The material described by Mg14CuCd 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 Cd(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, corners with eight equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Cd 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 Mg(5)Mg6CdCu cuboctahedra, corners with four equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6CdCu 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 Cu(1), and two equivalent Cd(1) atoms to form distorted MgMg8Cd2Cu2 cuboctahedra that share corners with two equivalent Mg(5)Mg6CdCu cuboctahedra, 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)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg10Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CdCu 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 two equivalent Mg(5)Mg6CdCu cuboctahedra, corners with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Cu2 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)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd 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, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CdCu cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), one Cu(1), and one Cd(1) atom to form distorted MgMg6CdCu cuboctahedra that share  a cornercorner with one Mg(2)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Cd2Cu2 cuboctahedra,  a cornercorner with one Cd(1)Mg10Cu2 cuboctahedra, corners with two equivalent Mg(1)Mg12 cuboctahedra, corners with two equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with four equivalent Mg(7)Mg11Cd cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Cu(1)Mg10Cd2 cuboctahedra,  an edgeedge with one Cd(1)Mg10Cu2 cuboctahedra, edges with two equivalent Mg(7)Mg11Cd cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg10Cu2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with four equivalent Mg(5)Mg6CdCu cuboctahedra. 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 Cu(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 Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with six equivalent Mg(7)Mg11Cd cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg10Cu2 cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Cu(1)Mg10Cd2 cuboctahedra. Cu(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cd(1) atoms to form CuMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Cd(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cu(1) atoms to form CdMg10Cu2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6CdCu cuboctahedra, corners with six equivalent Cd(1)Mg10Cu2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(5)Mg6CdCu cuboctahedra, and faces with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14CdCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.314
_cell_length_b   6.332
_cell_length_c   10.062
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.093
_symmetry_Int_Tables_number   1
_cell_volume   348.085
_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  0.168  0.334  0.625  1.0
  Mg  Mg1  1  0.170  0.835  0.625  1.0
  Mg  Mg2  1  0.673  0.338  0.125  1.0
  Mg  Mg3  1  0.666  0.331  0.625  1.0
  Mg  Mg4  1  0.673  0.836  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.328  0.170  0.362  1.0
  Mg  Mg7  1  0.328  0.170  0.888  1.0
  Mg  Mg8  1  0.328  0.658  0.362  1.0
  Mg  Mg9  1  0.328  0.658  0.888  1.0
  Mg  Mg10  1  0.840  0.170  0.368  1.0
  Mg  Mg11  1  0.840  0.170  0.882  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Cd  Cd14  1  0.161  0.830  0.125  1.0
  Cu  Cu15  1  0.165  0.333  0.125  1.0
[/CIF]
.
The material described by Mg14CuCd 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 Cd(1)Mg10Cu2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, corners with eight equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)Mg11Cd 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 Mg(5)Mg6CdCu cuboctahedra, corners with four equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(5)Mg6CdCu 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 Cu(1), and two equivalent Cd(1) atoms to form distorted MgMg8Cd2Cu2 cuboctahedra that share corners with two equivalent Mg(5)Mg6CdCu cuboctahedra, 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)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, edges with two equivalent Cu(1)Mg10Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CdCu 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 two equivalent Mg(5)Mg6CdCu cuboctahedra, corners with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, corners with four equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Cu2 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)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, faces with two equivalent Mg(7)Mg11Cd 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, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with six equivalent Mg(5)Mg6CdCu cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), one Cu(1), and one Cd(1) atom to form distorted MgMg6CdCu cuboctahedra that share  a cornercorner with one Mg(2)Mg12 cuboctahedra,  a cornercorner with one Mg(4)Mg12 cuboctahedra,  a cornercorner with one Mg(3)Mg8Cd2Cu2 cuboctahedra,  a cornercorner with one Cd(1)Mg10Cu2 cuboctahedra, corners with two equivalent Mg(1)Mg12 cuboctahedra, corners with two equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with four equivalent Mg(7)Mg11Cd cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra,  an edgeedge with one Mg(1)Mg12 cuboctahedra,  an edgeedge with one Mg(2)Mg12 cuboctahedra,  an edgeedge with one Cu(1)Mg10Cd2 cuboctahedra,  an edgeedge with one Cd(1)Mg10Cu2 cuboctahedra, edges with two equivalent Mg(7)Mg11Cd cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg10Cu2 cuboctahedra, faces with three equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with four equivalent Mg(5)Mg6CdCu cuboctahedra. 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 Cu(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 Cd(1) atom to form distorted MgMg11Cd cuboctahedra that share corners with six equivalent Mg(7)Mg11Cd cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg10Cu2 cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent Cu(1)Mg10Cd2 cuboctahedra. Cu(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cd(1) atoms to form CuMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Cu(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, corners with eight equivalent Mg(5)Mg6CdCu cuboctahedra, edges with two equivalent Cd(1)Mg10Cu2 cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg10Cu2 cuboctahedra, faces with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, and faces with six equivalent Mg(7)Mg11Cd cuboctahedra. Cd(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Cu(1) atoms to form CdMg10Cu2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(5)Mg6CdCu cuboctahedra, corners with six equivalent Cd(1)Mg10Cu2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Cu(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(7)Mg11Cd cuboctahedra, edges with four equivalent Mg(5)Mg6CdCu cuboctahedra, edges with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra, faces with two equivalent Mg(7)Mg11Cd cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Cu(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(5)Mg6CdCu cuboctahedra, and faces with four equivalent Mg(3)Mg8Cd2Cu2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14CdCu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.314
_cell_length_b   6.332
_cell_length_c   10.062
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.093
_symmetry_Int_Tables_number   1
_cell_volume   348.085
_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  0.168  0.334  0.625  1.0
  Mg  Mg1  1  0.170  0.835  0.625  1.0
  Mg  Mg2  1  0.673  0.338  0.125  1.0
  Mg  Mg3  1  0.666  0.331  0.625  1.0
  Mg  Mg4  1  0.673  0.836  0.125  1.0
  Mg  Mg5  1  0.666  0.834  0.625  1.0
  Mg  Mg6  1  0.328  0.170  0.362  1.0
  Mg  Mg7  1  0.328  0.170  0.888  1.0
  Mg  Mg8  1  0.328  0.658  0.362  1.0
  Mg  Mg9  1  0.328  0.658  0.888  1.0
  Mg  Mg10  1  0.840  0.170  0.368  1.0
  Mg  Mg11  1  0.840  0.170  0.882  1.0
  Mg  Mg12  1  0.833  0.667  0.375  1.0
  Mg  Mg13  1  0.833  0.667  0.875  1.0
  Cd  Cd14  1  0.161  0.830  0.125  1.0
  Cu  Cu15  1  0.165  0.333  0.125  1.0
[/CIF]
.