The material structure described by Mg14ZnGa 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 equivalent Mg(3), and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Mg10Ga2 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ga2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra, faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Zn(1); and one Ga(1) atom to form distorted MgMg10ZnGa cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)Mg10ZnGa cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZnGa cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ga(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ga2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14ZnGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.242
_cell_length_b   6.242
_cell_length_c   10.033
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   338.576
_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  0.330  0.170  0.374  1.0
  Mg  Mg7  1  0.330  0.170  0.876  1.0
  Mg  Mg8  1  0.330  0.661  0.374  1.0
  Mg  Mg9  1  0.330  0.661  0.876  1.0
  Mg  Mg10  1  0.839  0.170  0.374  1.0
  Mg  Mg11  1  0.839  0.170  0.876  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Zn  Zn14  1  0.167  0.333  0.125  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
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The material structure described by Mg14ZnGa 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 equivalent Mg(3), and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Mg10Ga2 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ga2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10ZnGa cuboctahedra, faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Mg10Ga2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10ZnGa cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Zn(1); and one Ga(1) atom to form distorted MgMg10ZnGa cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)Mg10ZnGa cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with two equivalent Ga(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZnGa cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra;  a faceface with one Ga(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ga2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ga2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; faces with three equivalent Ga(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ga2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Ga(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ga(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form GaMg12 cuboctahedra that share corners with six equivalent Ga(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)Mg10Ga2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZnGa cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ga2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZnGa cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14ZnGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.242
_cell_length_b   6.242
_cell_length_c   10.033
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   338.576
_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  0.330  0.170  0.374  1.0
  Mg  Mg7  1  0.330  0.170  0.876  1.0
  Mg  Mg8  1  0.330  0.661  0.374  1.0
  Mg  Mg9  1  0.330  0.661  0.876  1.0
  Mg  Mg10  1  0.839  0.170  0.374  1.0
  Mg  Mg11  1  0.839  0.170  0.876  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Zn  Zn14  1  0.167  0.333  0.125  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
.