The crystal structure described by BaCaMg14 crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Ca(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BaCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Ca2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, and faces with six equivalent Mg(6)CaMg11 cuboctahedra. Ca(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CaBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Ca(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, and faces with four equivalent Mg(5)BaCaMg10 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)Ca2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 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 Ca(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)CaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Ca(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBa2Ca2Mg8 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)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(5)BaCaMg10 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with eight equivalent Mg(5)BaCaMg10 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)Ca2Mg10 cuboctahedra, corners with four equivalent Ca(1)Ba2Mg10 cuboctahedra, corners with four equivalent Mg(3)Ba2Ca2Mg8 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)BaCaMg10 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 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)BaCaMg10 cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Ba(1), one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBaCaMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra, corners with ten equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Mg(6)CaMg11 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,  a faceface with one Ba(1)Ca2Mg10 cuboctahedra,  a faceface with one Ca(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Ca(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with six equivalent Mg(6)CaMg11 cuboctahedra, corners with eight equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(5)BaCaMg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ca(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)BaCaMg10 cuboctahedra. In the seventh 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 equivalent Mg(5) atoms. is represented by the CIF file [CIF]
data_BaCaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.730
_cell_length_b   6.673
_cell_length_c   10.749
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.722
_symmetry_Int_Tables_number   1
_cell_volume   419.249
_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  0.165  0.833  0.125  1.0
  Ca  Ca1  1  0.175  0.338  0.125  1.0
  Mg  Mg2  1  0.164  0.332  0.625  1.0
  Mg  Mg3  1  0.165  0.832  0.625  1.0
  Mg  Mg4  1  0.663  0.333  0.125  1.0
  Mg  Mg5  1  0.668  0.333  0.625  1.0
  Mg  Mg6  1  0.663  0.830  0.125  1.0
  Mg  Mg7  1  0.668  0.835  0.625  1.0
  Mg  Mg8  1  0.343  0.177  0.393  1.0
  Mg  Mg9  1  0.343  0.177  0.857  1.0
  Mg  Mg10  1  0.343  0.666  0.393  1.0
  Mg  Mg11  1  0.343  0.666  0.857  1.0
  Mg  Mg12  1  0.828  0.164  0.377  1.0
  Mg  Mg13  1  0.828  0.164  0.873  1.0
  Mg  Mg14  1  0.820  0.660  0.387  1.0
  Mg  Mg15  1  0.820  0.660  0.863  1.0
[/CIF]
.
The crystal structure described by BaCaMg14 crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Ca(1), two equivalent Mg(7), four equivalent Mg(3), and four equivalent Mg(5) atoms to form BaCa2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Ca2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, and faces with six equivalent Mg(6)CaMg11 cuboctahedra. Ca(1) is bonded to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms to form CaBa2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent Ca(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, and faces with four equivalent Mg(5)BaCaMg10 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)Ca2Mg10 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 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 Ca(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)BaCaMg10 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)CaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Ca(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBa2Ca2Mg8 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)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(5)BaCaMg10 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with two equivalent Ca(1)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with eight equivalent Mg(5)BaCaMg10 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)Ca2Mg10 cuboctahedra, corners with four equivalent Ca(1)Ba2Mg10 cuboctahedra, corners with four equivalent Mg(3)Ba2Ca2Mg8 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)BaCaMg10 cuboctahedra, edges with four equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 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)BaCaMg10 cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Ba(1), one Ca(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form distorted MgBaCaMg10 cuboctahedra that share corners with four equivalent Mg(6)CaMg11 cuboctahedra, corners with ten equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Ba(1)Ca2Mg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with two equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Mg(6)CaMg11 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,  a faceface with one Ba(1)Ca2Mg10 cuboctahedra,  a faceface with one Ca(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with four equivalent Mg(5)BaCaMg10 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Ca(1), one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and four equivalent Mg(5) atoms to form distorted MgCaMg11 cuboctahedra that share corners with six equivalent Mg(6)CaMg11 cuboctahedra, corners with eight equivalent Mg(5)BaCaMg10 cuboctahedra, edges with two equivalent Ca(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, edges with four equivalent Mg(5)BaCaMg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Ca(1)Ba2Mg10 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Ca2Mg8 cuboctahedra, faces with two equivalent Mg(6)CaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Ba(1)Ca2Mg10 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)BaCaMg10 cuboctahedra. In the seventh 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 equivalent Mg(5) atoms. is represented by the CIF file [CIF]
data_BaCaMg14
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.730
_cell_length_b   6.673
_cell_length_c   10.749
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.722
_symmetry_Int_Tables_number   1
_cell_volume   419.249
_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  0.165  0.833  0.125  1.0
  Ca  Ca1  1  0.175  0.338  0.125  1.0
  Mg  Mg2  1  0.164  0.332  0.625  1.0
  Mg  Mg3  1  0.165  0.832  0.625  1.0
  Mg  Mg4  1  0.663  0.333  0.125  1.0
  Mg  Mg5  1  0.668  0.333  0.625  1.0
  Mg  Mg6  1  0.663  0.830  0.125  1.0
  Mg  Mg7  1  0.668  0.835  0.625  1.0
  Mg  Mg8  1  0.343  0.177  0.393  1.0
  Mg  Mg9  1  0.343  0.177  0.857  1.0
  Mg  Mg10  1  0.343  0.666  0.393  1.0
  Mg  Mg11  1  0.343  0.666  0.857  1.0
  Mg  Mg12  1  0.828  0.164  0.377  1.0
  Mg  Mg13  1  0.828  0.164  0.873  1.0
  Mg  Mg14  1  0.820  0.660  0.387  1.0
  Mg  Mg15  1  0.820  0.660  0.863  1.0
[/CIF]
.