The crystal structure described by BaMg14Mn is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Mn(1) atoms to form BaMg10Mn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mn(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, and faces with four equivalent Mg(5)BaMg10Mn cuboctahedra. 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 Ba(1)Mg10Mn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mn(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Mn2 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 equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Mn(1) atoms to form distorted MgBa2Mg8Mn2 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)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mn(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(5)BaMg10Mn cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, and faces with eight equivalent Mg(5)BaMg10Mn 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 Ba(1)Mg10Mn2 cuboctahedra, corners with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, corners with four equivalent Mn(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)BaMg10Mn cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 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 equivalent Mg(5)BaMg10Mn 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 Mn(1) atom to form distorted MgBaMg10Mn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra, corners with ten equivalent Mg(5)BaMg10Mn cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mg(5)BaMg10Mn 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 Mn(1)Ba2Mg10 cuboctahedra,  a faceface with one Ba(1)Mg10Mn2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Mn(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a 12-coordinate geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Mn(1) atom. In the seventh Mg site, Mg(7) is bonded to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra, corners with eight equivalent Mg(5)BaMg10Mn cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with four equivalent Mg(5)BaMg10Mn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ba(1)Mg10Mn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 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 Mn(1)Ba2Mg10 cuboctahedra, and faces with four equivalent Mg(5)BaMg10Mn cuboctahedra. Mn(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form distorted MnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Mn(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with six equivalent Mg(7)BaMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaMg14Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.616
_cell_length_b   6.454
_cell_length_c   10.485
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.191
_symmetry_Int_Tables_number   1
_cell_volume   390.839
_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  0.150  0.825  0.125  1.0
  Mg  Mg1  1  0.161  0.331  0.625  1.0
  Mg  Mg2  1  0.169  0.834  0.625  1.0
  Mg  Mg3  1  0.648  0.333  0.125  1.0
  Mg  Mg4  1  0.664  0.326  0.625  1.0
  Mg  Mg5  1  0.648  0.814  0.125  1.0
  Mg  Mg6  1  0.664  0.838  0.625  1.0
  Mg  Mg7  1  0.341  0.181  0.385  1.0
  Mg  Mg8  1  0.341  0.181  0.865  1.0
  Mg  Mg9  1  0.341  0.660  0.385  1.0
  Mg  Mg10  1  0.341  0.660  0.865  1.0
  Mg  Mg11  1  0.848  0.174  0.359  1.0
  Mg  Mg12  1  0.848  0.174  0.891  1.0
  Mg  Mg13  1  0.825  0.662  0.394  1.0
  Mg  Mg14  1  0.825  0.662  0.856  1.0
  Mn  Mn15  1  0.189  0.344  0.125  1.0
[/CIF]
.
The crystal structure described by BaMg14Mn is beta-derived structured and crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Mn(1) atoms to form BaMg10Mn2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Mn2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mn(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, and faces with four equivalent Mg(5)BaMg10Mn cuboctahedra. 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 Ba(1)Mg10Mn2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn 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 equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mn(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Mn2 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 equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Mn(1) atoms to form distorted MgBa2Mg8Mn2 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)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mn(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(5)BaMg10Mn cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mn(1)Ba2Mg10 cuboctahedra, and faces with eight equivalent Mg(5)BaMg10Mn 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 Ba(1)Mg10Mn2 cuboctahedra, corners with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, corners with four equivalent Mn(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)BaMg10Mn cuboctahedra, edges with four equivalent Mg(7)BaMg11 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 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 equivalent Mg(5)BaMg10Mn 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 Mn(1) atom to form distorted MgBaMg10Mn cuboctahedra that share corners with four equivalent Mg(7)BaMg11 cuboctahedra, corners with ten equivalent Mg(5)BaMg10Mn cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with two equivalent Mg(5)BaMg10Mn 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 Mn(1)Ba2Mg10 cuboctahedra,  a faceface with one Ba(1)Mg10Mn2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one Mn(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(7)BaMg11 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded in a 12-coordinate geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Mn(1) atom. In the seventh Mg site, Mg(7) is bonded to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms to form distorted MgBaMg11 cuboctahedra that share corners with six equivalent Mg(7)BaMg11 cuboctahedra, corners with eight equivalent Mg(5)BaMg10Mn cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with four equivalent Mg(5)BaMg10Mn cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ba(1)Mg10Mn2 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Mn2 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 Mn(1)Ba2Mg10 cuboctahedra, and faces with four equivalent Mg(5)BaMg10Mn cuboctahedra. Mn(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form distorted MnBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Mn(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Mg10Mn2 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, edges with eight equivalent Mg(5)BaMg10Mn cuboctahedra, faces with two equivalent Ba(1)Mg10Mn2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Mg8Mn2 cuboctahedra, faces with four equivalent Mg(5)BaMg10Mn cuboctahedra, and faces with six equivalent Mg(7)BaMg11 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaMg14Mn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.616
_cell_length_b   6.454
_cell_length_c   10.485
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.191
_symmetry_Int_Tables_number   1
_cell_volume   390.839
_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  0.150  0.825  0.125  1.0
  Mg  Mg1  1  0.161  0.331  0.625  1.0
  Mg  Mg2  1  0.169  0.834  0.625  1.0
  Mg  Mg3  1  0.648  0.333  0.125  1.0
  Mg  Mg4  1  0.664  0.326  0.625  1.0
  Mg  Mg5  1  0.648  0.814  0.125  1.0
  Mg  Mg6  1  0.664  0.838  0.625  1.0
  Mg  Mg7  1  0.341  0.181  0.385  1.0
  Mg  Mg8  1  0.341  0.181  0.865  1.0
  Mg  Mg9  1  0.341  0.660  0.385  1.0
  Mg  Mg10  1  0.341  0.660  0.865  1.0
  Mg  Mg11  1  0.848  0.174  0.359  1.0
  Mg  Mg12  1  0.848  0.174  0.891  1.0
  Mg  Mg13  1  0.825  0.662  0.394  1.0
  Mg  Mg14  1  0.825  0.662  0.856  1.0
  Mn  Mn15  1  0.189  0.344  0.125  1.0
[/CIF]
.