The structure described by LiMg14Co crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form LiMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Li(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Li2Mg10 cuboctahedra, and faces with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra. 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 Li(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Li2Mg8Co2 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)Li2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)LiMg11 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)Li2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Li(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Co(1) atoms to form distorted MgLi2Mg8Co2 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)Li2Mg8Co2 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with two equivalent Co(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Co(1)Li2Mg10 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 Li(1)Mg10Co2 cuboctahedra, corners with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, corners with four equivalent Co(1)Li2Mg10 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)LiMg11 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), 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), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Li(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgLiMg11 cuboctahedra that share corners with six equivalent Mg(7)LiMg11 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Li(1)Mg10Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Li2Mg10 cuboctahedra. Co(1) is bonded to two equivalent Li(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CoLi2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, and faces with six equivalent Mg(7)LiMg11 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg14Co
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.292
_cell_length_b   6.389
_cell_length_c   9.834
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.509
_symmetry_Int_Tables_number   1
_cell_volume   340.570
_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
  Li  Li0  1  0.165  0.833  0.125  1.0
  Mg  Mg1  1  0.170  0.335  0.625  1.0
  Mg  Mg2  1  0.173  0.836  0.625  1.0
  Mg  Mg3  1  0.678  0.342  0.125  1.0
  Mg  Mg4  1  0.665  0.330  0.625  1.0
  Mg  Mg5  1  0.678  0.835  0.125  1.0
  Mg  Mg6  1  0.665  0.835  0.625  1.0
  Mg  Mg7  1  0.320  0.169  0.355  1.0
  Mg  Mg8  1  0.320  0.169  0.895  1.0
  Mg  Mg9  1  0.320  0.651  0.355  1.0
  Mg  Mg10  1  0.320  0.651  0.895  1.0
  Mg  Mg11  1  0.845  0.172  0.362  1.0
  Mg  Mg12  1  0.845  0.172  0.888  1.0
  Mg  Mg13  1  0.834  0.667  0.378  1.0
  Mg  Mg14  1  0.834  0.667  0.872  1.0
  Co  Co15  1  0.167  0.334  0.125  1.0
[/CIF]
.
The structure described by LiMg14Co crystallizes in the orthorhombic Amm2 space group. Li(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Co(1) atoms to form LiMg10Co2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Li(1)Mg10Co2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Co(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Co(1)Li2Mg10 cuboctahedra, and faces with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra. 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 Li(1)Mg10Co2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Li2Mg8Co2 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)Li2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)LiMg11 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)Li2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Li(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Co(1) atoms to form distorted MgLi2Mg8Co2 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)Li2Mg8Co2 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with two equivalent Co(1)Li2Mg10 cuboctahedra, edges with four equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent Co(1)Li2Mg10 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 Li(1)Mg10Co2 cuboctahedra, corners with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, corners with four equivalent Co(1)Li2Mg10 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)LiMg11 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 2-coordinate geometry to one Li(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), 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), and one Co(1) atom. In the seventh Mg site, Mg(7) is bonded to one Li(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgLiMg11 cuboctahedra that share corners with six equivalent Mg(7)LiMg11 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Li(1)Mg10Co2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Mg(7)LiMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Co(1)Li2Mg10 cuboctahedra. Co(1) is bonded to two equivalent Li(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CoLi2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Co(1)Li2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Li(1)Mg10Co2 cuboctahedra, edges with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, faces with two equivalent Li(1)Mg10Co2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Li2Mg8Co2 cuboctahedra, and faces with six equivalent Mg(7)LiMg11 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg14Co
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.292
_cell_length_b   6.389
_cell_length_c   9.834
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.509
_symmetry_Int_Tables_number   1
_cell_volume   340.570
_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
  Li  Li0  1  0.165  0.833  0.125  1.0
  Mg  Mg1  1  0.170  0.335  0.625  1.0
  Mg  Mg2  1  0.173  0.836  0.625  1.0
  Mg  Mg3  1  0.678  0.342  0.125  1.0
  Mg  Mg4  1  0.665  0.330  0.625  1.0
  Mg  Mg5  1  0.678  0.835  0.125  1.0
  Mg  Mg6  1  0.665  0.835  0.625  1.0
  Mg  Mg7  1  0.320  0.169  0.355  1.0
  Mg  Mg8  1  0.320  0.169  0.895  1.0
  Mg  Mg9  1  0.320  0.651  0.355  1.0
  Mg  Mg10  1  0.320  0.651  0.895  1.0
  Mg  Mg11  1  0.845  0.172  0.362  1.0
  Mg  Mg12  1  0.845  0.172  0.888  1.0
  Mg  Mg13  1  0.834  0.667  0.378  1.0
  Mg  Mg14  1  0.834  0.667  0.872  1.0
  Co  Co15  1  0.167  0.334  0.125  1.0
[/CIF]
.