The structure described by Mg14LaSn crystallizes in the orthorhombic Amm2 space group. There are seven 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)LaMg11 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)La2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and two equivalent Sn(1) atoms to form distorted MgLa2Mg8Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(5)LaMg10Sn cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, and faces with eight equivalent Mg(5)LaMg10Sn cuboctahedra. 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 Mg(3)La2Mg8Sn2 cuboctahedra, corners with four equivalent La(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)La2Mg10 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)LaMg10Sn cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 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 equivalent Mg(5)LaMg10Sn cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one La(1), and one Sn(1) atom to form distorted MgLaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(7)LaMg11 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 La(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Sn2 cuboctahedra,  a faceface with one Sn(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Sn(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one La(1) atom to form MgLaMg11 cuboctahedra that share corners with six equivalent Mg(7)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Sn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Sn2 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Sn(1)La2Mg10 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Sn cuboctahedra. La(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form LaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent La(1) atoms to form SnLa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Sn(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with six equivalent Mg(7)LaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_LaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.591
_cell_length_b   6.502
_cell_length_c   10.412
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.556
_symmetry_Int_Tables_number   1
_cell_volume   388.172
_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
  La  La0  1  0.164  0.832  0.125  1.0
  Mg  Mg1  1  0.164  0.332  0.625  1.0
  Mg  Mg2  1  0.165  0.833  0.625  1.0
  Mg  Mg3  1  0.663  0.338  0.125  1.0
  Mg  Mg4  1  0.667  0.332  0.625  1.0
  Mg  Mg5  1  0.663  0.825  0.125  1.0
  Mg  Mg6  1  0.667  0.835  0.625  1.0
  Mg  Mg7  1  0.338  0.173  0.385  1.0
  Mg  Mg8  1  0.338  0.173  0.865  1.0
  Mg  Mg9  1  0.338  0.665  0.385  1.0
  Mg  Mg10  1  0.338  0.665  0.865  1.0
  Mg  Mg11  1  0.833  0.166  0.371  1.0
  Mg  Mg12  1  0.833  0.166  0.879  1.0
  Mg  Mg13  1  0.827  0.664  0.385  1.0
  Mg  Mg14  1  0.827  0.664  0.865  1.0
  Sn  Sn15  1  0.176  0.338  0.125  1.0
[/CIF]
.
The structure described by Mg14LaSn crystallizes in the orthorhombic Amm2 space group. There are seven 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)LaMg11 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Sn(1)La2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and two equivalent Sn(1) atoms to form distorted MgLa2Mg8Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(5)LaMg10Sn cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, and faces with eight equivalent Mg(5)LaMg10Sn cuboctahedra. 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 Mg(3)La2Mg8Sn2 cuboctahedra, corners with four equivalent La(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)La2Mg10 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)LaMg10Sn cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 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 equivalent Mg(5)LaMg10Sn cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one La(1), and one Sn(1) atom to form distorted MgLaMg10Sn cuboctahedra that share corners with four equivalent Mg(7)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(7)LaMg11 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 La(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Sn2 cuboctahedra,  a faceface with one Sn(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Sn(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one La(1) atom to form MgLaMg11 cuboctahedra that share corners with six equivalent Mg(7)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Sn cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Sn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Sn2 cuboctahedra, faces with two equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, faces with three equivalent Sn(1)La2Mg10 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Sn cuboctahedra. La(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Sn(1) atoms to form LaMg10Sn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Sn(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(7)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(7)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Sn(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Sn cuboctahedra. Sn(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent La(1) atoms to form SnLa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Sn(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Sn cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(3)La2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Sn cuboctahedra, and faces with six equivalent Mg(7)LaMg11 cuboctahedra. is represented by the CIF file [CIF]
data_LaMg14Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.591
_cell_length_b   6.502
_cell_length_c   10.412
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.556
_symmetry_Int_Tables_number   1
_cell_volume   388.172
_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
  La  La0  1  0.164  0.832  0.125  1.0
  Mg  Mg1  1  0.164  0.332  0.625  1.0
  Mg  Mg2  1  0.165  0.833  0.625  1.0
  Mg  Mg3  1  0.663  0.338  0.125  1.0
  Mg  Mg4  1  0.667  0.332  0.625  1.0
  Mg  Mg5  1  0.663  0.825  0.125  1.0
  Mg  Mg6  1  0.667  0.835  0.625  1.0
  Mg  Mg7  1  0.338  0.173  0.385  1.0
  Mg  Mg8  1  0.338  0.173  0.865  1.0
  Mg  Mg9  1  0.338  0.665  0.385  1.0
  Mg  Mg10  1  0.338  0.665  0.865  1.0
  Mg  Mg11  1  0.833  0.166  0.371  1.0
  Mg  Mg12  1  0.833  0.166  0.879  1.0
  Mg  Mg13  1  0.827  0.664  0.385  1.0
  Mg  Mg14  1  0.827  0.664  0.865  1.0
  Sn  Sn15  1  0.176  0.338  0.125  1.0
[/CIF]
.