The structure described by CsMg14Hf crystallizes in the orthorhombic Amm2 space group. Cs(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Hf(1) atoms to form CsHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra, faces with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)CsMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Cs(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgCs2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 1-coordinate geometry to one Cs(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom. In the sixth Mg site, Mg(6) is bonded to one Cs(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgCsMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra, corners with six equivalent Mg(6)CsMg11 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Cs(1)Hf2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Hf(1)Cs2Mg10 cuboctahedra. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CsMg11 cuboctahedra, corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(6)CsMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Hf(1)Cs2Mg10 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Cs(1)Hf2Mg10 cuboctahedra, and faces with three equivalent Mg(1)Mg12 cuboctahedra. Hf(1) is bonded to two equivalent Cs(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form distorted HfCs2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(6)CsMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CsHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.573
_cell_length_b   6.713
_cell_length_c   10.520
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.710
_symmetry_Int_Tables_number   1
_cell_volume   399.113
_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
  Cs  Cs0  1  0.164  0.332  0.125  1.0
  Hf  Hf1  1  0.191  0.846  0.125  1.0
  Mg  Mg2  1  0.169  0.335  0.625  1.0
  Mg  Mg3  1  0.165  0.832  0.625  1.0
  Mg  Mg4  1  0.667  0.334  0.125  1.0
  Mg  Mg5  1  0.668  0.339  0.625  1.0
  Mg  Mg6  1  0.667  0.832  0.125  1.0
  Mg  Mg7  1  0.668  0.829  0.625  1.0
  Mg  Mg8  1  0.334  0.151  0.386  1.0
  Mg  Mg9  1  0.334  0.151  0.864  1.0
  Mg  Mg10  1  0.334  0.683  0.386  1.0
  Mg  Mg11  1  0.334  0.683  0.864  1.0
  Mg  Mg12  1  0.814  0.157  0.392  1.0
  Mg  Mg13  1  0.814  0.157  0.858  1.0
  Mg  Mg14  1  0.838  0.669  0.369  1.0
  Mg  Mg15  1  0.838  0.669  0.881  1.0
[/CIF]
.
The structure described by CsMg14Hf crystallizes in the orthorhombic Amm2 space group. Cs(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Hf(1) atoms to form CsHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra, faces with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)CsMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Cs(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Hf(1) atoms to form distorted MgCs2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Hf(1)Cs2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Cs(1)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, corners with four equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)CsMg11 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 1-coordinate geometry to one Cs(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom. In the sixth Mg site, Mg(6) is bonded to one Cs(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgCsMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra, corners with six equivalent Mg(6)CsMg11 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Cs(1)Hf2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with three equivalent Hf(1)Cs2Mg10 cuboctahedra. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)CsMg11 cuboctahedra, corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(6)CsMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Hf(1)Cs2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Hf(1)Cs2Mg10 cuboctahedra, faces with two equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(6)CsMg11 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Cs(1)Hf2Mg10 cuboctahedra, and faces with three equivalent Mg(1)Mg12 cuboctahedra. Hf(1) is bonded to two equivalent Cs(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form distorted HfCs2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Hf(1)Cs2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cs(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Cs(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(3)Cs2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(6)CsMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CsHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.573
_cell_length_b   6.713
_cell_length_c   10.520
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.710
_symmetry_Int_Tables_number   1
_cell_volume   399.113
_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
  Cs  Cs0  1  0.164  0.332  0.125  1.0
  Hf  Hf1  1  0.191  0.846  0.125  1.0
  Mg  Mg2  1  0.169  0.335  0.625  1.0
  Mg  Mg3  1  0.165  0.832  0.625  1.0
  Mg  Mg4  1  0.667  0.334  0.125  1.0
  Mg  Mg5  1  0.668  0.339  0.625  1.0
  Mg  Mg6  1  0.667  0.832  0.125  1.0
  Mg  Mg7  1  0.668  0.829  0.625  1.0
  Mg  Mg8  1  0.334  0.151  0.386  1.0
  Mg  Mg9  1  0.334  0.151  0.864  1.0
  Mg  Mg10  1  0.334  0.683  0.386  1.0
  Mg  Mg11  1  0.334  0.683  0.864  1.0
  Mg  Mg12  1  0.814  0.157  0.392  1.0
  Mg  Mg13  1  0.814  0.157  0.858  1.0
  Mg  Mg14  1  0.838  0.669  0.369  1.0
  Mg  Mg15  1  0.838  0.669  0.881  1.0
[/CIF]
.