The compound described by Ho4HfAl15 is Uranium Silicide-derived structured and crystallizes in the tetragonal P4/mmm space group. There are two inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to four equivalent Al(2), four equivalent Al(4), and four equivalent Al(5) atoms to form HoAl12 cuboctahedra that share corners with four equivalent Ho(1)Al12 cuboctahedra, corners with four equivalent Ho(2)Al12 cuboctahedra, corners with four equivalent Hf(1)Al12 cuboctahedra, edges with four equivalent Al(1)Hf4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Ho(2)Al12 cuboctahedra,  a faceface with one Hf(1)Al12 cuboctahedra, faces with four equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with four equivalent Al(2)Ho4Al8 cuboctahedra, and faces with four equivalent Al(5)Ho4Al8 cuboctahedra. In the second Ho site, Ho(2) is bonded to four equivalent Al(3), four equivalent Al(5), and four equivalent Al(6) atoms to form HoAl12 cuboctahedra that share corners with four equivalent Ho(1)Al12 cuboctahedra, corners with eight equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Ho(1)Al12 cuboctahedra, faces with four equivalent Al(3)Ho4Al8 cuboctahedra, faces with four equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Al(6)Ho4Al8 cuboctahedra, and faces with five equivalent Ho(2)Al12 cuboctahedra. Hf(1) is bonded to four equivalent Al(1) and eight equivalent Al(4) atoms to form HfAl12 cuboctahedra that share corners with four equivalent Hf(1)Al12 cuboctahedra, corners with eight equivalent Ho(1)Al12 cuboctahedra, edges with eight equivalent Al(2)Ho4Al8 cuboctahedra, edges with sixteen equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Hf(1)Al12 cuboctahedra, faces with four equivalent Al(1)Hf4Al8 cuboctahedra, and faces with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to four equivalent Hf(1) and eight equivalent Al(4) atoms to form AlHf4Al8 cuboctahedra that share corners with four equivalent Al(1)Hf4Al8 cuboctahedra, corners with eight equivalent Al(2)Ho4Al8 cuboctahedra, edges with eight equivalent Ho(1)Al12 cuboctahedra, edges with sixteen equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, faces with four equivalent Hf(1)Al12 cuboctahedra, faces with four equivalent Al(1)Hf4Al8 cuboctahedra, and faces with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra. In the second Al site, Al(2) is bonded to four equivalent Ho(1), four equivalent Al(4), and four equivalent Al(5) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(1)Hf4Al8 cuboctahedra, corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Hf(1)Al12 cuboctahedra, edges with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Al(1)Hf4Al8 cuboctahedra,  a faceface with one Al(3)Ho4Al8 cuboctahedra, faces with four equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with four equivalent Al(2)Ho4Al8 cuboctahedra, and faces with four equivalent Al(5)Ho4Al8 cuboctahedra. In the third Al site, Al(3) is bonded to four equivalent Ho(2), four equivalent Al(5), and four equivalent Al(6) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Al(2)Ho4Al8 cuboctahedra, faces with four equivalent Ho(2)Al12 cuboctahedra, faces with four equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Al(6)Ho4Al8 cuboctahedra, and faces with five equivalent Al(3)Ho4Al8 cuboctahedra. In the fourth Al site, Al(4) is bonded to two equivalent Ho(1), two equivalent Hf(1), two equivalent Al(1), two equivalent Al(2), and four equivalent Al(4) atoms to form distorted AlHo2Hf2Al8 cuboctahedra that share corners with four equivalent Al(5)Ho4Al8 cuboctahedra, corners with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Hf(1)Al12 cuboctahedra, edges with four equivalent Al(1)Hf4Al8 cuboctahedra, edges with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Al(5)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Hf(1)Al12 cuboctahedra, faces with two equivalent Al(1)Hf4Al8 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, and faces with nine equivalent Al(4)Ho2Hf2Al8 cuboctahedra. In the fifth Al site, Al(5) is bonded to two equivalent Ho(1), two equivalent Ho(2), two equivalent Al(2), two equivalent Al(3), and four equivalent Al(5) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, corners with four equivalent Al(5)Ho4Al8 cuboctahedra, corners with four equivalent Al(6)Ho4Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Al(4)Ho2Hf2Al8 