The structure described by BaMg14La crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3,3); four Mg(5,5); and two equivalent La(1) atoms to form BaLa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Ba2Mg10 cuboctahedra; edges with eight Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent La(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaLaMg10 cuboctahedra; and faces with six equivalent Mg(6)LaMg11 cuboctahedra. There are ten 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)La2Mg10 cuboctahedra; 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 Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent La(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaLaMg10 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Ba2Mg10 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 Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Ba(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaLaMg10 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 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 La(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 Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)La2Mg10 cuboctahedra; corners with four equivalent La(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)BaLaMg10 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 Mg(5,5)BaLaMg10 cuboctahedra. In the fifth 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 La(1) atom to form distorted MgBaLaMg10 cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra; corners with ten Mg(5,5)BaLaMg10 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with two equivalent Mg(5)BaLaMg10 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)Ba2Mg10 cuboctahedra;  a faceface with one Ba(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)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with four equivalent Mg(5)BaLaMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. 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 La(1) atom to form distorted MgBaLaMg10 cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaLaMg10 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with two equivalent Mg(5)BaLaMg10 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)Ba2Mg10 cuboctahedra;  a faceface with one Ba(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)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with four Mg(5,5)BaLaMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra; corners with eight Mg(5,5)BaLaMg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent La(1)Ba2Mg10 cuboctahedra; edges with four Mg(5,5)BaLaMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with four Mg(5,5)BaLaMg10 cuboctahedra. In the eighth Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1); one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms. In the ninth 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 La(1) atoms. In the tenth 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 La(1) atoms. La(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3,3); and four Mg(5,5) atoms to form LaBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent La(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(6)LaMg11 cuboctahedra; edges with eight Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Ba(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)BaLaMg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaLaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.722
_cell_length_b   6.686
_cell_length_c   10.724
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.824
_symmetry_Int_Tables_number   1
_cell_volume   418.102
_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  0.171  0.836  0.125  1.0
  La  La1  1  0.178  0.339  0.125  1.0
  Mg  Mg2  1  0.162  0.331  0.625  1.0
  Mg  Mg3  1  0.164  0.832  0.625  1.0
  Mg  Mg4  1  0.668  0.333  0.125  1.0
  Mg  Mg5  1  0.669  0.333  0.625  1.0
  Mg  Mg6  1  0.668  0.835  0.125  1.0
  Mg  Mg7  1  0.669  0.836  0.625  1.0
  Mg  Mg8  1  0.341  0.176  0.396  1.0
  Mg  Mg9  1  0.341  0.176  0.854  1.0
  Mg  Mg10  1  0.341  0.665  0.396  1.0
  Mg  Mg11  1  0.341  0.665  0.854  1.0
  Mg  Mg12  1  0.826  0.163  0.379  1.0
  Mg  Mg13  1  0.826  0.163  0.871  1.0
  Mg  Mg14  1  0.817  0.659  0.386  1.0
  Mg  Mg15  1  0.817  0.659  0.864  1.0
[/CIF]
.
The structure described by BaMg14La crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7); four Mg(3,3,3); four Mg(5,5); and two equivalent La(1) atoms to form BaLa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Ba(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Ba2Mg10 cuboctahedra; edges with eight Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent La(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaLaMg10 cuboctahedra; and faces with six equivalent Mg(6)LaMg11 cuboctahedra. There are ten 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)La2Mg10 cuboctahedra; 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 Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(2)Mg12 cuboctahedra; faces with two equivalent La(1)Ba2Mg10 cuboctahedra; faces with four Mg(5,5)BaLaMg10 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 Mg(5,5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Ba2Mg10 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 Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Ba(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with four Mg(5,5)BaLaMg10 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 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 La(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 Mg(5,5); two equivalent Mg(6); and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)La2Mg10 cuboctahedra; corners with four equivalent La(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)BaLaMg10 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 Mg(5,5)BaLaMg10 cuboctahedra. In the fifth 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 La(1) atom to form distorted MgBaLaMg10 cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra; corners with ten Mg(5,5)BaLaMg10 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with two equivalent Mg(5)BaLaMg10 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)Ba2Mg10 cuboctahedra;  a faceface with one Ba(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)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with four equivalent Mg(5)BaLaMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. 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 La(1) atom to form distorted MgBaLaMg10 cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra; corners with ten equivalent Mg(5)BaLaMg10 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with two equivalent Mg(5)BaLaMg10 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)Ba2Mg10 cuboctahedra;  a faceface with one Ba(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)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with four Mg(5,5)BaLaMg10 cuboctahedra; and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the seventh Mg site, Mg(6) is bonded to one Mg(1); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(7); four Mg(5,5); and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra; corners with eight Mg(5,5)BaLaMg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent La(1)Ba2Mg10 cuboctahedra; edges with four Mg(5,5)BaLaMg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one La(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)La2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg12 cuboctahedra; and faces with four Mg(5,5)BaLaMg10 cuboctahedra. In the eighth Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1); one Mg(2); two equivalent Mg(3); two equivalent Mg(4); two equivalent Mg(6); and four Mg(5,5) atoms. In the ninth 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 La(1) atoms. In the tenth 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 La(1) atoms. La(1) is bonded to two equivalent Ba(1); two equivalent Mg(6); four Mg(3,3,3); and four Mg(5,5) atoms to form LaBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra; corners with six equivalent La(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ba(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(6)LaMg11 cuboctahedra; edges with eight Mg(5,5)BaLaMg10 cuboctahedra; faces with two equivalent Ba(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(6)LaMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; and faces with four Mg(5,5)BaLaMg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaLaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.722
_cell_length_b   6.686
_cell_length_c   10.724
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.824
_symmetry_Int_Tables_number   1
_cell_volume   418.102
_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  0.171  0.836  0.125  1.0
  La  La1  1  0.178  0.339  0.125  1.0
  Mg  Mg2  1  0.162  0.331  0.625  1.0
  Mg  Mg3  1  0.164  0.832  0.625  1.0
  Mg  Mg4  1  0.668  0.333  0.125  1.0
  Mg  Mg5  1  0.669  0.333  0.625  1.0
  Mg  Mg6  1  0.668  0.835  0.125  1.0
  Mg  Mg7  1  0.669  0.836  0.625  1.0
  Mg  Mg8  1  0.341  0.176  0.396  1.0
  Mg  Mg9  1  0.341  0.176  0.854  1.0
  Mg  Mg10  1  0.341  0.665  0.396  1.0
  Mg  Mg11  1  0.341  0.665  0.854  1.0
  Mg  Mg12  1  0.826  0.163  0.379  1.0
  Mg  Mg13  1  0.826  0.163  0.871  1.0
  Mg  Mg14  1  0.817  0.659  0.386  1.0
  Mg  Mg15  1  0.817  0.659  0.864  1.0
[/CIF]
.