The material structure described by Ho4Co3Ga16 crystallizes in the tetragonal P4/mmm space group. Ho(1) is bonded to two equivalent Ga(1); two equivalent Ga(2); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form HoGa12 cuboctahedra that share corners with eight equivalent Ho(1)Ga12 cuboctahedra, edges with two equivalent Ga(2)Ho4Ga8 cuboctahedra, faces with two equivalent Ga(2)Ho4Ga8 cuboctahedra, faces with five equivalent Ho(1)Ga12 cuboctahedra, and faces with two equivalent Co(2)Ga6 octahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded in a body-centered cubic geometry to eight Ga(4,4,4,4,4,4,4) atoms. In the second Co site, Co(2) is bonded to two equivalent Ga(1) and four equivalent Ga(3) atoms to form CoGa6 octahedra that share corners with eight equivalent Ga(2)Ho4Ga8 cuboctahedra and faces with eight equivalent Ho(1)Ga12 cuboctahedra. There are ten inequivalent Ga sites. In the first Ga site, Ga(1) is bonded in a 9-coordinate geometry to four equivalent Ho(1); one Co(2); and four Ga(4,4,4,4) atoms. In the second Ga site, Ga(2) is bonded to four equivalent Ho(1); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form distorted GaHo4Ga8 cuboctahedra that share corners with four equivalent Ga(2)Ho4Ga8 cuboctahedra, corners with four equivalent Co(2)Ga6 octahedra, edges with four equivalent Ho(1)Ga12 cuboctahedra,  a faceface with one Ga(2)Ho4Ga8 cuboctahedra, and faces with four equivalent Ho(1)Ga12 cuboctahedra. The corner-sharing octahedral tilt angles are 49°. In the third Ga site, Ga(3) is bonded in a 9-coordinate geometry to four equivalent Ho(1), one Co(2), two equivalent Ga(2), and two equivalent Ga(3) atoms. In the fourth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the fifth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the sixth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the seventh Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4) atoms. In the eighth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4) atoms. In the ninth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the tenth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ho4Ga16Co3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.952
_cell_length_b   5.952
_cell_length_c   10.953
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   388.061
_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  1.000  0.500  0.195  1.0
  Ho  Ho1  1  0.000  0.500  0.805  1.0
  Ho  Ho2  1  0.500  1.000  0.805  1.0
  Ho  Ho3  1  0.500  0.000  0.195  1.0
  Ga  Ga4  1  1.000  1.000  0.219  1.0
  Ga  Ga5  1  0.000  0.000  0.781  1.0
  Ga  Ga6  1  0.500  0.500  0.195  1.0
  Ga  Ga7  1  0.500  0.500  0.805  1.0
  Ga  Ga8  1  0.281  0.281  0.000  1.0
  Ga  Ga9  1  0.719  0.719  1.000  1.0
  Ga  Ga10  1  0.281  0.719  0.000  1.0
  Ga  Ga11  1  0.719  0.281  0.000  1.0
  Ga  Ga12  1  0.250  0.250  0.385  1.0
  Ga  Ga13  1  0.750  0.750  0.385  1.0
  Ga  Ga14  1  0.250  0.750  0.615  1.0
  Ga  Ga15  1  0.750  0.250  0.615  1.0
  Ga  Ga16  1  0.750  0.750  0.615  1.0
  Ga  Ga17  1  0.250  0.250  0.615  1.0
  Ga  Ga18  1  0.250  0.750  0.385  1.0
  Ga  Ga19  1  0.750  0.250  0.385  1.0
  Co  Co20  1  0.000  0.500  0.500  1.0
  Co  Co21  1  0.500  0.000  0.500  1.0
  Co  Co22  1  1.000  0.000  0.000  1.0
[/CIF]
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The material structure described by Ho4Co3Ga16 crystallizes in the tetragonal P4/mmm space group. Ho(1) is bonded to two equivalent Ga(1); two equivalent Ga(2); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form HoGa12 cuboctahedra that share corners with eight equivalent Ho(1)Ga12 cuboctahedra, edges with two equivalent Ga(2)Ho4Ga8 cuboctahedra, faces with two equivalent Ga(2)Ho4Ga8 cuboctahedra, faces with five equivalent Ho(1)Ga12 cuboctahedra, and faces with two equivalent Co(2)Ga6 octahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded in a body-centered cubic geometry to eight Ga(4,4,4,4,4,4,4) atoms. In the second Co site, Co(2) is bonded to two equivalent Ga(1) and four equivalent Ga(3) atoms to form CoGa6 octahedra that share corners with eight equivalent Ga(2)Ho4Ga8 cuboctahedra and faces with eight equivalent Ho(1)Ga12 cuboctahedra. There are ten inequivalent Ga sites. In the first Ga site, Ga(1) is bonded in a 9-coordinate geometry to four equivalent Ho(1); one Co(2); and four Ga(4,4,4,4) atoms. In the second Ga site, Ga(2) is bonded to four equivalent Ho(1); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form distorted GaHo4Ga8 cuboctahedra that share corners with four equivalent Ga(2)Ho4Ga8 cuboctahedra, corners with four equivalent Co(2)Ga6 octahedra, edges with four equivalent Ho(1)Ga12 cuboctahedra,  a faceface with one Ga(2)Ho4Ga8 cuboctahedra, and faces with four equivalent Ho(1)Ga12 cuboctahedra. The corner-sharing octahedral tilt angles are 49°. In the third Ga site, Ga(3) is bonded in a 9-coordinate geometry to four equivalent Ho(1), one Co(2), two equivalent Ga(2), and two equivalent Ga(3) atoms. In the fourth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the fifth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the sixth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the seventh Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4) atoms. In the eighth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4) atoms. In the ninth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the tenth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Ho(1); two equivalent Co(1); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ho4Ga16Co3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.952
_cell_length_b   5.952
_cell_length_c   10.953
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   388.061
_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  1.000  0.500  0.195  1.0
  Ho  Ho1  1  0.000  0.500  0.805  1.0
  Ho  Ho2  1  0.500  1.000  0.805  1.0
  Ho  Ho3  1  0.500  0.000  0.195  1.0
  Ga  Ga4  1  1.000  1.000  0.219  1.0
  Ga  Ga5  1  0.000  0.000  0.781  1.0
  Ga  Ga6  1  0.500  0.500  0.195  1.0
  Ga  Ga7  1  0.500  0.500  0.805  1.0
  Ga  Ga8  1  0.281  0.281  0.000  1.0
  Ga  Ga9  1  0.719  0.719  1.000  1.0
  Ga  Ga10  1  0.281  0.719  0.000  1.0
  Ga  Ga11  1  0.719  0.281  0.000  1.0
  Ga  Ga12  1  0.250  0.250  0.385  1.0
  Ga  Ga13  1  0.750  0.750  0.385  1.0
  Ga  Ga14  1  0.250  0.750  0.615  1.0
  Ga  Ga15  1  0.750  0.250  0.615  1.0
  Ga  Ga16  1  0.750  0.750  0.615  1.0
  Ga  Ga17  1  0.250  0.250  0.615  1.0
  Ga  Ga18  1  0.250  0.750  0.385  1.0
  Ga  Ga19  1  0.750  0.250  0.385  1.0
  Co  Co20  1  0.000  0.500  0.500  1.0
  Co  Co21  1  0.500  0.000  0.500  1.0
  Co  Co22  1  1.000  0.000  0.000  1.0
[/CIF]
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