The compound described by HfNi3 is beta Cu3Ti-like structured and crystallizes in the hexagonal P6_3/mmc space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three Ni(1,1) and nine Ni(3,3) atoms to form HfNi12 cuboctahedra that share corners with three equivalent Hf(3)Ni12 cuboctahedra; corners with six equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with three Ni(2,2)Hf4Ni8 cuboctahedra; edges with six Ni(1,1)Hf4Ni8 cuboctahedra; edges with twelve Ni(3,3)Hf4Ni8 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with three Ni(1,1)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(2)Ni12 cuboctahedra; and faces with nine Ni(3,3)Hf4Ni8 cuboctahedra. In the second Hf site, Hf(2) is bonded to three Ni(2,2); three equivalent Ni(3); and six equivalent Ni(1) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(2)Ni12 cuboctahedra; corners with six equivalent Ni(1)Hf4Ni8 cuboctahedra; corners with six Ni(3,3)Hf4Ni8 cuboctahedra; edges with six equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with six Ni(2,2)Hf4Ni8 cuboctahedra; edges with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(3)Ni12 cuboctahedra; faces with three Ni(2,2)Hf4Ni8 cuboctahedra; faces with three equivalent Ni(3)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(1)Ni12 cuboctahedra; and faces with six equivalent Ni(1)Hf4Ni8 cuboctahedra. In the third Hf site, Hf(3) is bonded to six Ni(1,1) and six Ni(2,2) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Hf(3)Ni12 cuboctahedra; edges with six Ni(2,2)Hf4Ni8 cuboctahedra; edges with six Ni(3,3)Hf4Ni8 cuboctahedra; edges with twelve Ni(1,1)Hf4Ni8 cuboctahedra; faces with six equivalent Hf(2)Ni12 cuboctahedra; faces with six Ni(1,1)Hf4Ni8 cuboctahedra; and faces with six Ni(2,2)Hf4Ni8 cuboctahedra. There are seven inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one Hf(1); one Hf(3); two equivalent Hf(2); two Ni(2,2); two equivalent Ni(3); and four equivalent Ni(1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(1)Ni12 cuboctahedra; corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(3)Hf4Ni8 cuboctahedra; corners with ten equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(1)Ni12 cuboctahedra;  a faceface with one Hf(3)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with five equivalent Ni(1)Hf4Ni8 cuboctahedra; faces with five Ni(2,2)Hf4Ni8 cuboctahedra; and faces with six Ni(3,3)Hf4Ni8 cuboctahedra. In the second Ni site, Ni(1) is bonded to one Hf(1); one Hf(3); two equivalent Hf(2); two Ni(2,2); two equivalent Ni(3); and four equivalent Ni(1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(1)Ni12 cuboctahedra; corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(3)Hf4Ni8 cuboctahedra; corners with ten Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(1)Ni12 cuboctahedra;  a faceface with one Hf(3)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with five Ni(1,1)Hf4Ni8 cuboctahedra; faces with five Ni(2,2)Hf4Ni8 cuboctahedra; and faces with six Ni(3,3)Hf4Ni8 cuboctahedra. In the third Ni site, Ni(2) is bonded to two equivalent Hf(2); two equivalent Hf(3); four equivalent Ni(1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with eight equivalent Ni(1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with two equivalent Hf(3)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with ten equivalent Ni(1)Hf4Ni8 cuboctahedra. In the fourth Ni site, Ni(2) is bonded to two equivalent Hf(2), two equivalent Hf(3), four equivalent Ni(1), and four equivalent Ni(2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra, corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra, edges with two equivalent Hf(1)Ni12 cuboctahedra, edges with two equivalent Hf(3)Ni12 cuboctahedra, edges with four equivalent Hf(2)Ni12 