The material described by Mg3Mn crystallizes in the orthorhombic Pmm2 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), and four equivalent Mn(1) atoms to form MgMg8Mn4 cuboctahedra that share corners with eight equivalent Mn(1)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with two equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with four equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Mn4 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), four equivalent Mg(3), and four equivalent Mn(1) atoms to form distorted MgMg8Mn4 cuboctahedra that share corners with eight equivalent Mg(3)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with two equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with eight equivalent Mn(1)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Mn4 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Mn(1) atoms to form distorted MgMg10Mn2 cuboctahedra that share corners with eight equivalent Mg(2)Mg8Mn4 cuboctahedra, corners with ten equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, and faces with eight equivalent Mn(1)Mg10Mn2 cuboctahedra. Mn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Mn(1) atoms to form distorted MnMg10Mn2 cuboctahedra that share corners with eight equivalent Mg(1)Mg8Mn4 cuboctahedra, corners with ten equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with eight equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(3)Mg10Mn2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.095
_cell_length_b   4.900
_cell_length_c   5.301
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   80.411
_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  0.500  0.000  0.666  1.0
  Mg  Mg1  1  0.500  0.500  0.324  1.0
  Mg  Mg2  1  0.000  0.500  0.842  1.0
  Mn  Mn3  1  0.000  0.000  0.168  1.0
[/CIF]
.
The material described by Mg3Mn crystallizes in the orthorhombic Pmm2 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), and four equivalent Mn(1) atoms to form MgMg8Mn4 cuboctahedra that share corners with eight equivalent Mn(1)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with two equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with four equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Mn4 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), four equivalent Mg(3), and four equivalent Mn(1) atoms to form distorted MgMg8Mn4 cuboctahedra that share corners with eight equivalent Mg(3)Mg10Mn2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with two equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with eight equivalent Mn(1)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Mn4 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Mn(1) atoms to form distorted MgMg10Mn2 cuboctahedra that share corners with eight equivalent Mg(2)Mg8Mn4 cuboctahedra, corners with ten equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(2)Mg8Mn4 cuboctahedra, edges with four equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(3)Mg10Mn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, and faces with eight equivalent Mn(1)Mg10Mn2 cuboctahedra. Mn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Mn(1) atoms to form distorted MnMg10Mn2 cuboctahedra that share corners with eight equivalent Mg(1)Mg8Mn4 cuboctahedra, corners with ten equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mn(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Mn4 cuboctahedra, edges with eight equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(1)Mg8Mn4 cuboctahedra, faces with four equivalent Mg(2)Mg8Mn4 cuboctahedra, faces with four equivalent Mn(1)Mg10Mn2 cuboctahedra, and faces with eight equivalent Mg(3)Mg10Mn2 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.095
_cell_length_b   4.900
_cell_length_c   5.301
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   80.411
_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  0.500  0.000  0.666  1.0
  Mg  Mg1  1  0.500  0.500  0.324  1.0
  Mg  Mg2  1  0.000  0.500  0.842  1.0
  Mn  Mn3  1  0.000  0.000  0.168  1.0
[/CIF]
.