The material described by LiMg14Cd crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(1,1,1)Li2Mg10 cuboctahedra; edges with twelve Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(1,1,1)Li2Mg10 cuboctahedra; faces with six Mg(3,3)LiMg10Cd cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Li2Mg10 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Mg(1)Li2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Cd(1) atom to form distorted MgLiMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Cd cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four Mg(3,3)LiMg10Cd cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. In the sixth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); and one Cd(1) atom to form distorted MgLiMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Cd cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)LiMg10Cd cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LiMg10Cd cuboctahedra; edges with six Mg(1,1,1)Li2Mg10 cuboctahedra; edges with six Mg(3,3)LiMg10Cd cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three Mg(1,1,1)Li2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Li2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with twelve Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(3,3)LiMg10Cd cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg14Cd
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.350
_cell_length_b   6.350
_cell_length_c   10.306
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   359.926
_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  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.167  0.833  0.125  1.0
  Mg  Mg2  1  0.166  0.833  0.625  1.0
  Mg  Mg3  1  0.667  0.333  0.125  1.0
  Mg  Mg4  1  0.667  0.334  0.625  1.0
  Mg  Mg5  1  0.667  0.833  0.125  1.0
  Mg  Mg6  1  0.667  0.833  0.625  1.0
  Mg  Mg7  1  0.333  0.167  0.375  1.0
  Mg  Mg8  1  0.333  0.167  0.875  1.0
  Mg  Mg9  1  0.333  0.665  0.375  1.0
  Mg  Mg10  1  0.333  0.665  0.875  1.0
  Mg  Mg11  1  0.835  0.167  0.375  1.0
  Mg  Mg12  1  0.835  0.167  0.875  1.0
  Mg  Mg13  1  0.833  0.667  0.374  1.0
  Mg  Mg14  1  0.833  0.667  0.876  1.0
  Cd  Cd15  1  0.167  0.333  0.625  1.0
[/CIF]
.
The material described by LiMg14Cd crystallizes in the hexagonal P-6m2 space group. Li(1) is bonded to six Mg(1,1,1) and six Mg(3,3) atoms to form LiMg12 cuboctahedra that share corners with six equivalent Li(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(1,1,1)Li2Mg10 cuboctahedra; edges with twelve Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(1,1,1)Li2Mg10 cuboctahedra; faces with six Mg(3,3)LiMg10Cd cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Li(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Li2Mg10 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Mg(1)Li2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the fourth Mg site, Mg(1) is bonded to two equivalent Li(1); two equivalent Mg(4); four Mg(1,1); and four Mg(3,3) atoms to form MgLi2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Li2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(1,1)Li2Mg10 cuboctahedra; and faces with ten Mg(3,3)LiMg10Cd cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Cd(1) atom to form distorted MgLiMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Cd cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four Mg(3,3)LiMg10Cd cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. In the sixth Mg site, Mg(3) is bonded to one Li(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); and one Cd(1) atom to form distorted MgLiMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LiMg10Cd cuboctahedra; edges with two equivalent Li(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four Mg(1,1)Li2Mg10 cuboctahedra; edges with four equivalent Mg(3)LiMg10Cd cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra;  a faceface with one Li(1)Mg12 cuboctahedra;  a faceface with one Cd(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1,1)Li2Mg10 cuboctahedra; faces with five equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. In the seventh Mg site, Mg(4) is bonded to three Mg(1,1,1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LiMg10Cd cuboctahedra; edges with six Mg(1,1,1)Li2Mg10 cuboctahedra; edges with six Mg(3,3)LiMg10Cd cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Li(1)Mg12 cuboctahedra; faces with three Mg(1,1,1)Li2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with three equivalent Cd(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LiMg10Cd cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(1,1,1)Li2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with twelve Mg(3,3)LiMg10Cd cuboctahedra; faces with two equivalent Li(1)Mg12 cuboctahedra; faces with six Mg(3,3)LiMg10Cd cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the CIF file [CIF]
data_LiMg14Cd
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.350
_cell_length_b   6.350
_cell_length_c   10.306
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   359.926
_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  0.167  0.333  0.125  1.0
  Mg  Mg1  1  0.167  0.833  0.125  1.0
  Mg  Mg2  1  0.166  0.833  0.625  1.0
  Mg  Mg3  1  0.667  0.333  0.125  1.0
  Mg  Mg4  1  0.667  0.334  0.625  1.0
  Mg  Mg5  1  0.667  0.833  0.125  1.0
  Mg  Mg6  1  0.667  0.833  0.625  1.0
  Mg  Mg7  1  0.333  0.167  0.375  1.0
  Mg  Mg8  1  0.333  0.167  0.875  1.0
  Mg  Mg9  1  0.333  0.665  0.375  1.0
  Mg  Mg10  1  0.333  0.665  0.875  1.0
  Mg  Mg11  1  0.835  0.167  0.375  1.0
  Mg  Mg12  1  0.835  0.167  0.875  1.0
  Mg  Mg13  1  0.833  0.667  0.374  1.0
  Mg  Mg14  1  0.833  0.667  0.876  1.0
  Cd  Cd15  1  0.167  0.333  0.625  1.0
[/CIF]
.