The structure described by Mg14GaBi crystallizes in the orthorhombic Amm2 space group. 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 Mg(5)Mg6GaBi cuboctahedra, corners with four equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6GaBi 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 Ga(1)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra, corners with eight equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ga2Bi2 cuboctahedra that share corners with two equivalent Mg(5)Mg6GaBi cuboctahedra, 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)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Ga(1)Mg10Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, and faces with six equivalent Mg(5)Mg6GaBi 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 two equivalent Mg(5)Mg6GaBi cuboctahedra, corners with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, corners with four equivalent Ga(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Mg10Ga2 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(5)Mg6GaBi 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)Mg8Ga2Bi2 cuboctahedra, and faces with six equivalent Mg(5)Mg6GaBi cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), one Ga(1), and one Bi(1) atom to form distorted MgMg6GaBi cuboctahedra that share  a cornercorner with one Mg(1)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Ga2Bi2 cuboctahedra,  a cornercorner with one Ga(1)Mg10Bi2 cuboctahedra, corners with two equivalent Mg(2)Mg12 cuboctahedra, corners with two equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Ga(1)Mg10Bi2 cuboctahedra,  an edgeedge with one Bi(1)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg10Bi2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, and faces with four equivalent Mg(5)Mg6GaBi cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Ga(1) atom. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and one Bi(1) atom. Ga(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Bi(1) atoms to form GaMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6GaBi cuboctahedra, corners with six equivalent Ga(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Bi(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, edges with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg6GaBi cuboctahedra, and faces with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form BiMg10Ga2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra, edges with two equivalent Ga(1)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, edges with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14GaBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.381
_cell_length_b   6.576
_cell_length_c   10.298
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   121.016
_symmetry_Int_Tables_number   1
_cell_volume   370.375
_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  0.168  0.334  0.625  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.668  0.334  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.668  0.835  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.333  0.171  0.375  1.0
  Mg  Mg7  1  0.333  0.171  0.875  1.0
  Mg  Mg8  1  0.333  0.661  0.375  1.0
  Mg  Mg9  1  0.333  0.661  0.875  1.0
  Mg  Mg10  1  0.836  0.168  0.373  1.0
  Mg  Mg11  1  0.836  0.168  0.877  1.0
  Mg  Mg12  1  0.830  0.665  0.378  1.0
  Mg  Mg13  1  0.830  0.665  0.872  1.0
  Ga  Ga14  1  0.164  0.332  0.125  1.0
  Bi  Bi15  1  0.165  0.832  0.125  1.0
[/CIF]
.
The structure described by Mg14GaBi crystallizes in the orthorhombic Amm2 space group. 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 Mg(5)Mg6GaBi cuboctahedra, corners with four equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6GaBi 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 Ga(1)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra, corners with eight equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ga(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ga2Bi2 cuboctahedra that share corners with two equivalent Mg(5)Mg6GaBi cuboctahedra, 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)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, edges with two equivalent Ga(1)Mg10Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, and faces with six equivalent Mg(5)Mg6GaBi 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 two equivalent Mg(5)Mg6GaBi cuboctahedra, corners with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, corners with four equivalent Ga(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Mg10Ga2 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(5)Mg6GaBi 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)Mg8Ga2Bi2 cuboctahedra, and faces with six equivalent Mg(5)Mg6GaBi cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(6), one Ga(1), and one Bi(1) atom to form distorted MgMg6GaBi cuboctahedra that share  a cornercorner with one Mg(1)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Ga2Bi2 cuboctahedra,  a cornercorner with one Ga(1)Mg10Bi2 cuboctahedra, corners with two equivalent Mg(2)Mg12 cuboctahedra, corners with two equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Ga(1)Mg10Bi2 cuboctahedra,  an edgeedge with one Bi(1)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg10Bi2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, and faces with four equivalent Mg(5)Mg6GaBi cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Ga(1) atom. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and one Bi(1) atom. Ga(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Bi(1) atoms to form GaMg10Bi2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6GaBi cuboctahedra, corners with six equivalent Ga(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Bi(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, edges with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Bi(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)Mg6GaBi cuboctahedra, and faces with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form BiMg10Ga2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Bi(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6GaBi cuboctahedra, edges with two equivalent Ga(1)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(5)Mg6GaBi cuboctahedra, edges with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg10Bi2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Ga2Bi2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14GaBi
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.381
_cell_length_b   6.576
_cell_length_c   10.298
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   121.016
_symmetry_Int_Tables_number   1
_cell_volume   370.375
_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  0.168  0.334  0.625  1.0
  Mg  Mg1  1  0.168  0.834  0.625  1.0
  Mg  Mg2  1  0.668  0.334  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.668  0.835  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.333  0.171  0.375  1.0
  Mg  Mg7  1  0.333  0.171  0.875  1.0
  Mg  Mg8  1  0.333  0.661  0.375  1.0
  Mg  Mg9  1  0.333  0.661  0.875  1.0
  Mg  Mg10  1  0.836  0.168  0.373  1.0
  Mg  Mg11  1  0.836  0.168  0.877  1.0
  Mg  Mg12  1  0.830  0.665  0.378  1.0
  Mg  Mg13  1  0.830  0.665  0.872  1.0
  Ga  Ga14  1  0.164  0.332  0.125  1.0
  Bi  Bi15  1  0.165  0.832  0.125  1.0
[/CIF]
.