The crystal structure described by BaMg14Sn crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form BaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. There are nine inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Sn(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Sn(1) atoms. In the sixth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten Mg(5,5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four equivalent Mg(5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the eighth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom. In the ninth Mg site, Mg(7) is bonded to one Ba(1); one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(5,5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5) atoms to form SnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. is represented by the CIF card [CIF]
data_BaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.641
_cell_length_b   6.634
_cell_length_c   10.529
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.962
_symmetry_Int_Tables_number   1
_cell_volume   401.872
_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  0.165  0.833  0.125  1.0
  Mg  Mg1  1  0.163  0.332  0.625  1.0
  Mg  Mg2  1  0.166  0.833  0.625  1.0
  Mg  Mg3  1  0.662  0.338  0.125  1.0
  Mg  Mg4  1  0.668  0.332  0.625  1.0
  Mg  Mg5  1  0.662  0.824  0.125  1.0
  Mg  Mg6  1  0.668  0.836  0.625  1.0
  Mg  Mg7  1  0.338  0.177  0.388  1.0
  Mg  Mg8  1  0.338  0.177  0.862  1.0
  Mg  Mg9  1  0.338  0.660  0.388  1.0
  Mg  Mg10  1  0.338  0.660  0.862  1.0
  Mg  Mg11  1  0.833  0.167  0.370  1.0
  Mg  Mg12  1  0.833  0.167  0.880  1.0
  Mg  Mg13  1  0.822  0.661  0.389  1.0
  Mg  Mg14  1  0.822  0.661  0.861  1.0
  Sn  Sn15  1  0.184  0.342  0.125  1.0
[/CIF]
.
The crystal structure described by BaMg14Sn crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3); four Mg(5,5); and two equivalent Sn(1) atoms to form BaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. There are nine inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2); two equivalent Mg(6); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with six equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Sn(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; faces with four equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1); two equivalent Mg(7); four equivalent Mg(4); and four Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Sn(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Sn2 cuboctahedra; corners with four equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with eight Mg(5,5)BaMg10Sn cuboctahedra. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(3); two Mg(5,5); two equivalent Mg(6); two equivalent Mg(7); and two equivalent Sn(1) atoms. In the sixth Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(5) is bonded to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Sn(1) atom to form distorted MgBaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra; corners with ten Mg(5,5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Mg(7)BaMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Sn(1)Ba2Mg10 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra;  a faceface with one Sn(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with four equivalent Mg(5)BaMg10Sn cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the eighth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one Sn(1) atom. In the ninth Mg site, Mg(7) is bonded to one Ba(1); one Mg(2); two Mg(3,3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra; corners with eight equivalent Mg(5)BaMg10Sn cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with two equivalent Mg(2)Mg12 cuboctahedra; edges with four Mg(5,5)BaMg10Sn cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Ba(1)Mg10Sn2 cuboctahedra;  a faceface with one Mg(2)Mg12 cuboctahedra; faces with two equivalent Mg(7)BaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Ba2Mg10 cuboctahedra; and faces with four Mg(5,5)BaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3); and four Mg(5,5) atoms to form SnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent Sn(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)Mg10Sn2 cuboctahedra; edges with eight Mg(5,5)BaMg10Sn cuboctahedra; faces with two equivalent Ba(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaMg10Sn cuboctahedra; and faces with six equivalent Mg(7)BaMg11 cuboctahedra. is represented by the CIF card [CIF]
data_BaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.641
_cell_length_b   6.634
_cell_length_c   10.529
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.962
_symmetry_Int_Tables_number   1
_cell_volume   401.872
_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  0.165  0.833  0.125  1.0
  Mg  Mg1  1  0.163  0.332  0.625  1.0
  Mg  Mg2  1  0.166  0.833  0.625  1.0
  Mg  Mg3  1  0.662  0.338  0.125  1.0
  Mg  Mg4  1  0.668  0.332  0.625  1.0
  Mg  Mg5  1  0.662  0.824  0.125  1.0
  Mg  Mg6  1  0.668  0.836  0.625  1.0
  Mg  Mg7  1  0.338  0.177  0.388  1.0
  Mg  Mg8  1  0.338  0.177  0.862  1.0
  Mg  Mg9  1  0.338  0.660  0.388  1.0
  Mg  Mg10  1  0.338  0.660  0.862  1.0
  Mg  Mg11  1  0.833  0.167  0.370  1.0
  Mg  Mg12  1  0.833  0.167  0.880  1.0
  Mg  Mg13  1  0.822  0.661  0.389  1.0
  Mg  Mg14  1  0.822  0.661  0.861  1.0
  Sn  Sn15  1  0.184  0.342  0.125  1.0
[/CIF]
.