The structure described by Mg14TiGa crystallizes in the hexagonal P-6m2 space group. There are four 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10TiGa cuboctahedra. In the second 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 Ti(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Ti2 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)Mg10TiGa cuboctahedra, faces with two equivalent Mg(1)Mg10Ti2 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)Mg10TiGa cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Ti(1), and one Ga(1) atom to form distorted MgMg10TiGa cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)Mg10TiGa cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg10TiGa cuboctahedra,  a faceface with one Ti(1)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with five equivalent Mg(1)Mg10Ti2 cuboctahedra, and faces with six equivalent Mg(3)Mg10TiGa cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(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)Mg10TiGa cuboctahedra, edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with six equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with three equivalent Mg(1)Mg10Ti2 cuboctahedra, faces with three equivalent Ti(1)Mg12 cuboctahedra, faces with three equivalent Ga(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)Mg10TiGa cuboctahedra. Ti(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Ti2 cuboctahedra, faces with six equivalent Mg(3)Mg10TiGa cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ga(1) is bonded to six equivalent Mg(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)Mg10Ti2 cuboctahedra, edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Ti(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with six equivalent Mg(3)Mg10TiGa cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14TiGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.293
_cell_length_b   6.293
_cell_length_c   10.192
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   349.514
_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  0.169  0.835  0.125  1.0
  Mg  Mg1  1  0.166  0.833  0.625  1.0
  Mg  Mg2  1  0.665  0.331  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.665  0.835  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.330  0.170  0.375  1.0
  Mg  Mg7  1  0.330  0.170  0.875  1.0
  Mg  Mg8  1  0.330  0.659  0.375  1.0
  Mg  Mg9  1  0.330  0.659  0.875  1.0
  Mg  Mg10  1  0.841  0.170  0.375  1.0
  Mg  Mg11  1  0.841  0.170  0.875  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Ti  Ti14  1  0.167  0.333  0.125  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
.
The structure described by Mg14TiGa crystallizes in the hexagonal P-6m2 space group. There are four 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Ga(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Ti(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra, and faces with ten equivalent Mg(3)Mg10TiGa cuboctahedra. In the second 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 Ti(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg10Ti2 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)Mg10TiGa cuboctahedra, faces with two equivalent Mg(1)Mg10Ti2 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)Mg10TiGa cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Ti(1), and one Ga(1) atom to form distorted MgMg10TiGa cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)Mg10TiGa cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg12 cuboctahedra, edges with two equivalent Ga(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg10TiGa cuboctahedra,  a faceface with one Ti(1)Mg12 cuboctahedra,  a faceface with one Ga(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with five equivalent Mg(1)Mg10Ti2 cuboctahedra, and faces with six equivalent Mg(3)Mg10TiGa cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(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)Mg10TiGa cuboctahedra, edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with six equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with three equivalent Mg(1)Mg10Ti2 cuboctahedra, faces with three equivalent Ti(1)Mg12 cuboctahedra, faces with three equivalent Ga(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)Mg10TiGa cuboctahedra. Ti(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Ga(1)Mg12 cuboctahedra, faces with six equivalent Mg(1)Mg10Ti2 cuboctahedra, faces with six equivalent Mg(3)Mg10TiGa cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ga(1) is bonded to six equivalent Mg(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)Mg10Ti2 cuboctahedra, edges with six equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with twelve equivalent Mg(3)Mg10TiGa cuboctahedra, faces with two equivalent Ti(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with six equivalent Mg(3)Mg10TiGa cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_Mg14TiGa
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.293
_cell_length_b   6.293
_cell_length_c   10.192
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   349.514
_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  0.169  0.835  0.125  1.0
  Mg  Mg1  1  0.166  0.833  0.625  1.0
  Mg  Mg2  1  0.665  0.331  0.125  1.0
  Mg  Mg3  1  0.667  0.334  0.625  1.0
  Mg  Mg4  1  0.665  0.835  0.125  1.0
  Mg  Mg5  1  0.667  0.833  0.625  1.0
  Mg  Mg6  1  0.330  0.170  0.375  1.0
  Mg  Mg7  1  0.330  0.170  0.875  1.0
  Mg  Mg8  1  0.330  0.659  0.375  1.0
  Mg  Mg9  1  0.330  0.659  0.875  1.0
  Mg  Mg10  1  0.841  0.170  0.375  1.0
  Mg  Mg11  1  0.841  0.170  0.875  1.0
  Mg  Mg12  1  0.833  0.667  0.373  1.0
  Mg  Mg13  1  0.833  0.667  0.877  1.0
  Ti  Ti14  1  0.167  0.333  0.125  1.0
  Ga  Ga15  1  0.167  0.333  0.625  1.0
[/CIF]
.