The compound described by Mg14LaMn crystallizes in the hexagonal P-6m2 space group. There are four 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 Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent Mn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mn(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Mn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with two equivalent La(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent La(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)La2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Mn cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one La(1), and one Mn(1) atom to form distorted MgLaMg10Mn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)LaMg10Mn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg12 cuboctahedra, edges with two equivalent Mn(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)LaMg10Mn cuboctahedra, edges with four equivalent Mg(1)Mg10Mn2 cuboctahedra,  a faceface with one La(1)Mg12 cuboctahedra,  a faceface with one Mn(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)La2Mg10 cuboctahedra, faces with five equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with six equivalent Mg(3)LaMg10Mn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, edges with six equivalent Mg(2)La2Mg10 cuboctahedra, edges with six equivalent Mg(3)LaMg10Mn cuboctahedra, edges with six equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)La2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with three equivalent La(1)Mg12 cuboctahedra, faces with three equivalent Mn(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)LaMg10Mn cuboctahedra. La(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with six equivalent Mg(2)La2Mg10 cuboctahedra, edges with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mn(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)La2Mg10 cuboctahedra, faces with six equivalent Mg(3)LaMg10Mn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Mn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form MnMg12 cuboctahedra that share corners with six equivalent Mn(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)La2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent La(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)LaMg10Mn cuboctahedra, faces with six equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.545
_cell_length_b   6.545
_cell_length_c   10.277
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   381.269
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.164  0.832  0.125  1.0
  Mg  Mg2  1  0.180  0.840  0.625  1.0
  Mg  Mg3  1  0.668  0.336  0.125  1.0
  Mg  Mg4  1  0.660  0.320  0.625  1.0
  Mg  Mg5  1  0.668  0.832  0.125  1.0
  Mg  Mg6  1  0.660  0.840  0.625  1.0
  Mg  Mg7  1  0.333  0.167  0.362  1.0
  Mg  Mg8  1  0.333  0.167  0.888  1.0
  Mg  Mg9  1  0.333  0.666  0.362  1.0
  Mg  Mg10  1  0.333  0.666  0.888  1.0
  Mg  Mg11  1  0.834  0.167  0.362  1.0
  Mg  Mg12  1  0.834  0.167  0.888  1.0
  Mg  Mg13  1  0.833  0.667  0.381  1.0
  Mg  Mg14  1  0.833  0.667  0.869  1.0
  Mn  Mn15  1  0.167  0.333  0.125  1.0
[/CIF]
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The compound described by Mg14LaMn crystallizes in the hexagonal P-6m2 space group. There are four 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 Mn(1) atoms to form MgMg10Mn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent Mn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mn(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Mn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with two equivalent La(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent La(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)La2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Mn cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one La(1), and one Mn(1) atom to form distorted MgLaMg10Mn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)LaMg10Mn cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg12 cuboctahedra, edges with two equivalent Mn(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)LaMg10Mn cuboctahedra, edges with four equivalent Mg(1)Mg10Mn2 cuboctahedra,  a faceface with one La(1)Mg12 cuboctahedra,  a faceface with one Mn(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)La2Mg10 cuboctahedra, faces with five equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with six equivalent Mg(3)LaMg10Mn cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(1), three equivalent Mg(2), and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra, corners with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, edges with six equivalent Mg(2)La2Mg10 cuboctahedra, edges with six equivalent Mg(3)LaMg10Mn cuboctahedra, edges with six equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)La2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Mn2 cuboctahedra, faces with three equivalent La(1)Mg12 cuboctahedra, faces with three equivalent Mn(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)LaMg10Mn cuboctahedra. La(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with six equivalent Mg(2)La2Mg10 cuboctahedra, edges with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent Mn(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)La2Mg10 cuboctahedra, faces with six equivalent Mg(3)LaMg10Mn cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Mn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form MnMg12 cuboctahedra that share corners with six equivalent Mn(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)La2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Mn2 cuboctahedra, edges with twelve equivalent Mg(3)LaMg10Mn cuboctahedra, faces with two equivalent La(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)LaMg10Mn cuboctahedra, faces with six equivalent Mg(1)Mg10Mn2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_LaMg14Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.545
_cell_length_b   6.545
_cell_length_c   10.277
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   381.269
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.164  0.832  0.125  1.0
  Mg  Mg2  1  0.180  0.840  0.625  1.0
  Mg  Mg3  1  0.668  0.336  0.125  1.0
  Mg  Mg4  1  0.660  0.320  0.625  1.0
  Mg  Mg5  1  0.668  0.832  0.125  1.0
  Mg  Mg6  1  0.660  0.840  0.625  1.0
  Mg  Mg7  1  0.333  0.167  0.362  1.0
  Mg  Mg8  1  0.333  0.167  0.888  1.0
  Mg  Mg9  1  0.333  0.666  0.362  1.0
  Mg  Mg10  1  0.333  0.666  0.888  1.0
  Mg  Mg11  1  0.834  0.167  0.362  1.0
  Mg  Mg12  1  0.834  0.167  0.888  1.0
  Mg  Mg13  1  0.833  0.667  0.381  1.0
  Mg  Mg14  1  0.833  0.667  0.869  1.0
  Mn  Mn15  1  0.167  0.333  0.125  1.0
[/CIF]
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