cuboctahedra,  a faceface with one Al(6)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Ho(2)Al12 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Al(3)Ho4Al8 cuboctahedra, and faces with eight equivalent Al(5)Ho4Al8 cuboctahedra. In the sixth Al site, Al(6) is bonded to four equivalent Ho(2), four equivalent Al(3), and four equivalent Al(6) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(6)Ho4Al8 cuboctahedra, corners with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, faces with two equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Ho(2)Al12 cuboctahedra, faces with four equivalent Al(3)Ho4Al8 cuboctahedra, and faces with eight equivalent Al(6)Ho4Al8 cuboctahedra. is represented by the CIF file [CIF]
data_Ho4HfAl15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.217
_cell_length_b   4.217
_cell_length_c   21.098
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   375.155
_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
  Ho  Ho0  1  0.000  0.000  0.197  1.0
  Ho  Ho1  1  0.000  0.000  0.399  1.0
  Ho  Ho2  1  0.000  0.000  0.601  1.0
  Ho  Ho3  1  0.000  0.000  0.803  1.0
  Hf  Hf4  1  0.000  0.000  0.000  1.0
  Al  Al5  1  0.500  0.500  0.000  1.0
  Al  Al6  1  0.500  0.500  0.198  1.0
  Al  Al7  1  0.500  0.500  0.399  1.0
  Al  Al8  1  0.500  0.500  0.601  1.0
  Al  Al9  1  0.500  0.500  0.802  1.0
  Al  Al10  1  0.500  0.000  0.095  1.0
  Al  Al11  1  0.500  0.000  0.298  1.0
  Al  Al12  1  0.500  0.000  0.500  1.0
  Al  Al13  1  0.500  0.000  0.702  1.0
  Al  Al14  1  0.500  0.000  0.905  1.0
  Al  Al15  1  0.000  0.500  0.095  1.0
  Al  Al16  1  0.000  0.500  0.298  1.0
  Al  Al17  1  0.000  0.500  0.500  1.0
  Al  Al18  1  0.000  0.500  0.702  1.0
  Al  Al19  1  0.000  0.500  0.905  1.0
[/CIF]
.
The compound described by Ho4HfAl15 is Uranium Silicide-derived structured and crystallizes in the tetragonal P4/mmm space group. There are two inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to four equivalent Al(2), four equivalent Al(4), and four equivalent Al(5) atoms to form HoAl12 cuboctahedra that share corners with four equivalent Ho(1)Al12 cuboctahedra, corners with four equivalent Ho(2)Al12 cuboctahedra, corners with four equivalent Hf(1)Al12 cuboctahedra, edges with four equivalent Al(1)Hf4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Ho(2)Al12 cuboctahedra,  a faceface with one Hf(1)Al12 cuboctahedra, faces with four equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with four equivalent Al(2)Ho4Al8 cuboctahedra, and faces with four equivalent Al(5)Ho4Al8 cuboctahedra. In the second Ho site, Ho(2) is bonded to four equivalent Al(3), four equivalent Al(5), and four equivalent Al(6) atoms to form HoAl12 cuboctahedra that share corners with four equivalent Ho(1)Al12 cuboctahedra, corners with eight equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Ho(1)Al12 cuboctahedra, faces with four equivalent Al(3)Ho4Al8 cuboctahedra, faces with four equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Al(6)Ho4Al8 cuboctahedra, and faces with five equivalent Ho(2)Al12 cuboctahedra. Hf(1) is bonded to four equivalent Al(1) and eight equivalent Al(4) atoms to form HfAl12 cuboctahedra that share corners with four equivalent Hf(1)Al12 cuboctahedra, corners with eight equivalent Ho(1)Al12 cuboctahedra, edges with eight equivalent Al(2)Ho4Al8 cuboctahedra, edges with sixteen equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Hf(1)Al12 cuboctahedra, faces with four equivalent Al(1)Hf4Al8 cuboctahedra, and faces with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to four equivalent Hf(1) and eight equivalent Al(4) atoms to form AlHf4Al8 cuboctahedra that share corners with four equivalent Al(1)Hf4Al8 cuboctahedra, corners with eight equivalent Al(2)Ho4Al8 cuboctahedra, edges with eight equivalent Ho(1)Al12 cuboctahedra, edges with sixteen equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, faces with four equivalent Hf(1)Al12 cuboctahedra, faces with four equivalent Al(1)Hf4Al8 cuboctahedra, and faces with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra. In the second Al site, Al(2) is bonded to four equivalent Ho(1), four equivalent Al(4), and four equivalent Al(5) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(1)Hf4Al8 cuboctahedra, corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Hf(1)Al12 