The material described by Mg6CoGa crystallizes in the orthorhombic Amm2 space group. There are nine 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the second 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg10Co2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Co(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Co(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Co2 cuboctahedra. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Co2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Co2 cuboctahedra; edges with four equivalent Mg(2)Mg10Co2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Co2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Co(1)Mg10Ga2 cuboctahedra. In the seventh 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the eighth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the ninth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. Co(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form CoMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Co2 cuboctahedra; corners with six equivalent Co(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with four equivalent Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Co(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Co2 cuboctahedra; faces with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Co(1) atoms to form GaMg10Co2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Co2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Co(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1,1)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 Mg(1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Co2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6GaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.811
_cell_length_b   6.026
_cell_length_c   6.026
_cell_angle_alpha   119.601
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   151.913
_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  0.000  0.167  0.833  1.0
  Ga  Ga1  1  0.500  0.326  0.674  1.0
  Mg  Mg2  1  0.000  0.659  0.832  1.0
  Mg  Mg3  1  0.000  0.168  0.341  1.0
  Mg  Mg4  1  0.000  0.666  0.334  1.0
  Mg  Mg5  1  0.500  0.855  0.674  1.0
  Mg  Mg6  1  0.500  0.326  0.145  1.0
  Mg  Mg7  1  0.500  0.833  0.167  1.0
[/CIF]
.
The material described by Mg6CoGa crystallizes in the orthorhombic Amm2 space group. There are nine 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the second 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1,1); four Mg(3,3); and two equivalent Co(1) atoms to form distorted MgMg10Co2 cuboctahedra that share corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg10Co2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Co(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Co(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Co2 cuboctahedra. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Co2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Co2 cuboctahedra; edges with four equivalent Mg(2)Mg10Co2 cuboctahedra; edges with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Co2 cuboctahedra; faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Co(1)Mg10Ga2 cuboctahedra. In the seventh 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 Mg(2)Mg10Co2 cuboctahedra; corners with four equivalent Co(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with two 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 Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)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; and faces with four Mg(1,1)Mg8Ga2Co2 cuboctahedra. In the eighth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. In the ninth Mg site, Mg(3) is bonded in a 12-coordinate geometry 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. Co(1) is bonded to two equivalent Mg(2); four Mg(1,1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form CoMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Co2 cuboctahedra; corners with six equivalent Co(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with two equivalent Mg(2)Mg10Co2 cuboctahedra; edges with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; edges with four equivalent Ga(1)Mg10Co2 cuboctahedra; faces with two equivalent Mg(2)Mg10Co2 cuboctahedra; faces with two equivalent Co(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Co2 cuboctahedra; faces with four Mg(1,1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3,3,3); and two equivalent Co(1) atoms to form GaMg10Co2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Co2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Co(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1,1)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 Mg(1,1)Mg8Ga2Co2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Co2 cuboctahedra. is represented by the CIF file [CIF]
data_Mg6GaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.811
_cell_length_b   6.026
_cell_length_c   6.026
_cell_angle_alpha   119.601
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   151.913
_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  0.000  0.167  0.833  1.0
  Ga  Ga1  1  0.500  0.326  0.674  1.0
  Mg  Mg2  1  0.000  0.659  0.832  1.0
  Mg  Mg3  1  0.000  0.168  0.341  1.0
  Mg  Mg4  1  0.000  0.666  0.334  1.0
  Mg  Mg5  1  0.500  0.855  0.674  1.0
  Mg  Mg6  1  0.500  0.326  0.145  1.0
  Mg  Mg7  1  0.500  0.833  0.167  1.0
[/CIF]
.