The structure described by Ba5Mg18Ge13 crystallizes in the trigonal P31m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 15-coordinate geometry to three equivalent Mg(3), six equivalent Mg(2), and six equivalent Ge(2) atoms. In the second Ba site, Ba(2) is bonded in a 16-coordinate geometry to two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), two equivalent Ge(1), two equivalent Ge(4), and four equivalent Ge(3) atoms. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 1-coordinate geometry to one Ge(1) and four equivalent Ge(2) atoms. In the second Mg site, Mg(2) is bonded to one Ba(2), two equivalent Ba(1), two equivalent Ge(1), and two equivalent Ge(2) atoms to form MgBa3Ge4 tetrahedra that share corners with two equivalent Mg(4)Ba2Ge4 tetrahedra, corners with two equivalent Mg(3)Ba3Ge4 tetrahedra, corners with six equivalent Mg(2)Ba3Ge4 tetrahedra,  an edgeedge with one Mg(4)Ba2Ge4 tetrahedra, edges with two equivalent Mg(2)Ba3Ge4 tetrahedra, edges with four equivalent Mg(3)Ba3Ge4 tetrahedra, faces with two equivalent Mg(3)Ba3Ge4 tetrahedra, and faces with three equivalent Mg(2)Ba3Ge4 tetrahedra. In the third Mg site, Mg(3) is bonded to one Ba(1), two equivalent Ba(2), one Ge(1), one Ge(3), and two equivalent Ge(2) atoms to form MgBa3Ge4 tetrahedra that share corners with two equivalent Mg(4)Ba2Ge4 tetrahedra, corners with two equivalent Mg(2)Ba3Ge4 tetrahedra, corners with five equivalent Mg(3)Ba3Ge4 tetrahedra, edges with two equivalent Mg(3)Ba3Ge4 tetrahedra, edges with four equivalent Mg(2)Ba3Ge4 tetrahedra,  a faceface with one Mg(3)Ba3Ge4 tetrahedra, faces with two equivalent Mg(4)Ba2Ge4 tetrahedra, and faces with two equivalent Mg(2)Ba3Ge4 tetrahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Ba(2), two equivalent Ge(2), and two equivalent Ge(3) atoms to form MgBa2Ge4 tetrahedra that share corners with four equivalent Mg(4)Ba2Ge4 tetrahedra, corners with four equivalent Mg(2)Ba3Ge4 tetrahedra, corners with four equivalent Mg(3)Ba3Ge4 tetrahedra, edges with two equivalent Mg(2)Ba3Ge4 tetrahedra, and faces with four equivalent Mg(3)Ba3Ge4 tetrahedra. There are four inequivalent Ge sites. In the first Ge site, Ge(3) is bonded in a 9-coordinate geometry to four equivalent Ba(2), two equivalent Mg(3), two equivalent Mg(4), and one Ge(4) atom. In the second Ge site, Ge(4) is bonded in a 9-coordinate geometry to six equivalent Ba(2) and three equivalent Ge(3) atoms. In the third Ge site, Ge(1) is bonded in a 9-coordinate geometry to two equivalent Ba(2), one Mg(1), two equivalent Mg(3), and four equivalent Mg(2) atoms. In the fourth Ge site, Ge(2) is bonded in a 9-coordinate geometry to two equivalent Ba(1), one Mg(4), two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms. is represented by the CIF card [CIF]
data_Ba5Mg18Ge13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   14.669
_cell_length_b   14.669
_cell_length_c   4.511
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   840.562
