The material described by NaMg14La crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Mg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaLaMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(1,1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Na(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one La(1) atom to form distorted MgNaLaMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaLaMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four Mg(3,3)NaLaMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)La2Mg10 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Na(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one La(1) atom to form distorted MgNaLaMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaLaMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaLaMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)La2Mg10 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)NaLaMg10 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three Mg(1,1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Na2Mg10 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. La(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six Mg(1,1)La2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaLaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.672
_cell_length_b   6.672
_cell_length_c   10.392
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   400.591
_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  0.167  0.333  0.625  1.0
  La  La1  1  0.167  0.333  0.125  1.0
  Mg  Mg2  1  0.174  0.837  0.125  1.0
  Mg  Mg3  1  0.169  0.834  0.625  1.0
  Mg  Mg4  1  0.663  0.326  0.125  1.0
  Mg  Mg5  1  0.666  0.331  0.625  1.0
  Mg  Mg6  1  0.663  0.837  0.125  1.0
  Mg  Mg7  1  0.666  0.834  0.625  1.0
  Mg  Mg8  1  0.337  0.163  0.378  1.0
  Mg  Mg9  1  0.337  0.163  0.872  1.0
  Mg  Mg10  1  0.337  0.673  0.378  1.0
  Mg  Mg11  1  0.337  0.673  0.872  1.0
  Mg  Mg12  1  0.827  0.163  0.378  1.0
  Mg  Mg13  1  0.827  0.163  0.872  1.0
  Mg  Mg14  1  0.833  0.667  0.372  1.0
  Mg  Mg15  1  0.833  0.667  0.878  1.0
[/CIF]
.
The material described by NaMg14La crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Mg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaLaMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Na2Mg10 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(1,1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaLaMg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Na(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one La(1) atom to form distorted MgNaLaMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaLaMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four Mg(3,3)NaLaMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)La2Mg10 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Na(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one La(1) atom to form distorted MgNaLaMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaLaMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaLaMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)La2Mg10 cuboctahedra; faces with five equivalent Mg(2)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)NaLaMg10 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three Mg(1,1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Na2Mg10 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. La(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Na2Mg10 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaLaMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six Mg(1,1)La2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)NaLaMg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaLaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.672
_cell_length_b   6.672
_cell_length_c   10.392
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   400.591
_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  0.167  0.333  0.625  1.0
  La  La1  1  0.167  0.333  0.125  1.0
  Mg  Mg2  1  0.174  0.837  0.125  1.0
  Mg  Mg3  1  0.169  0.834  0.625  1.0
  Mg  Mg4  1  0.663  0.326  0.125  1.0
  Mg  Mg5  1  0.666  0.331  0.625  1.0
  Mg  Mg6  1  0.663  0.837  0.125  1.0
  Mg  Mg7  1  0.666  0.834  0.625  1.0
  Mg  Mg8  1  0.337  0.163  0.378  1.0
  Mg  Mg9  1  0.337  0.163  0.872  1.0
  Mg  Mg10  1  0.337  0.673  0.378  1.0
  Mg  Mg11  1  0.337  0.673  0.872  1.0
  Mg  Mg12  1  0.827  0.163  0.378  1.0
  Mg  Mg13  1  0.827  0.163  0.872  1.0
  Mg  Mg14  1  0.833  0.667  0.372  1.0
  Mg  Mg15  1  0.833  0.667  0.878  1.0
[/CIF]
.