The compound described by Mg14AlBi crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlBi 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 Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 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)Mg10AlBi cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 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)Mg10AlBi cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Al(1), and one Bi(1) atom to form distorted MgMg10AlBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10AlBi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; faces with five equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Al(1); and one Bi(1) atom to form distorted MgMg10AlBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four Mg(3,3)Mg10AlBi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; faces with five equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(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)Mg10AlBi cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg10AlBi cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Al2 cuboctahedra; faces with three equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. Al(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10AlBi 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 equivalent Mg(1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10AlBi cuboctahedra; faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14AlBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.426
_cell_length_b   6.426
_cell_length_c   10.377
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   371.136
_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
  Mg  Mg0  1  0.166  0.833  0.125  1.0
  Mg  Mg1  1  0.166  0.833  0.625  1.0
  Mg  Mg2  1  0.667  0.334  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.667  0.833  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.335  0.165  0.369  1.0
  Mg  Mg7  1  0.335  0.165  0.881  1.0
  Mg  Mg8  1  0.335  0.670  0.369  1.0
  Mg  Mg9  1  0.335  0.670  0.881  1.0
  Mg  Mg10  1  0.830  0.165  0.369  1.0
  Mg  Mg11  1  0.830  0.165  0.881  1.0
  Mg  Mg12  1  0.833  0.667  0.376  1.0
  Mg  Mg13  1  0.833  0.667  0.874  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  Bi  Bi15  1  0.167  0.333  0.625  1.0
[/CIF]
.
The compound described by Mg14AlBi crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Al(1) atoms to form MgMg10Al2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)Mg10AlBi 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 Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Bi2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 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)Mg10AlBi cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 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)Mg10AlBi cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Al(1), and one Bi(1) atom to form distorted MgMg10AlBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10AlBi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; faces with five equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Al(1); and one Bi(1) atom to form distorted MgMg10AlBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10AlBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four Mg(3,3)Mg10AlBi cuboctahedra; edges with four equivalent Mg(2)Mg10Bi2 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; faces with five equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(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)Mg10AlBi cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with six Mg(3,3)Mg10AlBi cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Al2 cuboctahedra; faces with three equivalent Mg(2)Mg10Bi2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10AlBi cuboctahedra. Al(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Al2 cuboctahedra; faces with six Mg(3,3)Mg10AlBi 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 equivalent Mg(1)Mg10Al2 cuboctahedra; edges with six equivalent Mg(2)Mg10Bi2 cuboctahedra; edges with twelve Mg(3,3)Mg10AlBi cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10AlBi cuboctahedra; faces with six equivalent Mg(2)Mg10Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14AlBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.426
_cell_length_b   6.426
_cell_length_c   10.377
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   371.136
_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
  Mg  Mg0  1  0.166  0.833  0.125  1.0
  Mg  Mg1  1  0.166  0.833  0.625  1.0
  Mg  Mg2  1  0.667  0.334  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.667  0.833  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.335  0.165  0.369  1.0
  Mg  Mg7  1  0.335  0.165  0.881  1.0
  Mg  Mg8  1  0.335  0.670  0.369  1.0
  Mg  Mg9  1  0.335  0.670  0.881  1.0
  Mg  Mg10  1  0.830  0.165  0.369  1.0
  Mg  Mg11  1  0.830  0.165  0.881  1.0
  Mg  Mg12  1  0.833  0.667  0.376  1.0
  Mg  Mg13  1  0.833  0.667  0.874  1.0
  Al  Al14  1  0.167  0.333  0.125  1.0
  Bi  Bi15  1  0.167  0.333  0.625  1.0
[/CIF]
.