cuboctahedra, edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra, edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra, edges with eight equivalent Ni(1)Hf4Ni8 cuboctahedra, faces with two equivalent Hf(2)Ni12 cuboctahedra, faces with two equivalent Hf(3)Ni12 cuboctahedra, faces with four equivalent Ni(2)Hf4Ni8 cuboctahedra, and faces with ten equivalent Ni(1)Hf4Ni8 cuboctahedra. In the fifth Ni site, Ni(2) is bonded to two equivalent Hf(2); two equivalent Hf(3); four Ni(1,1); and four equivalent Ni(2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra; edges with four Ni(3,3)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with two equivalent Hf(3)Ni12 cuboctahedra; faces with four equivalent Ni(2)Hf4Ni8 cuboctahedra; and faces with ten Ni(1,1)Hf4Ni8 cuboctahedra. In the sixth Ni site, Ni(3) is bonded to one Hf(2); three equivalent Hf(1); two equivalent Ni(1); and six Ni(3,3) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with three equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with four Ni(1,1)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  an edgeedge with one Hf(3)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with eight Ni(3,3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six equivalent Ni(1)Hf4Ni8 cuboctahedra; and faces with nine Ni(3,3)Hf4Ni8 cuboctahedra. In the seventh Ni site, Ni(3) is bonded to one Hf(2), three equivalent Hf(1), two equivalent Ni(1), and six equivalent Ni(3) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with three equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with four equivalent Ni(1)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  an edgeedge with one Hf(3)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with eight equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(1,1)Hf4Ni8 cuboctahedra; and faces with nine equivalent Ni(3)Hf4Ni8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfNi3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.220
_cell_length_b   5.220
_cell_length_c   21.191
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   500.081
_cell_formula_units_Z   10
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  0.333  0.667  0.954  1.0
  Hf  Hf1  1  0.667  0.333  0.454  1.0
  Hf  Hf2  1  0.667  0.333  0.046  1.0
  Hf  Hf3  1  0.333  0.667  0.546  1.0
  Hf  Hf4  1  0.333  0.667  0.151  1.0
  Hf  Hf5  1  0.667  0.333  0.651  1.0
  Hf  Hf6  1  0.667  0.333  0.849  1.0
  Hf  Hf7  1  0.333  0.667  0.349  1.0
  Hf  Hf8  1  0.000  0.000  0.750  1.0
  Hf  Hf9  1  0.000  0.000  0.250  1.0
  Ni  Ni10  1  0.832  0.168  0.350  1.0
  Ni  Ni11  1  0.832  0.665  0.350  1.0
  Ni  Ni12  1  0.335  0.168  0.350  1.0
  Ni  Ni13  1  0.665  0.832  0.850  1.0
  Ni  Ni14  1  0.168  0.335  0.650  1.0
  Ni  Ni15  1  0.168  0.832  0.850  1.0
  Ni  Ni16  1  0.168  0.335  0.850  1.0
  Ni  Ni17  1  0.832  0.168  0.150  1.0
  Ni  Ni18  1  0.335  0.168  0.150  1.0
  Ni  Ni19  1  0.665  0.832  0.650  1.0
  Ni  Ni20  1  0.511  0.022  0.250  1.0
  Ni  Ni21  1  0.489  0.511  0.750  1.0
  Ni  Ni22  1  0.022  0.511  0.750  1.0
  Ni  Ni23  1  0.978  0.489  0.250  1.0
  Ni  Ni24  1  0.511  0.489  0.250  1.0
  Ni  Ni25  1  0.489  0.978  0.750  1.0
  Ni  Ni26  1  0.156  0.312  0.051  1.0
  Ni  Ni27  1  0.844  0.156  0.551  1.0
  Ni  Ni28  1  0.312  0.156  0.551  1.0
  Ni  Ni29  1  0.688  0.844  0.051  1.0
  Ni  Ni30  1  0.156  0.844  0.051  1.0
  Ni  Ni31  1  0.844  0.688  0.949  1.0
  Ni  Ni32  1  0.844  0.156  0.949  1.0
  Ni  Ni33  1  0.844  0.688  0.551  1.0
  Ni  Ni34  1  0.312  0.156  0.949  1.0
  Ni  Ni35  1  0.688  0.844  0.449  1.0
  Ni  Ni36  1  0.156  0.312  0.449  1.0
  Ni  Ni37  1  0.156  0.844  0.449  1.0
  Ni  Ni38  1  0.832  0.665  0.150  1.0
  Ni  Ni39  1  0.168  0.832  0.650  1.0
[/CIF]
.
