The crystal structure described by NaMg14Hf crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four Mg(5,5); and two equivalent Hf(1) atoms to form NaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Na(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Na2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaHfMg10 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 Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Na(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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 Mg(3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 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 Na(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Na2Mg10 cuboctahedra; corners with six Mg(4,4)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(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the sixth 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 Na(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Na2Mg10 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(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 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 two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(3,3)Na2Hf2Mg8 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 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 two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the ninth Mg site, Mg(6) is bonded to one Na(1); one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)NaMg11 cuboctahedra; corners with eight Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)NaHfMg10 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Na(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the eleventh Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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 Mg(3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. Hf(1) is bonded to two equivalent Na(1); two equivalent Mg(7); four Mg(3,3,3); and four Mg(5,5) atoms to form HfNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Na2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_NaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.439
_cell_length_b   6.503
_cell_length_c   10.296
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.326
_symmetry_Int_Tables_number   1
_cell_volume   372.119
_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
  Na  Na0  1  0.169  0.335  0.125  1.0
  Hf  Hf1  1  0.174  0.837  0.125  1.0
  Mg  Mg2  1  0.167  0.333  0.625  1.0
  Mg  Mg3  1  0.166  0.833  0.625  1.0
  Mg  Mg4  1  0.662  0.336  0.125  1.0
  Mg  Mg5  1  0.667  0.334  0.625  1.0
  Mg  Mg6  1  0.662  0.826  0.125  1.0
  Mg  Mg7  1  0.667  0.834  0.625  1.0
  Mg  Mg8  1  0.332  0.160  0.375  1.0
  Mg  Mg9  1  0.332  0.160  0.875  1.0
  Mg  Mg10  1  0.332  0.672  0.375  1.0
  Mg  Mg11  1  0.332  0.672  0.875  1.0
  Mg  Mg12  1  0.830  0.165  0.376  1.0
  Mg  Mg13  1  0.830  0.165  0.874  1.0
  Mg  Mg14  1  0.839  0.670  0.373  1.0
  Mg  Mg15  1  0.839  0.670  0.877  1.0
[/CIF]
.
The crystal structure described by NaMg14Hf crystallizes in the orthorhombic Amm2 space group. Na(1) is bonded to two equivalent Mg(6); four Mg(3,3,3); four Mg(5,5); and two equivalent Hf(1) atoms to form NaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Na(1)Hf2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(7)HfMg11 cuboctahedra. There are eleven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Na2Mg10 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaHfMg10 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 Mg(4,4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Na(1)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; corners with eight Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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 Mg(3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 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 Na(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Na2Mg10 cuboctahedra; corners with six Mg(4,4)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(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the sixth 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 Na(1)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; corners with four equivalent Hf(1)Na2Mg10 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(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 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 two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(3,3)Na2Hf2Mg8 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to one Na(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with ten Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 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 two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with four Mg(4,4)Mg12 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the ninth Mg site, Mg(6) is bonded to one Na(1); one Mg(1); two Mg(3,3); two Mg(4,4); two equivalent Mg(7); and four Mg(5,5) atoms to form distorted MgNaMg11 cuboctahedra that share corners with four equivalent Mg(7)HfMg11 cuboctahedra; corners with six equivalent Mg(6)NaMg11 cuboctahedra; corners with eight Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(7)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Hf2Mg10 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; faces with three equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the tenth Mg site, Mg(7) is bonded to one Mg(2); two Mg(3,3); two Mg(4,4); two equivalent Mg(6); four Mg(5,5); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(6)NaMg11 cuboctahedra; corners with six equivalent Mg(7)HfMg11 cuboctahedra; corners with eight Mg(5,5)NaHfMg10 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(6)NaMg11 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four Mg(4,4)Mg12 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with four Mg(5,5)NaHfMg10 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Hf(1)Na2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two Mg(4,4)Mg12 cuboctahedra; faces with two Mg(3,3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with three equivalent Na(1)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)NaHfMg10 cuboctahedra. In the eleventh Mg site, Mg(3) is bonded to two equivalent Na(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 MgNa2Hf2Mg8 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 Mg(3,3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four equivalent Mg(5)NaHfMg10 cuboctahedra; edges with four equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(3)Na2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(6)NaMg11 cuboctahedra; faces with two equivalent Hf(1)Na2Mg10 cuboctahedra; and faces with eight Mg(5,5)NaHfMg10 cuboctahedra. Hf(1) is bonded to two equivalent Na(1); two equivalent Mg(7); four Mg(3,3,3); and four Mg(5,5) atoms to form HfNa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Hf(1)Na2Mg10 cuboctahedra; corners with eight Mg(4,4)Mg12 cuboctahedra; edges with two equivalent Na(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(7)HfMg11 cuboctahedra; edges with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; edges with eight Mg(5,5)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(7)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with four Mg(3,3,3)Na2Hf2Mg8 cuboctahedra; faces with four Mg(5,5)NaHfMg10 cuboctahedra; and faces with six equivalent Mg(6)NaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_NaHfMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.439
_cell_length_b   6.503
_cell_length_c   10.296
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.326
_symmetry_Int_Tables_number   1
_cell_volume   372.119
_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
  Na  Na0  1  0.169  0.335  0.125  1.0
  Hf  Hf1  1  0.174  0.837  0.125  1.0
  Mg  Mg2  1  0.167  0.333  0.625  1.0
  Mg  Mg3  1  0.166  0.833  0.625  1.0
  Mg  Mg4  1  0.662  0.336  0.125  1.0
  Mg  Mg5  1  0.667  0.334  0.625  1.0
  Mg  Mg6  1  0.662  0.826  0.125  1.0
  Mg  Mg7  1  0.667  0.834  0.625  1.0
  Mg  Mg8  1  0.332  0.160  0.375  1.0
  Mg  Mg9  1  0.332  0.160  0.875  1.0
  Mg  Mg10  1  0.332  0.672  0.375  1.0
  Mg  Mg11  1  0.332  0.672  0.875  1.0
  Mg  Mg12  1  0.830  0.165  0.376  1.0
  Mg  Mg13  1  0.830  0.165  0.874  1.0
  Mg  Mg14  1  0.839  0.670  0.373  1.0
  Mg  Mg15  1  0.839  0.670  0.877  1.0
[/CIF]
.