cuboctahedra, edges with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Al(1)Hf4Al8 cuboctahedra,  a faceface with one Al(3)Ho4Al8 cuboctahedra, faces with four equivalent Ho(1)Al12 cuboctahedra, faces with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, faces with four equivalent Al(2)Ho4Al8 cuboctahedra, and faces with four equivalent Al(5)Ho4Al8 cuboctahedra. In the third Al site, Al(3) is bonded to four equivalent Ho(2), four equivalent Al(5), and four equivalent Al(6) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(2)Ho4Al8 cuboctahedra, corners with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Al(2)Ho4Al8 cuboctahedra, faces with four equivalent Ho(2)Al12 cuboctahedra, faces with four equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Al(6)Ho4Al8 cuboctahedra, and faces with five equivalent Al(3)Ho4Al8 cuboctahedra. In the fourth Al site, Al(4) is bonded to two equivalent Ho(1), two equivalent Hf(1), two equivalent Al(1), two equivalent Al(2), and four equivalent Al(4) atoms to form distorted AlHo2Hf2Al8 cuboctahedra that share corners with four equivalent Al(5)Ho4Al8 cuboctahedra, corners with eight equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Hf(1)Al12 cuboctahedra, edges with four equivalent Al(1)Hf4Al8 cuboctahedra, edges with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(5)Ho4Al8 cuboctahedra,  a faceface with one Al(5)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Hf(1)Al12 cuboctahedra, faces with two equivalent Al(1)Hf4Al8 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, and faces with nine equivalent Al(4)Ho2Hf2Al8 cuboctahedra. In the fifth Al site, Al(5) is bonded to two equivalent Ho(1), two equivalent Ho(2), two equivalent Al(2), two equivalent Al(3), and four equivalent Al(5) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, corners with four equivalent Al(5)Ho4Al8 cuboctahedra, corners with four equivalent Al(6)Ho4Al8 cuboctahedra, edges with four equivalent Ho(1)Al12 cuboctahedra, edges with four equivalent Ho(2)Al12 cuboctahedra, edges with four equivalent Al(4)Ho2Hf2Al8 cuboctahedra, edges with four equivalent Al(2)Ho4Al8 cuboctahedra, edges with four equivalent Al(3)Ho4Al8 cuboctahedra, edges with four equivalent Al(6)Ho4Al8 cuboctahedra,  a faceface with one Al(4)Ho2Hf2Al8 cuboctahedra,  a faceface with one Al(6)Ho4Al8 cuboctahedra, faces with two equivalent Ho(1)Al12 cuboctahedra, faces with two equivalent Ho(2)Al12 cuboctahedra, faces with two equivalent Al(2)Ho4Al8 cuboctahedra, faces with two equivalent Al(3)Ho4Al8 cuboctahedra, and faces with eight equivalent Al(5)Ho4Al8 cuboctahedra. In the sixth Al site, Al(6) is bonded to four equivalent Ho(2), four equivalent Al(3), and four equivalent Al(6) atoms to form distorted AlHo4Al8 cuboctahedra that share corners with four equivalent Al(6)Ho4Al8 cuboctahedra, corners with eight equivalent Al(5)Ho4Al8 cuboctahedra, edges with eight equivalent Ho(2)Al12 cuboctahedra, edges with eight equivalent Al(3)Ho4Al8 cuboctahedra, edges with eight equivalent Al(5)Ho4Al8 cuboctahedra, faces with two equivalent Al(5)Ho4Al8 cuboctahedra, faces with four equivalent Ho(2)Al12 cuboctahedra, faces with four equivalent Al(3)Ho4Al8 cuboctahedra, and faces with eight equivalent Al(6)Ho4Al8 cuboctahedra. is represented by the CIF file [CIF]
data_Ho4HfAl15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.217
_cell_length_b   4.217
_cell_length_c   21.098
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   375.155
_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
  Ho  Ho0  1  0.000  0.000  0.197  1.0
  Ho  Ho1  1  0.000  0.000  0.399  1.0
  Ho  Ho2  1  0.000  0.000  0.601  1.0
  Ho  Ho3  1  0.000  0.000  0.803  1.0
  Hf  Hf4  1  0.000  0.000  0.000  1.0
  Al  Al5  1  0.500  0.500  0.000  1.0
  Al  Al6  1  0.500  0.500  0.198  1.0
  Al  Al7  1  0.500  0.500  0.399  1.0
  Al  Al8  1  0.500  0.500  0.601  1.0
  Al  Al9  1  0.500  0.500  0.802  1.0
  Al  Al10  1  0.500  0.000  0.095  1.0
  Al  Al11  1  0.500  0.000  0.298  1.0
  Al  Al12  1  0.500  0.000  0.500  1.0
  Al  Al13  1  0.500  0.000  0.702  1.0
  Al  Al14  1  0.500  0.000  0.905  1.0
  Al  Al15  1  0.000  0.500  0.095  1.0
  Al  Al16  1  0.000  0.500  0.298  1.0
  Al  Al17  1  0.000  0.500  0.500  1.0
  Al  Al18  1  0.000  0.500  0.702  1.0
  Al  Al19  1  0.000  0.500  0.905  1.0
[/CIF]
.