The material described by BaMg14Sn crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.580
_cell_length_b   6.580
_cell_length_c   10.761
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   403.484
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.162  0.831  0.125  1.0
  Mg  Mg2  1  0.179  0.839  0.625  1.0
  Mg  Mg3  1  0.669  0.338  0.125  1.0
  Mg  Mg4  1  0.661  0.321  0.625  1.0
  Mg  Mg5  1  0.669  0.831  0.125  1.0
  Mg  Mg6  1  0.661  0.839  0.625  1.0
  Mg  Mg7  1  0.339  0.161  0.363  1.0
  Mg  Mg8  1  0.339  0.161  0.887  1.0
  Mg  Mg9  1  0.339  0.677  0.363  1.0
  Mg  Mg10  1  0.339  0.677  0.887  1.0
  Mg  Mg11  1  0.823  0.161  0.363  1.0
  Mg  Mg12  1  0.823  0.161  0.887  1.0
  Mg  Mg13  1  0.833  0.667  0.382  1.0
  Mg  Mg14  1  0.833  0.667  0.868  1.0
  Sn  Sn15  1  0.167  0.333  0.125  1.0
[/CIF]
.
The material described by BaMg14Sn crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Sn cuboctahedra. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Sn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Sn cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.580
_cell_length_b   6.580
_cell_length_c   10.761
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   403.484
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.162  0.831  0.125  1.0
  Mg  Mg2  1  0.179  0.839  0.625  1.0
  Mg  Mg3  1  0.669  0.338  0.125  1.0
  Mg  Mg4  1  0.661  0.321  0.625  1.0
  Mg  Mg5  1  0.669  0.831  0.125  1.0
  Mg  Mg6  1  0.661  0.839  0.625  1.0
  Mg  Mg7  1  0.339  0.161  0.363  1.0
  Mg  Mg8  1  0.339  0.161  0.887  1.0
  Mg  Mg9  1  0.339  0.677  0.363  1.0
  Mg  Mg10  1  0.339  0.677  0.887  1.0
  Mg  Mg11  1  0.823  0.161  0.363  1.0
  Mg  Mg12  1  0.823  0.161  0.887  1.0
  Mg  Mg13  1  0.833  0.667  0.382  1.0
  Mg  Mg14  1  0.833  0.667  0.868  1.0
  Sn  Sn15  1  0.167  0.333  0.125  1.0
[/CIF]
.