The compound described by MgZn crystallizes in the orthorhombic Amm2 space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), four equivalent Mg(3), two equivalent Zn(1), and two equivalent Zn(2) atoms to form distorted MgMg8Zn4 cuboctahedra that share corners with six equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with six equivalent Mg(1)Mg8Zn4 cuboctahedra, corners with eight equivalent Zn(1)Mg6Zn4 cuboctahedra,  an edgeedge with one Zn(1)Mg6Zn4 cuboctahedra, edges with three equivalent Mg(2)Mg4Zn8 cuboctahedra, edges with four equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with eight equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(2)Mg8Zn4 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Zn(1), two equivalent Zn(3), and four equivalent Zn(2) atoms to form distorted MgMg4Zn8 cuboctahedra that share corners with six equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with six equivalent Mg(1)Mg8Zn4 cuboctahedra, corners with eight equivalent Zn(1)Mg6Zn4 cuboctahedra,  an edgeedge with one Zn(1)Mg6Zn4 cuboctahedra, edges with three equivalent Mg(1)Mg8Zn4 cuboctahedra, edges with four equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(2)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(3)Mg4Zn8 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), four equivalent Mg(1), two equivalent Zn(1), two equivalent Zn(2), and two equivalent Zn(3) atoms to form distorted MgMg6Zn6 cuboctahedra that share corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Zn(3)Mg4Zn8 cuboctahedra, edges with three equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(1)Mg6Zn4 cuboctahedra. There are three inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), and four equivalent Zn(3) atoms to form distorted ZnMg6Zn4 cuboctahedra that share corners with four equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with four equivalent Zn(1)Mg6Zn4 cuboctahedra, corners with eight equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn4 cuboctahedra,  an edgeedge with one Mg(2)Mg4Zn8 cuboctahedra,  an edgeedge with one Mg(1)Mg8Zn4 cuboctahedra, edges with eight equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(1)Mg6Zn4 cuboctahedra, and faces with six equivalent Mg(3)Mg6Zn6 cuboctahedra. In the second Zn site, Zn(2) is bonded to two equivalent Mg(1), two equivalent Mg(3), four equivalent Mg(2), two equivalent Zn(2), and two equivalent Zn(3) atoms to form distorted ZnMg8Zn4 cuboctahedra that share corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with three equivalent Zn(3)Mg4Zn8 cuboctahedra, edges with four equivalent Mg(2)Mg4Zn8 cuboctahedra, edges with eight equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(2)Mg8Zn4 cuboctahedra, and faces with six equivalent Mg(1)Mg8Zn4 cuboctahedra. In the third Zn site, Zn(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), two equivalent Zn(2), two equivalent Zn(3), and four equivalent Zn(1) atoms to form distorted ZnMg4Zn8 cuboctahedra that share corners with four equivalent Zn(1)Mg6Zn4 cuboctahedra, corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with three equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(1)Mg6Zn4 cuboctahedra, and faces with six equivalent Mg(2)Mg4Zn8 cuboctahedra. is represented by the CIF card [CIF]
data_MgZn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.740
_cell_length_b   7.740
_cell_length_c   4.800
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   157.273
_symmetry_Int_Tables_number   1
_cell_volume   111.092
_cell_formula_units_Z   3
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  0.998  0.002  0.000  1.0
  Mg  Mg1  1  0.673  0.327  0.000  1.0
  Mg  Mg2  1  0.439  0.561  0.500  1.0
  Zn  Zn3  1  0.333  0.667  0.000  1.0
  Zn  Zn4  1  0.113  0.887  0.500  1.0
  Zn  Zn5  1  0.776  0.224  0.500  1.0
[/CIF]
.
