The material described by Mg6YHf crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Y2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Y2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Y(1)Hf2Mg10 cuboctahedra. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. Y(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form YHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Y(1) atoms to form HfY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Y2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Y2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_YHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.187
_cell_length_b   6.527
_cell_length_c   6.541
_cell_angle_alpha   119.932
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   191.891
_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
  Hf  Hf0  1  0.500  0.664  0.328  1.0
  Mg  Mg1  1  0.000  0.827  0.170  1.0
  Mg  Mg2  1  0.000  0.342  0.170  1.0
  Mg  Mg3  1  0.000  0.335  0.670  1.0
  Mg  Mg4  1  0.500  0.665  0.835  1.0
  Mg  Mg5  1  0.500  0.169  0.835  1.0
  Mg  Mg6  1  0.500  0.165  0.330  1.0
  Y  Y7  1  0.000  0.832  0.663  1.0
[/CIF]
.
The material described by Mg6YHf crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(3)Y2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Y(1) atoms to form MgY2Mg10 cuboctahedra that share corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Y2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)Y2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with ten Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(1,1)Y2Hf2Mg8 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Y2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Y2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(2)Y2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Y(1)Hf2Mg10 cuboctahedra. In the seventh Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Y(1), and two equivalent Hf(1) atoms to form MgY2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with four equivalent Y(1)Hf2Mg10 cuboctahedra; corners with ten Mg(1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with two equivalent Y(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four equivalent Mg(1)Y2Hf2Mg8 cuboctahedra; and faces with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra. Y(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Hf(1) atoms to form YHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Y2Mg10 cuboctahedra; corners with six equivalent Y(1)Hf2Mg10 cuboctahedra; corners with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Y2Mg10 cuboctahedra; edges with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)Y2Mg10 cuboctahedra; edges with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(2)Y2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Y(1) atoms to form HfY2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)Y2Mg10 cuboctahedra; corners with eight Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; edges with four equivalent Y(1)Hf2Mg10 cuboctahedra; edges with eight Mg(1,1,1)Y2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Y(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)Y2Mg10 cuboctahedra; faces with four Mg(1,1)Y2Hf2Mg8 cuboctahedra; faces with four Mg(3,3)Y2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(2)Y2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_YHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.187
_cell_length_b   6.527
_cell_length_c   6.541
_cell_angle_alpha   119.932
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   191.891
_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
  Hf  Hf0  1  0.500  0.664  0.328  1.0
  Mg  Mg1  1  0.000  0.827  0.170  1.0
  Mg  Mg2  1  0.000  0.342  0.170  1.0
  Mg  Mg3  1  0.000  0.335  0.670  1.0
  Mg  Mg4  1  0.500  0.665  0.835  1.0
  Mg  Mg5  1  0.500  0.169  0.835  1.0
  Mg  Mg6  1  0.500  0.165  0.330  1.0
  Y  Y7  1  0.000  0.832  0.663  1.0
[/CIF]
.