The material described by Mg14LaBi crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first 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 Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 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)LaMg10Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(1,1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)La2Mg10 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Mg(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 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 Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Bi(1) atom to form distorted MgLaMg10Bi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)LaMg10Bi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Bi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Bi(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)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)LaMg10Bi cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Bi(1) atom to form distorted MgLaMg10Bi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Bi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Bi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Bi(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)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Bi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LaMg10Bi cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)LaMg10Bi cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Bi 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)Mg10Bi2 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(1,1)La2Mg10 cuboctahedra; faces with six Mg(3,3)LaMg10Bi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Bi(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with twelve Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(3,3)LaMg10Bi cuboctahedra; faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Bi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.541
_cell_length_b   6.541
_cell_length_c   10.754
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   398.484
_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
  La  La0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.177  0.839  0.125  1.0
  Mg  Mg2  1  0.162  0.831  0.625  1.0
  Mg  Mg3  1  0.661  0.323  0.125  1.0
  Mg  Mg4  1  0.669  0.338  0.625  1.0
  Mg  Mg5  1  0.661  0.839  0.125  1.0
  Mg  Mg6  1  0.669  0.831  0.625  1.0
  Mg  Mg7  1  0.335  0.165  0.377  1.0
  Mg  Mg8  1  0.335  0.165  0.873  1.0
  Mg  Mg9  1  0.335  0.670  0.377  1.0
  Mg  Mg10  1  0.335  0.670  0.873  1.0
  Mg  Mg11  1  0.830  0.165  0.377  1.0
  Mg  Mg12  1  0.830  0.165  0.873  1.0
  Mg  Mg13  1  0.833  0.667  0.366  1.0
  Mg  Mg14  1  0.833  0.667  0.884  1.0
  Bi  Bi15  1  0.167  0.333  0.625  1.0
[/CIF]
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The material described by Mg14LaBi crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first 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 Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 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)LaMg10Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(1,1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)La2Mg10 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Mg(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 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 Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Bi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Bi(1) atom to form distorted MgLaMg10Bi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)LaMg10Bi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Bi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Bi(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)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)LaMg10Bi cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Bi(1) atom to form distorted MgLaMg10Bi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Bi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Bi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Bi(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)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Bi cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LaMg10Bi cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)LaMg10Bi cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Bi 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)Mg10Bi2 cuboctahedra; edges with six Mg(1,1)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(1,1)La2Mg10 cuboctahedra; faces with six Mg(3,3)LaMg10Bi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Bi(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)La2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with twelve Mg(3,3)LaMg10Bi cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(3,3)LaMg10Bi cuboctahedra; faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Bi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.541
_cell_length_b   6.541
_cell_length_c   10.754
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   398.484
_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
  La  La0  1  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.177  0.839  0.125  1.0
  Mg  Mg2  1  0.162  0.831  0.625  1.0
  Mg  Mg3  1  0.661  0.323  0.125  1.0
  Mg  Mg4  1  0.669  0.338  0.625  1.0
  Mg  Mg5  1  0.661  0.839  0.125  1.0
  Mg  Mg6  1  0.669  0.831  0.625  1.0
  Mg  Mg7  1  0.335  0.165  0.377  1.0
  Mg  Mg8  1  0.335  0.165  0.873  1.0
  Mg  Mg9  1  0.335  0.670  0.377  1.0
  Mg  Mg10  1  0.335  0.670  0.873  1.0
  Mg  Mg11  1  0.830  0.165  0.377  1.0
  Mg  Mg12  1  0.830  0.165  0.873  1.0
  Mg  Mg13  1  0.833  0.667  0.366  1.0
  Mg  Mg14  1  0.833  0.667  0.884  1.0
  Bi  Bi15  1  0.167  0.333  0.625  1.0
[/CIF]
.