The material described by Mn9Au31 crystallizes in the tetragonal P4/m space group. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one Au(3), one Au(4), two equivalent Au(1), two equivalent Au(2), two equivalent Au(5), two equivalent Au(7), and two equivalent Au(8) atoms to form a mixture of edge, face, and corner-sharing MnAu12 cuboctahedra. In the second Mn site, Mn(2) is bonded to one Au(1), one Au(9), two equivalent Au(2), two equivalent Au(4), two equivalent Au(5), and four equivalent Au(6) atoms to form MnAu12 cuboctahedra that share corners with five equivalent Mn(2)Au12 cuboctahedra, edges with two equivalent Au(9)Mn4Au8 cuboctahedra, edges with six equivalent Mn(1)Au12 cuboctahedra,  a faceface with one Au(9)Mn4Au8 cuboctahedra, and faces with four equivalent Mn(2)Au12 cuboctahedra. In the third Mn site, Mn(3) is bonded to four equivalent Au(7) and eight equivalent Au(3) atoms to form a mixture of edge and face-sharing MnAu12 cuboctahedra. There are nine inequivalent Au sites. In the first Au site, Au(7) is bonded in a 3-coordinate geometry to one Mn(3) and two equivalent Mn(1) atoms. In the second Au site, Au(8) is bonded in a distorted square co-planar geometry to four equivalent Mn(1) atoms. In the third Au site, Au(9) is bonded to four equivalent Mn(2) and eight equivalent Au(6) atoms to form distorted AuMn4Au8 cuboctahedra that share corners with four equivalent Au(1)Mn3 cuboctahedra, corners with eight equivalent Au(5)Mn4 cuboctahedra, edges with four equivalent Au(2)Mn4 cuboctahedra, edges with eight equivalent Mn(2)Au12 cuboctahedra, faces with two equivalent Au(9)Mn4Au8 cuboctahedra, and faces with four equivalent Mn(2)Au12 cuboctahedra. In the fourth Au site, Au(1) is bonded to one Mn(2) and two equivalent Mn(1) atoms to form distorted AuMn3 cuboctahedra that share  a cornercorner with one Au(9)Mn4Au8 cuboctahedra, corners with two equivalent Au(1)Mn3 cuboctahedra, corners with two equivalent Au(5)Mn4 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra,  an edgeedge with one Au(2)Mn4 cuboctahedra, and edges with two equivalent Au(5)Mn4 cuboctahedra. In the fifth Au site, Au(2) is bonded to two equivalent Mn(1) and two equivalent Mn(2) atoms to form distorted AuMn4 cuboctahedra that share corners with four equivalent Au(1)Mn3 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra, corners with four equivalent Au(5)Mn4 cuboctahedra,  an edgeedge with one Au(1)Mn3 cuboctahedra,  an edgeedge with one Au(9)Mn4Au8 cuboctahedra, and edges with two equivalent Au(5)Mn4 cuboctahedra. In the sixth Au site, Au(3) is bonded in a 3-coordinate geometry to one Mn(1) and two equivalent Mn(3) atoms. In the seventh Au site, Au(4) is bonded in a 3-coordinate geometry to one Mn(1) and two equivalent Mn(2) atoms. In the eighth Au site, Au(5) is bonded to two equivalent Mn(1) and two equivalent Mn(2) atoms to form distorted AuMn4 cuboctahedra that share corners with two equivalent Au(1)Mn3 cuboctahedra, corners with two equivalent Au(5)Mn4 cuboctahedra, corners with two equivalent Au(9)Mn4Au8 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra,  an edgeedge with one Au(5)Mn4 cuboctahedra, edges with two equivalent Au(1)Mn3 cuboctahedra, and edges with two equivalent Au(2)Mn4 cuboctahedra. In the ninth Au site, Au(6) is bonded in a distorted rectangular see-saw-like geometry to four equivalent Mn(2) and two equivalent Au(9) atoms. is represented by the CIF file [CIF]
data_Mn9Au31
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.936
