The material structure described by MgHo5 crystallizes in the trigonal R32 space group. Mg(1) is bonded to six Ho(1,1,1,1,1,1) and six Ho(2,2) atoms to form MgHo12 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Mg(1)Ho12 cuboctahedra; edges with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra. There are eleven inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the second Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the third Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the fourth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the fifth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra. In the sixth Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra. In the seventh Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra. In the eighth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four equivalent Ho(2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the ninth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the tenth Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the eleventh Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. is represented by the CIF card [CIF]
data_Ho5Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.552
_cell_length_b   6.552
_cell_length_c   6.552
_cell_angle_alpha   55.483
_cell_angle_beta   55.483
_cell_angle_gamma   55.483
_symmetry_Int_Tables_number   1
_cell_volume   178.034
_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  0.500  0.162  0.838  1.0
  Ho  Ho1  1  0.162  0.838  0.500  1.0
  Ho  Ho2  1  0.838  0.500  0.162  1.0
  Ho  Ho3  1  0.332  0.332  0.332  1.0
  Ho  Ho4  1  0.668  0.668  0.668  1.0
  Mg  Mg5  1  0.000  0.000  0.000  1.0
[/CIF]
.
The material structure described by MgHo5 crystallizes in the trigonal R32 space group. Mg(1) is bonded to six Ho(1,1,1,1,1,1) and six Ho(2,2) atoms to form MgHo12 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Mg(1)Ho12 cuboctahedra; edges with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra. There are eleven inequivalent Ho sites. In the first Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the second Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the third Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the fourth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the fifth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1,1)Ho10Mg2 cuboctahedra. In the sixth Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra. In the seventh Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2,2)Ho9Mg3 cuboctahedra. In the eighth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four equivalent Ho(2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the ninth Ho site, Ho(2) is bonded to three equivalent Mg(1); three equivalent Ho(2); and six Ho(1,1,1,1,1) atoms to form HoHo9Mg3 cuboctahedra that share corners with six equivalent Mg(1)Ho12 cuboctahedra; corners with twelve Ho(2,2,2)Ho9Mg3 cuboctahedra; edges with six equivalent Ho(2)Ho9Mg3 cuboctahedra; edges with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with four Ho(2,2)Ho9Mg3 cuboctahedra; and faces with twelve Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra. In the tenth Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. In the eleventh Ho site, Ho(1) is bonded to two equivalent Mg(1); four Ho(2,2,2); and six Ho(1,1) atoms to form HoHo10Mg2 cuboctahedra that share corners with eighteen Ho(1,1,1,1,1)Ho10Mg2 cuboctahedra; edges with four equivalent Mg(1)Ho12 cuboctahedra; edges with six equivalent Ho(1)Ho10Mg2 cuboctahedra; edges with eight Ho(2,2,2)Ho9Mg3 cuboctahedra; faces with four equivalent Mg(1)Ho12 cuboctahedra; faces with eight Ho(1,1,1,1)Ho10Mg2 cuboctahedra; and faces with eight Ho(2,2,2)Ho9Mg3 cuboctahedra. is represented by the CIF card [CIF]
data_Ho5Mg
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.552
_cell_length_b   6.552
_cell_length_c   6.552
_cell_angle_alpha   55.483
_cell_angle_beta   55.483
_cell_angle_gamma   55.483
_symmetry_Int_Tables_number   1
_cell_volume   178.034
_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  0.500  0.162  0.838  1.0
  Ho  Ho1  1  0.162  0.838  0.500  1.0
  Ho  Ho2  1  0.838  0.500  0.162  1.0
  Ho  Ho3  1  0.332  0.332  0.332  1.0
  Ho  Ho4  1  0.668  0.668  0.668  1.0
  Mg  Mg5  1  0.000  0.000  0.000  1.0
[/CIF]
.