The compound described by HfNi3 is beta Cu3Ti-like structured and crystallizes in the hexagonal P6_3/mmc space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three Ni(1,1) and nine Ni(3,3) atoms to form HfNi12 cuboctahedra that share corners with three equivalent Hf(3)Ni12 cuboctahedra; corners with six equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with three Ni(2,2)Hf4Ni8 cuboctahedra; edges with six Ni(1,1)Hf4Ni8 cuboctahedra; edges with twelve Ni(3,3)Hf4Ni8 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with three Ni(1,1)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(2)Ni12 cuboctahedra; and faces with nine Ni(3,3)Hf4Ni8 cuboctahedra. In the second Hf site, Hf(2) is bonded to three Ni(2,2); three equivalent Ni(3); and six equivalent Ni(1) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(2)Ni12 cuboctahedra; corners with six equivalent Ni(1)Hf4Ni8 cuboctahedra; corners with six Ni(3,3)Hf4Ni8 cuboctahedra; edges with six equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with six Ni(2,2)Hf4Ni8 cuboctahedra; edges with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(3)Ni12 cuboctahedra; faces with three Ni(2,2)Hf4Ni8 cuboctahedra; faces with three equivalent Ni(3)Hf4Ni8 cuboctahedra; faces with four equivalent Hf(1)Ni12 cuboctahedra; and faces with six equivalent Ni(1)Hf4Ni8 cuboctahedra. In the third Hf site, Hf(3) is bonded to six Ni(1,1) and six Ni(2,2) atoms to form HfNi12 cuboctahedra that share corners with six equivalent Hf(1)Ni12 cuboctahedra; corners with six equivalent Hf(3)Ni12 cuboctahedra; edges with six Ni(2,2)Hf4Ni8 cuboctahedra; edges with six Ni(3,3)Hf4Ni8 cuboctahedra; edges with twelve Ni(1,1)Hf4Ni8 cuboctahedra; faces with six equivalent Hf(2)Ni12 cuboctahedra; faces with six Ni(1,1)Hf4Ni8 cuboctahedra; and faces with six Ni(2,2)Hf4Ni8 cuboctahedra. There are seven inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one Hf(1); one Hf(3); two equivalent Hf(2); two Ni(2,2); two equivalent Ni(3); and four equivalent Ni(1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(1)Ni12 cuboctahedra; corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(3)Hf4Ni8 cuboctahedra; corners with ten equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(1)Ni12 cuboctahedra;  a faceface with one Hf(3)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with five equivalent Ni(1)Hf4Ni8 cuboctahedra; faces with five Ni(2,2)Hf4Ni8 cuboctahedra; and faces with six Ni(3,3)Hf4Ni8 cuboctahedra. In the second Ni site, Ni(1) is bonded to one Hf(1); one Hf(3); two equivalent Hf(2); two Ni(2,2); two equivalent Ni(3); and four equivalent Ni(1) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(1)Ni12 cuboctahedra; corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with four equivalent Ni(3)Hf4Ni8 cuboctahedra; corners with ten Ni(1,1)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(1)Ni12 cuboctahedra;  a faceface with one Hf(3)Ni12 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with five Ni(1,1)Hf4Ni8 cuboctahedra; faces with five Ni(2,2)Hf4Ni8 cuboctahedra; and faces with six Ni(3,3)Hf4Ni8 cuboctahedra. In the third Ni site, Ni(2) is bonded to two equivalent Hf(2); two equivalent Hf(3); four equivalent Ni(1); and four Ni(2,2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Hf(2)Ni12 cuboctahedra; edges with four Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with eight equivalent Ni(1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with two equivalent Hf(3)Ni12 cuboctahedra; faces with four Ni(2,2)Hf4Ni8 cuboctahedra; and faces with ten equivalent Ni(1)Hf4Ni8 cuboctahedra. In the fourth Ni site, Ni(2) is bonded to two equivalent Hf(2), two equivalent Hf(3), four equivalent Ni(1), and four equivalent Ni(2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra, corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra, edges with two equivalent Hf(1)Ni12 cuboctahedra, edges with two equivalent Hf(3)Ni12 cuboctahedra, edges with four equivalent Hf(2)Ni12 cuboctahedra, edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra, edges with four equivalent Ni(3)Hf4Ni8 cuboctahedra, edges with eight equivalent Ni(1)Hf4Ni8 cuboctahedra, faces with two equivalent Hf(2)Ni12 