The compound described by MgZn crystallizes in the orthorhombic Amm2 space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), four equivalent Mg(3), two equivalent Zn(1), and two equivalent Zn(2) atoms to form distorted MgMg8Zn4 cuboctahedra that share corners with six equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with six equivalent Mg(1)Mg8Zn4 cuboctahedra, corners with eight equivalent Zn(1)Mg6Zn4 cuboctahedra,  an edgeedge with one Zn(1)Mg6Zn4 cuboctahedra, edges with three equivalent Mg(2)Mg4Zn8 cuboctahedra, edges with four equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with eight equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(2)Mg8Zn4 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Zn(1), two equivalent Zn(3), and four equivalent Zn(2) atoms to form distorted MgMg4Zn8 cuboctahedra that share corners with six equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with six equivalent Mg(1)Mg8Zn4 cuboctahedra, corners with eight equivalent Zn(1)Mg6Zn4 cuboctahedra,  an edgeedge with one Zn(1)Mg6Zn4 cuboctahedra, edges with three equivalent Mg(1)Mg8Zn4 cuboctahedra, edges with four equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(2)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(3)Mg4Zn8 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), four equivalent Mg(1), two equivalent Zn(1), two equivalent Zn(2), and two equivalent Zn(3) atoms to form distorted MgMg6Zn6 cuboctahedra that share corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Zn(3)Mg4Zn8 cuboctahedra, edges with three equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn4 cuboctahedra, and faces with six equivalent Zn(1)Mg6Zn4 cuboctahedra. There are three inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), and four equivalent Zn(3) atoms to form distorted ZnMg6Zn4 cuboctahedra that share corners with four equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with four equivalent Zn(1)Mg6Zn4 cuboctahedra, corners with eight equivalent Mg(2)Mg4Zn8 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn4 cuboctahedra,  an edgeedge with one Mg(2)Mg4Zn8 cuboctahedra,  an edgeedge with one Mg(1)Mg8Zn4 cuboctahedra, edges with eight equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with two equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(1)Mg6Zn4 cuboctahedra, and faces with six equivalent Mg(3)Mg6Zn6 cuboctahedra. In the second Zn site, Zn(2) is bonded to two equivalent Mg(1), two equivalent Mg(3), four equivalent Mg(2), two equivalent Zn(2), and two equivalent Zn(3) atoms to form distorted ZnMg8Zn4 cuboctahedra that share corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with three equivalent Zn(3)Mg4Zn8 cuboctahedra, edges with four equivalent Mg(2)Mg4Zn8 cuboctahedra, edges with eight equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with two equivalent Zn(1)Mg6Zn4 cuboctahedra, faces with four equivalent Mg(2)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(2)Mg8Zn4 cuboctahedra, and faces with six equivalent Mg(1)Mg8Zn4 cuboctahedra. In the third Zn site, Zn(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), two equivalent Zn(2), two equivalent Zn(3), and four equivalent Zn(1) atoms to form distorted ZnMg4Zn8 cuboctahedra that share corners with four equivalent Zn(1)Mg6Zn4 cuboctahedra, corners with six equivalent Mg(3)Mg6Zn6 cuboctahedra, corners with six equivalent Zn(3)Mg4Zn8 cuboctahedra, corners with six equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with three equivalent Mg(3)Mg6Zn6 cuboctahedra, edges with three equivalent Zn(2)Mg8Zn4 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Mg(3)Mg6Zn6 cuboctahedra, faces with two equivalent Mg(1)Mg8Zn4 cuboctahedra, faces with two equivalent Zn(2)Mg8Zn4 cuboctahedra, faces with four equivalent Zn(3)Mg4Zn8 cuboctahedra, faces with four equivalent Zn(1)Mg6Zn4 cuboctahedra, and faces with six equivalent Mg(2)Mg4Zn8 cuboctahedra. is represented by the CIF card [CIF]
data_MgZn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.740
_cell_length_b   7.740
_cell_length_c   4.800
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   157.273
_symmetry_Int_Tables_number   1
_cell_volume   111.092
_cell_formula_units_Z   3
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  0.998  0.002  0.000  1.0
  Mg  Mg1  1  0.673  0.327  0.000  1.0
  Mg  Mg2  1  0.439  0.561  0.500  1.0
  Zn  Zn3  1  0.333  0.667  0.000  1.0
  Zn  Zn4  1  0.113  0.887  0.500  1.0
  Zn  Zn5  1  0.776  0.224  0.500  1.0
[/CIF]
.