The material structure described by Mg6CoGa 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 Co(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Co2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Co(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Co2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Co2 cuboctahedra, corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg10Co2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Co(1)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(3)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Co(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Co2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Co2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Ga(1)Mg10Co2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Co(1)Mg10Ga2 cuboctahedra. Co(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form CoMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Co2 cuboctahedra, corners with six equivalent Co(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Ga(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Co(1) atoms to form GaMg10Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Co2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6GaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.764
_cell_length_b   5.999
_cell_length_c   5.999
_cell_angle_alpha   119.541
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   149.127
_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
  Co  Co0  1  0.500  0.167  0.833  1.0
  Ga  Ga1  1  0.500  0.668  0.332  1.0
  Mg  Mg2  1  0.500  0.665  0.832  1.0
  Mg  Mg3  1  0.500  0.168  0.335  1.0
  Mg  Mg4  1  1.000  0.849  0.672  1.0
  Mg  Mg5  1  1.000  0.328  0.151  1.0
  Mg  Mg6  1  0.000  0.325  0.675  1.0
  Mg  Mg7  1  0.000  0.831  0.169  1.0
[/CIF]
.
The material structure described by Mg6CoGa 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 Co(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Mg10Co2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Co(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Co2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Co2 cuboctahedra, corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg10Co2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Co(1)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(3)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Co(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Co2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Co2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, edges with four equivalent Ga(1)Mg10Co2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Co(1)Mg10Ga2 cuboctahedra. Co(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form CoMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Co2 cuboctahedra, corners with six equivalent Co(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Ga(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg10Co2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(3)Mg10Co2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Co(1) atoms to form GaMg10Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Co(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ga2Co2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ga2Co2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Co2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg6GaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.764
_cell_length_b   5.999
_cell_length_c   5.999
_cell_angle_alpha   119.541
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   149.127
_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
  Co  Co0  1  0.500  0.167  0.833  1.0
  Ga  Ga1  1  0.500  0.668  0.332  1.0
  Mg  Mg2  1  0.500  0.665  0.832  1.0
  Mg  Mg3  1  0.500  0.168  0.335  1.0
  Mg  Mg4  1  1.000  0.849  0.672  1.0
  Mg  Mg5  1  1.000  0.328  0.151  1.0
  Mg  Mg6  1  0.000  0.325  0.675  1.0
  Mg  Mg7  1  0.000  0.831  0.169  1.0
[/CIF]
.