_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
  Ba  Ba0  1  0.333  0.667  0.997  1.0
  Ba  Ba1  1  0.667  0.333  0.997  1.0
  Ba  Ba2  1  0.821  1.000  0.496  1.0
  Ba  Ba3  1  1.000  0.821  0.496  1.0
  Ba  Ba4  1  0.179  0.179  0.496  1.0
  Mg  Mg5  1  0.441  0.000  0.005  1.0
  Mg  Mg6  1  0.000  0.441  0.005  1.0
  Mg  Mg7  1  0.559  0.559  0.005  1.0
  Mg  Mg8  1  0.516  0.878  0.496  1.0
  Mg  Mg9  1  0.122  0.639  0.496  1.0
  Mg  Mg10  1  0.361  0.484  0.496  1.0
  Mg  Mg11  1  0.639  0.122  0.496  1.0
  Mg  Mg12  1  0.484  0.361  0.496  1.0
  Mg  Mg13  1  0.878  0.516  0.496  1.0
  Mg  Mg14  1  0.822  0.198  0.997  1.0
  Mg  Mg15  1  0.802  0.624  0.997  1.0
  Mg  Mg16  1  0.376  0.178  0.997  1.0
  Mg  Mg17  1  0.624  0.802  0.997  1.0
  Mg  Mg18  1  0.178  0.376  0.997  1.0
  Mg  Mg19  1  0.198  0.822  0.997  1.0
  Mg  Mg20  1  0.282  1.000  0.500  1.0
  Mg  Mg21  1  1.000  0.282  0.500  1.0
  Mg  Mg22  1  0.718  0.718  0.500  1.0
  Ge  Ge23  1  0.629  1.000  0.996  1.0
  Ge  Ge24  1  1.000  0.629  0.996  1.0
  Ge  Ge25  1  0.371  0.371  0.996  1.0
  Ge  Ge26  1  0.523  0.691  0.497  1.0
  Ge  Ge27  1  0.309  0.832  0.497  1.0
  Ge  Ge28  1  0.168  0.477  0.497  1.0
  Ge  Ge29  1  0.832  0.309  0.497  1.0
  Ge  Ge30  1  0.477  0.168  0.497  1.0
  Ge  Ge31  1  0.691  0.523  0.497  1.0
  Ge  Ge32  1  0.174  0.000  0.001  1.0
  Ge  Ge33  1  0.000  0.174  0.001  1.0
  Ge  Ge34  1  0.826  0.826  0.001  1.0
  Ge  Ge35  1  1.000  1.000  0.976  1.0
[/CIF]
.
The structure described by Ba5Mg18Ge13 crystallizes in the trigonal P31m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 15-coordinate geometry to three equivalent Mg(3), six equivalent Mg(2), and six equivalent Ge(2) atoms. In the second Ba site, Ba(2) is bonded in a 16-coordinate geometry to two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), two equivalent Ge(1), two equivalent Ge(4), and four equivalent Ge(3) atoms. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 1-coordinate geometry to one Ge(1) and four equivalent Ge(2) atoms. In the second Mg site, Mg(2) is bonded to one Ba(2), two equivalent Ba(1), two equivalent Ge(1), and two equivalent Ge(2) atoms to form MgBa3Ge4 tetrahedra that share corners with two equivalent Mg(4)Ba2Ge4 tetrahedra, corners with two equivalent Mg(3)Ba3Ge4 tetrahedra, corners with six equivalent Mg(2)Ba3Ge4 tetrahedra,  an edgeedge with one Mg(4)Ba2Ge4 tetrahedra, edges with two equivalent Mg(2)Ba3Ge4 tetrahedra, edges with four equivalent Mg(3)Ba3Ge4 tetrahedra, faces with two equivalent Mg(3)Ba3Ge4 tetrahedra, and faces with three equivalent Mg(2)Ba3Ge4 tetrahedra. In the third Mg site, Mg(3) is bonded to one Ba(1), two equivalent Ba(2), one Ge(1), one Ge(3), and two equivalent Ge(2) atoms to form MgBa3Ge4 tetrahedra that share corners with two equivalent Mg(4)Ba2Ge4 tetrahedra, corners with two equivalent Mg(2)Ba3Ge4 tetrahedra, corners with five equivalent Mg(3)Ba3Ge4 tetrahedra, edges with two equivalent Mg(3)Ba3Ge4 tetrahedra, edges with four