The material structure described by Mg6GaAl crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Al2 cuboctahedra, edges with two equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Al2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Al(1)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted GaMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Al2 cuboctahedra. Al(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form AlMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6AlGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.129
_cell_length_b   6.151
_cell_length_c   6.188
_cell_angle_alpha   119.803
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.390
_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
  Al  Al0  1  1.000  0.834  0.667  1.0
  Ga  Ga1  1  0.500  0.667  0.334  1.0
  Mg  Mg2  1  1.000  0.336  0.169  1.0
  Mg  Mg3  1  1.000  0.833  0.169  1.0
  Mg  Mg4  1  1.000  0.333  0.666  1.0
  Mg  Mg5  1  0.500  0.163  0.830  1.0
  Mg  Mg6  1  0.500  0.668  0.830  1.0
  Mg  Mg7  1  0.500  0.167  0.334  1.0
[/CIF]
.
The material structure described by Mg6GaAl crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Al2 cuboctahedra, edges with two equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Al2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Al(1)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted GaMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Al2 cuboctahedra. Al(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form AlMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Al2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(3)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6AlGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.129
_cell_length_b   6.151
_cell_length_c   6.188
_cell_angle_alpha   119.803
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.390
_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
  Al  Al0  1  1.000  0.834  0.667  1.0
  Ga  Ga1  1  0.500  0.667  0.334  1.0
  Mg  Mg2  1  1.000  0.336  0.169  1.0
  Mg  Mg3  1  1.000  0.833  0.169  1.0
  Mg  Mg4  1  1.000  0.333  0.666  1.0
  Mg  Mg5  1  0.500  0.163  0.830  1.0
  Mg  Mg6  1  0.500  0.668  0.830  1.0
  Mg  Mg7  1  0.500  0.167  0.334  1.0
[/CIF]
.