The material described by Mg14TiCo crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ti cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ti(1), and two equivalent Co(1) atoms to form distorted MgMg8Ti2Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, and faces with two equivalent Co(1)Mg10Ti2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, corners with four equivalent Ti(1)Mg10Co2 cuboctahedra, corners with four equivalent Co(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ti(1), and one Co(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with six equivalent Mg(7)Mg11Ti cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Ti(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Ti2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form TiMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ti(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Ti2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra. Co(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ti(1) atoms to form CoMg10Ti2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ti cuboctahedra. is represented by the CIF card [CIF]
data_Mg14TiCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.291
_cell_length_b   6.125
_cell_length_c   9.950
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.129
_symmetry_Int_Tables_number   1
_cell_volume   334.902
_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  0.333  0.625  1.0
  Mg  Mg1  1  0.170  0.835  0.625  1.0
  Mg  Mg2  1  0.661  0.337  0.125  1.0
  Mg  Mg3  1  0.663  0.329  0.625  1.0
  Mg  Mg4  1  0.661  0.824  0.125  1.0
  Mg  Mg5  1  0.663  0.834  0.625  1.0
  Mg  Mg6  1  0.327  0.167  0.359  1.0
  Mg  Mg7  1  0.327  0.167  0.891  1.0
  Mg  Mg8  1  0.327  0.660  0.359  1.0
  Mg  Mg9  1  0.327  0.660  0.891  1.0
  Mg  Mg10  1  0.853  0.177  0.357  1.0
  Mg  Mg11  1  0.853  0.177  0.893  1.0
  Mg  Mg12  1  0.843  0.671  0.376  1.0
  Mg  Mg13  1  0.843  0.671  0.874  1.0
  Ti  Ti14  1  0.150  0.825  0.125  1.0
  Co  Co15  1  0.166  0.333  0.125  1.0
[/CIF]
.
The material described by Mg14TiCo crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ti(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ti cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Co(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Ti(1), and two equivalent Co(1) atoms to form distorted MgMg8Ti2Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with two equivalent Co(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, and faces with two equivalent Co(1)Mg10Ti2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, corners with four equivalent Ti(1)Mg10Co2 cuboctahedra, corners with four equivalent Co(1)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one Ti(1), and one Co(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ti(1) atom to form distorted MgMg11Ti cuboctahedra that share corners with six equivalent Mg(7)Mg11Ti cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Ti(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Mg10Ti2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form TiMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ti(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(7)Mg11Ti cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Mg(7)Mg11Ti cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Mg10Ti2 cuboctahedra, and faces with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra. Co(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ti(1) atoms to form CoMg10Ti2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ti(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Ti(1)Mg10Co2 cuboctahedra, faces with four equivalent Mg(3)Mg8Ti2Co2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Ti cuboctahedra. is represented by the CIF card [CIF]
data_Mg14TiCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.291
_cell_length_b   6.125
_cell_length_c   9.950
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.129
_symmetry_Int_Tables_number   1
_cell_volume   334.902
_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  0.333  0.625  1.0
  Mg  Mg1  1  0.170  0.835  0.625  1.0
  Mg  Mg2  1  0.661  0.337  0.125  1.0
  Mg  Mg3  1  0.663  0.329  0.625  1.0
  Mg  Mg4  1  0.661  0.824  0.125  1.0
  Mg  Mg5  1  0.663  0.834  0.625  1.0
  Mg  Mg6  1  0.327  0.167  0.359  1.0
  Mg  Mg7  1  0.327  0.167  0.891  1.0
  Mg  Mg8  1  0.327  0.660  0.359  1.0
  Mg  Mg9  1  0.327  0.660  0.891  1.0
  Mg  Mg10  1  0.853  0.177  0.357  1.0
  Mg  Mg11  1  0.853  0.177  0.893  1.0
  Mg  Mg12  1  0.843  0.671  0.376  1.0
  Mg  Mg13  1  0.843  0.671  0.874  1.0
  Ti  Ti14  1  0.150  0.825  0.125  1.0
  Co  Co15  1  0.166  0.333  0.125  1.0
[/CIF]
.