48  1  0.000  0.000  0.000  1.0
  Zn  Zn49  1  0.000  0.000  0.500  1.0
[/CIF]
.
The material structure described by Pr3Zn22 crystallizes in the tetragonal I4_1/amd space group. There are two inequivalent Pr sites. In the first Pr site, Pr(1) is bonded in a 18-coordinate geometry to two equivalent Zn(3), two equivalent Zn(4), six equivalent Zn(2), and eight equivalent Zn(1) atoms. In the second Pr site, Pr(2) is bonded in a 20-coordinate geometry to four equivalent Zn(3), four equivalent Zn(4), four equivalent Zn(5), and eight equivalent Zn(1) atoms. There are five inequivalent Zn sites. In the first Zn site, Zn(3) is bonded to one Pr(1), one Pr(2), one Zn(3), one Zn(5), two equivalent Zn(2), two equivalent Zn(4), and four equivalent Zn(1) atoms to form distorted ZnPr2Zn10 cuboctahedra that share  a cornercorner with one Zn(5)Pr2Zn10 cuboctahedra, corners with two equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with two equivalent Zn(5)Pr2Zn10 cuboctahedra, edges with two equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with three equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with ten equivalent Zn(1)Pr3Zn9 cuboctahedra. In the second Zn site, Zn(1) is bonded to one Pr(2), two equivalent Pr(1), one Zn(5), two equivalent Zn(1), two equivalent Zn(2), two equivalent Zn(3), and two equivalent Zn(4) atoms to form distorted ZnPr3Zn9 cuboctahedra that share corners with two equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eleven equivalent Zn(1)Pr3Zn9 cuboctahedra,  an edgeedge with one Zn(3)Pr2Zn10 cuboctahedra,  an edgeedge with one Zn(4)Pr2Zn10 cuboctahedra,  an edgeedge with one Zn(5)Pr2Zn10 cuboctahedra, edges with five equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with six equivalent Zn(1)Pr3Zn9 cuboctahedra. In the third Zn site, Zn(4) is bonded to one Pr(1), one Pr(2), one Zn(2), one Zn(4), two equivalent Zn(3), two equivalent Zn(5), and four equivalent Zn(1) atoms to form distorted ZnPr2Zn10 cuboctahedra that share corners with two equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with five equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with two equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with three equivalent Zn(4)Pr2Zn10 cuboctahedra, faces with five equivalent Zn(3)Pr2Zn10 cuboctahedra, and faces with ten equivalent Zn(1)Pr3Zn9 cuboctahedra. In the fourth Zn site, Zn(5) is bonded to two equivalent Pr(2), two equivalent Zn(3), four equivalent Zn(1), and four equivalent Zn(4) atoms to form ZnPr2Zn10 cuboctahedra that share corners with two equivalent Zn(3)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(4)Pr2Zn10 cuboctahedra, corners with four equivalent Zn(5)Pr2Zn10 cuboctahedra, corners with eight equivalent Zn(1)Pr3Zn9 cuboctahedra, edges with four equivalent Zn(3)Pr2Zn10 cuboctahedra, edges with four equivalent Zn(1)Pr3Zn9 cuboctahedra, faces with two equivalent Zn(5)Pr2Zn10 cuboctahedra, faces with four equivalent Zn(3)Pr2Zn10 cuboctahedra, faces with four equivalent Zn(4)Pr2Zn10 cuboctahedra, and faces with eight equivalent Zn(1)Pr3Zn9 cuboctahedra. In the fifth Zn site, Zn(2) is bonded in a 12-coordinate geometry to three equivalent Pr(1), one Zn(4), two equivalent Zn(2), two equivalent Zn(3), and four equivalent Zn(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Pr3Zn22
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.807
_cell_length_b   8.807
_cell_length_c   12.247
_cell_angle_alpha   111.074
_cell_angle_beta   111.074
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   817.932
_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
  Pr  Pr0  1  0.496  0.746  0.993  1.0
  Pr  Pr1  1  0.746  0.496  0.493  1.0
  Pr  Pr2  1  0.504  0.254  0.007  1.0
  Pr  Pr3  1  0.254  0.504  0.507  1.0
  Pr  Pr4  1  0.125  0.875  0.250  1.0
  Pr  Pr5  1  0.875  0.125  0.750  1.0
  Zn  Zn6  1  0.422  0.195  0.377  1.0
  Zn  Zn7  1  0.422  0.682  0.377  1.0
  Zn  Zn8  1  0.195  0.422  0.877  1.0
  Zn  Zn9  1  0.195  0.956  0.877  1.0
  Zn  Zn10  1  0.956  0.195  0.377  1.0
  Zn  Zn11  1  0.956  0.682  0.377  1.0
  Zn  Zn12  1  0.682  0.422  0.877  1.0
  Zn  Zn13  1  0.682  0.956  0.877  1.0
  Zn  Zn14  1  0.578  0.805  0.623  1.0
  Zn  Zn15  1  0.578  0.318  0.623  1.0
  Zn  Zn16  1  0.805  0.578  0.123  1.0
  Zn  Zn17  1  0.805  0.044  0.123  1.0
  Zn  Zn18  1  0.044  0.805  0.623  1.0
  Zn  Zn19  1  0.044  0.318  0.623  1.0
  Zn  Zn20  1  0.318  0.578  0.123  1.0
  Zn  Zn21  1  0.318  0.044  0.123  1.0
  Zn  Zn22  1  0.147  0.623  0.746  1.0
  Zn  Zn23  1  0.623  0.147  0.246  1.0
  Zn  Zn24  1  0.623  0.599  0.246  1.0
  Zn  Zn25  1  0.599  0.623  0.746  1.0
  Zn  Zn26  1  0.853  0.377  0.254  1.0
  Zn  Zn27  1  0.377  0.853  0.754  1.0
  Zn  Zn28  1  0.377  0.401  0.754  1.0
  Zn  Zn29  1  0.401  0.377  0.254  1.0
  Zn  Zn30  1  0.487  0.884  0.268  1.0
  Zn  Zn31  1  0.884  0.487  0.768  1.0
  Zn  Zn32  1  0.884  0.780  0.768  1.0
  Zn  Zn33  1  0.780  0.884  0.268  1.0
  Zn  Zn34  1  0.513  0.116  0.732  1.0
  Zn  Zn35  1  0.116  0.513  0.232  1.0
  Zn  Zn36  1  0.116  0.220  0.232  1.0
  Zn  Zn37  1  0.220  0.116  0.732  1.0
  Zn  Zn38  1  0.835  0.736  0.972  1.0
  Zn  Zn39  1  0.736  0.835  0.472  1.0
  Zn  Zn40  1  0.736  0.136  0.472  1.0
  Zn  Zn41  1  0.136  0.736  0.972  1.0
  Zn  Zn42  1  0.165  0.264  0.028  1.0
  Zn  Zn43  1  0.264  0.165  0.528  1.0
  Zn  Zn44  1  0.264  0.864  0.528  1.0
  Zn  Zn45  1  0.864  0.264  0.028  1.0
  Zn  Zn46  1  0.500  0.000  0.500  1.0
  Zn  Zn47  1  0.000  0.500  0.000  1.0
  Zn  Zn48  1  0.000  0.000  0.000  1.0
  Zn  Zn49  1  0.000  0.000  0.500  1.0
[/CIF]
.