_cell_length_b   12.936
_cell_length_c   4.023
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   673.194
_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
  Mn  Mn0  1  0.650  0.950  0.500  1.0
  Mn  Mn1  1  0.950  0.350  0.500  1.0
  Mn  Mn2  1  0.050  0.650  0.500  1.0
  Mn  Mn3  1  0.350  0.050  0.500  1.0
  Mn  Mn4  1  0.702  0.602  0.000  1.0
  Mn  Mn5  1  0.602  0.298  0.000  1.0
  Mn  Mn6  1  0.398  0.702  0.000  1.0
  Mn  Mn7  1  0.298  0.398  0.000  1.0
  Mn  Mn8  1  0.000  0.000  0.000  1.0
  Au  Au9  1  0.697  0.099  0.000  1.0
  Au  Au10  1  0.901  0.697  0.000  1.0
  Au  Au11  1  0.400  0.200  0.000  1.0
  Au  Au12  1  0.200  0.600  0.000  1.0
  Au  Au13  1  0.800  0.400  0.000  1.0
  Au  Au14  1  0.600  0.800  0.000  1.0
  Au  Au15  1  0.046  0.148  0.500  1.0
  Au  Au16  1  0.148  0.954  0.500  1.0
  Au  Au17  1  0.852  0.046  0.500  1.0
  Au  Au18  1  0.954  0.852  0.500  1.0
  Au  Au19  1  0.254  0.253  0.500  1.0
  Au  Au20  1  0.253  0.746  0.500  1.0
  Au  Au21  1  0.747  0.254  0.500  1.0
  Au  Au22  1  0.746  0.747  0.500  1.0
  Au  Au23  1  0.150  0.450  0.500  1.0
  Au  Au24  1  0.450  0.850  0.500  1.0
  Au  Au25  1  0.550  0.150  0.500  1.0
  Au  Au26  1  0.850  0.550  0.500  1.0
  Au  Au27  1  0.453  0.350  0.500  1.0
  Au  Au28  1  0.350  0.547  0.500  1.0
  Au  Au29  1  0.650  0.453  0.500  1.0
  Au  Au30  1  0.547  0.650  0.500  1.0
  Au  Au31  1  0.303  0.901  0.000  1.0
  Au  Au32  1  0.099  0.303  0.000  1.0
  Au  Au33  1  0.797  0.902  0.000  1.0
  Au  Au34  1  0.902  0.203  0.000  1.0
  Au  Au35  1  0.098  0.797  0.000  1.0
  Au  Au36  1  0.203  0.098  0.000  1.0
  Au  Au37  1  0.000  0.500  0.000  1.0
  Au  Au38  1  0.500  0.000  0.000  1.0
  Au  Au39  1  0.500  0.500  0.000  1.0
[/CIF]
.
The material described by Mn9Au31 crystallizes in the tetragonal P4/m space group. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one Au(3), one Au(4), two equivalent Au(1), two equivalent Au(2), two equivalent Au(5), two equivalent Au(7), and two equivalent Au(8) atoms to form a mixture of edge, face, and corner-sharing MnAu12 cuboctahedra. In the second Mn site, Mn(2) is bonded to one Au(1), one Au(9), two equivalent Au(2), two equivalent Au(4), two equivalent Au(5), and four equivalent Au(6) atoms to form MnAu12 cuboctahedra that share corners with five equivalent Mn(2)Au12 cuboctahedra, edges with two equivalent Au(9)Mn4Au8 cuboctahedra, edges with six equivalent Mn(1)Au12 cuboctahedra,  a faceface with one Au(9)Mn4Au8 cuboctahedra, and faces with four equivalent Mn(2)Au12 cuboctahedra. In the third Mn site, Mn(3) is bonded to four equivalent Au(7) and eight equivalent Au(3) atoms to form a mixture of edge and face-sharing MnAu12 cuboctahedra. There are nine inequivalent Au sites. In the first Au site, Au(7) is bonded in a 3-coordinate geometry to one Mn(3) and two equivalent Mn(1) atoms. In the second Au site, Au(8) is bonded in a distorted square co-planar geometry to four equivalent Mn(1) atoms. In the third Au site, Au(9) is bonded to four equivalent Mn(2) and eight equivalent Au(6) atoms to form distorted AuMn4Au8 cuboctahedra that share corners with four equivalent Au(1)Mn3 cuboctahedra, corners with eight equivalent Au(5)Mn4 cuboctahedra, edges with four equivalent Au(2)Mn4 cuboctahedra, edges with eight equivalent Mn(2)Au12 cuboctahedra, faces with two equivalent Au(9)Mn4Au8 cuboctahedra, and faces with four equivalent Mn(2)Au12 cuboctahedra. In the fourth Au site, Au(1) is bonded to one Mn(2) and two equivalent