equivalent Mg(2)Ba3Ge4 tetrahedra,  a faceface with one Mg(3)Ba3Ge4 tetrahedra, faces with two equivalent Mg(4)Ba2Ge4 tetrahedra, and faces with two equivalent Mg(2)Ba3Ge4 tetrahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Ba(2), two equivalent Ge(2), and two equivalent Ge(3) atoms to form MgBa2Ge4 tetrahedra that share corners with four equivalent Mg(4)Ba2Ge4 tetrahedra, corners with four equivalent Mg(2)Ba3Ge4 tetrahedra, corners with four equivalent Mg(3)Ba3Ge4 tetrahedra, edges with two equivalent Mg(2)Ba3Ge4 tetrahedra, and faces with four equivalent Mg(3)Ba3Ge4 tetrahedra. There are four inequivalent Ge sites. In the first Ge site, Ge(3) is bonded in a 9-coordinate geometry to four equivalent Ba(2), two equivalent Mg(3), two equivalent Mg(4), and one Ge(4) atom. In the second Ge site, Ge(4) is bonded in a 9-coordinate geometry to six equivalent Ba(2) and three equivalent Ge(3) atoms. In the third Ge site, Ge(1) is bonded in a 9-coordinate geometry to two equivalent Ba(2), one Mg(1), two equivalent Mg(3), and four equivalent Mg(2) atoms. In the fourth Ge site, Ge(2) is bonded in a 9-coordinate geometry to two equivalent Ba(1), one Mg(4), two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms. is represented by the CIF card [CIF]
data_Ba5Mg18Ge13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   14.669
_cell_length_b   14.669
_cell_length_c   4.511
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.001
_symmetry_Int_Tables_number   1
_cell_volume   840.562
_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
  Ba  Ba0  1  0.333  0.667  0.997  1.0
  Ba  Ba1  1  0.667  0.333  0.997  1.0
  Ba  Ba2  1  0.821  1.000  0.496  1.0
  Ba  Ba3  1  1.000  0.821  0.496  1.0
  Ba  Ba4  1  0.179  0.179  0.496  1.0
  Mg  Mg5  1  0.441  0.000  0.005  1.0
  Mg  Mg6  1  0.000  0.441  0.005  1.0
  Mg  Mg7  1  0.559  0.559  0.005  1.0
  Mg  Mg8  1  0.516  0.878  0.496  1.0
  Mg  Mg9  1  0.122  0.639  0.496  1.0
  Mg  Mg10  1  0.361  0.484  0.496  1.0
  Mg  Mg11  1  0.639  0.122  0.496  1.0
  Mg  Mg12  1  0.484  0.361  0.496  1.0
  Mg  Mg13  1  0.878  0.516  0.496  1.0
  Mg  Mg14  1  0.822  0.198  0.997  1.0
  Mg  Mg15  1  0.802  0.624  0.997  1.0
  Mg  Mg16  1  0.376  0.178  0.997  1.0
  Mg  Mg17  1  0.624  0.802  0.997  1.0
  Mg  Mg18  1  0.178  0.376  0.997  1.0
  Mg  Mg19  1  0.198  0.822  0.997  1.0
  Mg  Mg20  1  0.282  1.000  0.500  1.0
  Mg  Mg21  1  1.000  0.282  0.500  1.0
  Mg  Mg22  1  0.718  0.718  0.500  1.0
  Ge  Ge23  1  0.629  1.000  0.996  1.0
  Ge  Ge24  1  1.000  0.629  0.996  1.0
  Ge  Ge25  1  0.371  0.371  0.996  1.0
  Ge  Ge26  1  0.523  0.691  0.497  1.0
  Ge  Ge27  1  0.309  0.832  0.497  1.0
  Ge  Ge28  1  0.168  0.477  0.497  1.0
  Ge  Ge29  1  0.832  0.309  0.497  1.0
  Ge  Ge30  1  0.477  0.168  0.497  1.0
  Ge  Ge31  1  0.691  0.523  0.497  1.0
  Ge  Ge32  1  0.174  0.000  0.001  1.0
  Ge  Ge33  1  0.000  0.174  0.001  1.0
  Ge  Ge34  1  0.826  0.826  0.001  1.0
  Ge  Ge35  1  1.000  1.000  0.976  1.0
[/CIF]
.