cuboctahedra, faces with two equivalent Hf(3)Ni12 cuboctahedra, faces with four equivalent Ni(2)Hf4Ni8 cuboctahedra, and faces with ten equivalent Ni(1)Hf4Ni8 cuboctahedra. In the fifth Ni site, Ni(2) is bonded to two equivalent Hf(2); two equivalent Hf(3); four Ni(1,1); and four equivalent Ni(2) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with six equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra; edges with two equivalent Hf(1)Ni12 cuboctahedra; edges with two equivalent Hf(3)Ni12 cuboctahedra; edges with four equivalent Hf(2)Ni12 cuboctahedra; edges with four equivalent Ni(2)Hf4Ni8 cuboctahedra; edges with four Ni(3,3)Hf4Ni8 cuboctahedra; edges with eight Ni(1,1)Hf4Ni8 cuboctahedra; faces with two equivalent Hf(2)Ni12 cuboctahedra; faces with two equivalent Hf(3)Ni12 cuboctahedra; faces with four equivalent Ni(2)Hf4Ni8 cuboctahedra; and faces with ten Ni(1,1)Hf4Ni8 cuboctahedra. In the sixth Ni site, Ni(3) is bonded to one Hf(2); three equivalent Hf(1); two equivalent Ni(1); and six Ni(3,3) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with three equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with four Ni(1,1)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  an edgeedge with one Hf(3)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with eight Ni(3,3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six equivalent Ni(1)Hf4Ni8 cuboctahedra; and faces with nine Ni(3,3)Hf4Ni8 cuboctahedra. In the seventh Ni site, Ni(3) is bonded to one Hf(2), three equivalent Hf(1), two equivalent Ni(1), and six equivalent Ni(3) atoms to form distorted NiHf4Ni8 cuboctahedra that share corners with two equivalent Hf(2)Ni12 cuboctahedra; corners with three equivalent Ni(2)Hf4Ni8 cuboctahedra; corners with four equivalent Ni(1)Hf4Ni8 cuboctahedra; corners with six equivalent Ni(3)Hf4Ni8 cuboctahedra;  an edgeedge with one Hf(3)Ni12 cuboctahedra; edges with two equivalent Hf(2)Ni12 cuboctahedra; edges with two Ni(2,2)Hf4Ni8 cuboctahedra; edges with four equivalent Hf(1)Ni12 cuboctahedra; edges with four equivalent Ni(1)Hf4Ni8 cuboctahedra; edges with eight equivalent Ni(3)Hf4Ni8 cuboctahedra;  a faceface with one Hf(2)Ni12 cuboctahedra; faces with three equivalent Hf(1)Ni12 cuboctahedra; faces with six Ni(1,1)Hf4Ni8 cuboctahedra; and faces with nine equivalent Ni(3)Hf4Ni8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfNi3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.220
_cell_length_b   5.220
_cell_length_c   21.191
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   500.081
_cell_formula_units_Z   10
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  0.333  0.667  0.954  1.0
  Hf  Hf1  1  0.667  0.333  0.454  1.0
  Hf  Hf2  1  0.667  0.333  0.046  1.0
  Hf  Hf3  1  0.333  0.667  0.546  1.0
  Hf  Hf4  1  0.333  0.667  0.151  1.0
  Hf  Hf5  1  0.667  0.333  0.651  1.0
  Hf  Hf6  1  0.667  0.333  0.849  1.0
  Hf  Hf7  1  0.333  0.667  0.349  1.0
  Hf  Hf8  1  0.000  0.000  0.750  1.0
  Hf  Hf9  1  0.000  0.000  0.250  1.0
  Ni  Ni10  1  0.832  0.168  0.350  1.0
  Ni  Ni11  1  0.832  0.665  0.350  1.0
  Ni  Ni12  1  0.335  0.168  0.350  1.0
  Ni  Ni13  1  0.665  0.832  0.850  1.0
  Ni  Ni14  1  0.168  0.335  0.650  1.0
  Ni  Ni15  1  0.168  0.832  0.850  1.0
  Ni  Ni16  1  0.168  0.335  0.850  1.0
  Ni  Ni17  1  0.832  0.168  0.150  1.0
  Ni  Ni18  1  0.335  0.168  0.150  1.0
  Ni  Ni19  1  0.665  0.832  0.650  1.0
  Ni  Ni20  1  0.511  0.022  0.250  1.0
  Ni  Ni21  1  0.489  0.511  0.750  1.0
  Ni  Ni22  1  0.022  0.511  0.750  1.0
  Ni  Ni23  1  0.978  0.489  0.250  1.0
  Ni  Ni24  1  0.511  0.489  0.250  1.0
  Ni  Ni25  1  0.489  0.978  0.750  1.0
  Ni  Ni26  1  0.156  0.312  0.051  1.0
  Ni  Ni27  1  0.844  0.156  0.551  1.0
  Ni  Ni28  1  0.312  0.156  0.551  1.0
  Ni  Ni29  1  0.688  0.844  0.051  1.0
  Ni  Ni30  1  0.156  0.844  0.051  1.0
  Ni  Ni31  1  0.844  0.688  0.949  1.0
  Ni  Ni32  1  0.844  0.156  0.949  1.0
  Ni  Ni33  1  0.844  0.688  0.551  1.0
  Ni  Ni34  1  0.312  0.156  0.949  1.0
  Ni  Ni35  1  0.688  0.844  0.449  1.0
  Ni  Ni36  1  0.156  0.312  0.449  1.0
  Ni  Ni37  1  0.156  0.844  0.449  1.0
  Ni  Ni38  1  0.832  0.665  0.150  1.0
  Ni  Ni39  1  0.168  0.832  0.650  1.0
[/CIF]
.