The structure described by Mg14LaSi 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 six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Si2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, and faces with four equivalent Mg(4)Mg12 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 La(1)Mg10Si2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)LaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 11-coordinate geometry to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and one Si(1) atom. 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 La(1)Mg10Si2 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)LaMg10Si cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(6)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)LaMg10Si 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 Si(1) atom to form distorted MgLaMg10Si cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(6)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)Mg10Si2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Si2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Si cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Si cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Si(1) atom. La(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Si(1) atoms to form LaMg10Si2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Si2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Si cuboctahedra. Si(1) is bonded in a 10-coordinate geometry to two equivalent Mg(3), two equivalent Mg(7), four equivalent Mg(5), and two equivalent La(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Si
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.534
_cell_length_b   6.331
_cell_length_c   10.331
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.976
_symmetry_Int_Tables_number   1
_cell_volume   373.834
_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  0.154  0.327  0.125  1.0
  Mg  Mg1  1  0.166  0.333  0.625  1.0
  Mg  Mg2  1  0.160  0.830  0.625  1.0
  Mg  Mg3  1  0.650  0.316  0.125  1.0
  Mg  Mg4  1  0.666  0.337  0.625  1.0
  Mg  Mg5  1  0.650  0.834  0.125  1.0
  Mg  Mg6  1  0.666  0.828  0.625  1.0
  Mg  Mg7  1  0.337  0.162  0.381  1.0
  Mg  Mg8  1  0.337  0.162  0.869  1.0
  Mg  Mg9  1  0.337  0.675  0.381  1.0
  Mg  Mg10  1  0.337  0.675  0.869  1.0
  Mg  Mg11  1  0.829  0.164  0.387  1.0
  Mg  Mg12  1  0.829  0.164  0.863  1.0
  Mg  Mg13  1  0.846  0.673  0.360  1.0
  Mg  Mg14  1  0.846  0.673  0.890  1.0
  Si  Si15  1  0.191  0.846  0.125  1.0
[/CIF]
.
The structure described by Mg14LaSi 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 six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Si2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, and faces with four equivalent Mg(4)Mg12 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 La(1)Mg10Si2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)LaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 11-coordinate geometry to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and one Si(1) atom. 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 La(1)Mg10Si2 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)LaMg10Si cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(6)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)LaMg10Si 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 Si(1) atom to form distorted MgLaMg10Si cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(6)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)Mg10Si2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with four equivalent Mg(5)LaMg10Si cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Si cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Si2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Si cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Si2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Si cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Si(1) atom. La(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Si(1) atoms to form LaMg10Si2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Si2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Si cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Si cuboctahedra. Si(1) is bonded in a 10-coordinate geometry to two equivalent Mg(3), two equivalent Mg(7), four equivalent Mg(5), and two equivalent La(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Si
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.534
_cell_length_b   6.331
_cell_length_c   10.331
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.976
_symmetry_Int_Tables_number   1
_cell_volume   373.834
_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  0.154  0.327  0.125  1.0
  Mg  Mg1  1  0.166  0.333  0.625  1.0
  Mg  Mg2  1  0.160  0.830  0.625  1.0
  Mg  Mg3  1  0.650  0.316  0.125  1.0
  Mg  Mg4  1  0.666  0.337  0.625  1.0
  Mg  Mg5  1  0.650  0.834  0.125  1.0
  Mg  Mg6  1  0.666  0.828  0.625  1.0
  Mg  Mg7  1  0.337  0.162  0.381  1.0
  Mg  Mg8  1  0.337  0.162  0.869  1.0
  Mg  Mg9  1  0.337  0.675  0.381  1.0
  Mg  Mg10  1  0.337  0.675  0.869  1.0
  Mg  Mg11  1  0.829  0.164  0.387  1.0
  Mg  Mg12  1  0.829  0.164  0.863  1.0
  Mg  Mg13  1  0.846  0.673  0.360  1.0
  Mg  Mg14  1  0.846  0.673  0.890  1.0
  Si  Si15  1  0.191  0.846  0.125  1.0
[/CIF]
.