Mn(1) atoms to form distorted AuMn3 cuboctahedra that share  a cornercorner with one Au(9)Mn4Au8 cuboctahedra, corners with two equivalent Au(1)Mn3 cuboctahedra, corners with two equivalent Au(5)Mn4 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra,  an edgeedge with one Au(2)Mn4 cuboctahedra, and edges with two equivalent Au(5)Mn4 cuboctahedra. In the fifth Au site, Au(2) is bonded to two equivalent Mn(1) and two equivalent Mn(2) atoms to form distorted AuMn4 cuboctahedra that share corners with four equivalent Au(1)Mn3 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra, corners with four equivalent Au(5)Mn4 cuboctahedra,  an edgeedge with one Au(1)Mn3 cuboctahedra,  an edgeedge with one Au(9)Mn4Au8 cuboctahedra, and edges with two equivalent Au(5)Mn4 cuboctahedra. In the sixth Au site, Au(3) is bonded in a 3-coordinate geometry to one Mn(1) and two equivalent Mn(3) atoms. In the seventh Au site, Au(4) is bonded in a 3-coordinate geometry to one Mn(1) and two equivalent Mn(2) atoms. In the eighth Au site, Au(5) is bonded to two equivalent Mn(1) and two equivalent Mn(2) atoms to form distorted AuMn4 cuboctahedra that share corners with two equivalent Au(1)Mn3 cuboctahedra, corners with two equivalent Au(5)Mn4 cuboctahedra, corners with two equivalent Au(9)Mn4Au8 cuboctahedra, corners with four equivalent Au(2)Mn4 cuboctahedra,  an edgeedge with one Au(5)Mn4 cuboctahedra, edges with two equivalent Au(1)Mn3 cuboctahedra, and edges with two equivalent Au(2)Mn4 cuboctahedra. In the ninth Au site, Au(6) is bonded in a distorted rectangular see-saw-like geometry to four equivalent Mn(2) and two equivalent Au(9) atoms. is represented by the CIF file [CIF]
data_Mn9Au31
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.936
_cell_length_b   12.936
_cell_length_c   4.023
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   673.194
_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
  Mn  Mn0  1  0.650  0.950  0.500  1.0
  Mn  Mn1  1  0.950  0.350  0.500  1.0
  Mn  Mn2  1  0.050  0.650  0.500  1.0
  Mn  Mn3  1  0.350  0.050  0.500  1.0
  Mn  Mn4  1  0.702  0.602  0.000  1.0
  Mn  Mn5  1  0.602  0.298  0.000  1.0
  Mn  Mn6  1  0.398  0.702  0.000  1.0
  Mn  Mn7  1  0.298  0.398  0.000  1.0
  Mn  Mn8  1  0.000  0.000  0.000  1.0
  Au  Au9  1  0.697  0.099  0.000  1.0
  Au  Au10  1  0.901  0.697  0.000  1.0
  Au  Au11  1  0.400  0.200  0.000  1.0
  Au  Au12  1  0.200  0.600  0.000  1.0
  Au  Au13  1  0.800  0.400  0.000  1.0
  Au  Au14  1  0.600  0.800  0.000  1.0
  Au  Au15  1  0.046  0.148  0.500  1.0
  Au  Au16  1  0.148  0.954  0.500  1.0
  Au  Au17  1  0.852  0.046  0.500  1.0
  Au  Au18  1  0.954  0.852  0.500  1.0
  Au  Au19  1  0.254  0.253  0.500  1.0
  Au  Au20  1  0.253  0.746  0.500  1.0
  Au  Au21  1  0.747  0.254  0.500  1.0
  Au  Au22  1  0.746  0.747  0.500  1.0
  Au  Au23  1  0.150  0.450  0.500  1.0
  Au  Au24  1  0.450  0.850  0.500  1.0
  Au  Au25  1  0.550  0.150  0.500  1.0
  Au  Au26  1  0.850  0.550  0.500  1.0
  Au  Au27  1  0.453  0.350  0.500  1.0
  Au  Au28  1  0.350  0.547  0.500  1.0
  Au  Au29  1  0.650  0.453  0.500  1.0
  Au  Au30  1  0.547  0.650  0.500  1.0
  Au  Au31  1  0.303  0.901  0.000  1.0
  Au  Au32  1  0.099  0.303  0.000  1.0
  Au  Au33  1  0.797  0.902  0.000  1.0
  Au  Au34  1  0.902  0.203  0.000  1.0
  Au  Au35  1  0.098  0.797  0.000  1.0
  Au  Au36  1  0.203  0.098  0.000  1.0
  Au  Au37  1  0.000  0.500  0.000  1.0
  Au  Au38  1  0.500  0.000  0.000  1.0
  Au  Au39  1  0.500  0.500  0.000  1.0
[/CIF]
.