The compound described by Ba4Nb3O12 crystallizes in the hexagonal P6_3mc space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Nb(2)O6 octahedra, and faces with three equivalent Nb(3)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Nb(1)O6 octahedra, and faces with three equivalent Nb(3)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra,  a faceface with one Nb(3)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 5°. In the second Nb site, Nb(2) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form NbO6 octahedra that share corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 4°. In the third Nb site, Nb(3) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Nb(2), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ba(2), one Ba(3), two equivalent Ba(4), and one Nb(1) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(4), two equivalent Ba(2), and one Nb(2) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Nb(1), and one Nb(3) atom. is represented by the CIF file [CIF]
data_Ba4Nb3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.922
_cell_length_b   5.922
_cell_length_c   19.459
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   590.942
_cell_formula_units_Z   2
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  0.000  0.000  0.010  1.0
  Ba  Ba1  1  0.000  0.000  0.510  1.0
  Ba  Ba2  1  0.333  0.667  0.145  1.0
  Ba  Ba3  1  0.333  0.667  0.369  1.0
  Ba  Ba4  1  0.333  0.667  0.744  1.0
  Ba  Ba5  1  0.667  0.333  0.244  1.0
  Ba  Ba6  1  0.667  0.333  0.645  1.0
  Ba  Ba7  1  0.667  0.333  0.869  1.0
  Nb  Nb8  1  0.000  0.000  0.303  1.0
  Nb  Nb9  1  0.000  0.000  0.803  1.0
  Nb  Nb10  1  0.333  0.667  0.565  1.0
  Nb  Nb11  1  0.333  0.667  0.936  1.0
  Nb  Nb12  1  0.667  0.333  0.065  1.0
  Nb  Nb13  1  0.667  0.333  0.436  1.0
  O  O14  1  0.005  0.503  0.994  1.0
  O  O15  1  0.995  0.497  0.494  1.0
  O  O16  1  0.163  0.837  0.259  1.0
  O  O17  1  0.176  0.824  0.616  1.0
  O  O18  1  0.170  0.830  0.877  1.0
  O  O19  1  0.163  0.327  0.259  1.0
  O  O20  1  0.176  0.353  0.616  1.0
  O  O21  1  0.170  0.340  0.877  1.0
  O  O22  1  0.673  0.837  0.259  1.0
  O  O23  1  0.647  0.824  0.616  1.0
  O  O24  1  0.660  0.830  0.877  1.0
  O  O25  1  0.497  0.503  0.994  1.0
  O  O26  1  0.503  0.497  0.494  1.0
  O  O27  1  0.353  0.176  0.116  1.0
  O  O28  1  0.340  0.170  0.377  1.0
  O  O29  1  0.327  0.163  0.759  1.0
  O  O30  1  0.497  0.995  0.994  1.0
  O  O31  1  0.503  0.005  0.494  1.0
  O  O32  1  0.824  0.647  0.116  1.0
  O  O33  1  0.830  0.660  0.377  1.0
  O  O34  1  0.837  0.673  0.759  1.0
  O  O35  1  0.824  0.176  0.116  1.0
  O  O36  1  0.830  0.170  0.377  1.0
  O  O37  1  0.837  0.163  0.759  1.0
[/CIF]
.
The compound described by Ba4Nb3O12 crystallizes in the hexagonal P6_3mc space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(1) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Nb(2)O6 octahedra, and faces with three equivalent Nb(3)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Nb(1)O6 octahedra, and faces with three equivalent Nb(3)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to three equivalent O(3), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra,  a faceface with one Nb(3)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 5°. In the second Nb site, Nb(2) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form NbO6 octahedra that share corners with three equivalent Nb(3)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra,  a faceface with one Ba(4)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 4°. In the third Nb site, Nb(3) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Nb(2), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ba(2), one Ba(3), two equivalent Ba(4), and one Nb(1) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), one Ba(4), two equivalent Ba(2), and one Nb(2) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Nb(1), and one Nb(3) atom. is represented by the CIF file [CIF]
data_Ba4Nb3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.922
_cell_length_b   5.922
_cell_length_c   19.459
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   590.942
_cell_formula_units_Z   2
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  0.000  0.000  0.010  1.0
  Ba  Ba1  1  0.000  0.000  0.510  1.0
  Ba  Ba2  1  0.333  0.667  0.145  1.0
  Ba  Ba3  1  0.333  0.667  0.369  1.0
  Ba  Ba4  1  0.333  0.667  0.744  1.0
  Ba  Ba5  1  0.667  0.333  0.244  1.0
  Ba  Ba6  1  0.667  0.333  0.645  1.0
  Ba  Ba7  1  0.667  0.333  0.869  1.0
  Nb  Nb8  1  0.000  0.000  0.303  1.0
  Nb  Nb9  1  0.000  0.000  0.803  1.0
  Nb  Nb10  1  0.333  0.667  0.565  1.0
  Nb  Nb11  1  0.333  0.667  0.936  1.0
  Nb  Nb12  1  0.667  0.333  0.065  1.0
  Nb  Nb13  1  0.667  0.333  0.436  1.0
  O  O14  1  0.005  0.503  0.994  1.0
  O  O15  1  0.995  0.497  0.494  1.0
  O  O16  1  0.163  0.837  0.259  1.0
  O  O17  1  0.176  0.824  0.616  1.0
  O  O18  1  0.170  0.830  0.877  1.0
  O  O19  1  0.163  0.327  0.259  1.0
  O  O20  1  0.176  0.353  0.616  1.0
  O  O21  1  0.170  0.340  0.877  1.0
  O  O22  1  0.673  0.837  0.259  1.0
  O  O23  1  0.647  0.824  0.616  1.0
  O  O24  1  0.660  0.830  0.877  1.0
  O  O25  1  0.497  0.503  0.994  1.0
  O  O26  1  0.503  0.497  0.494  1.0
  O  O27  1  0.353  0.176  0.116  1.0
  O  O28  1  0.340  0.170  0.377  1.0
  O  O29  1  0.327  0.163  0.759  1.0
  O  O30  1  0.497  0.995  0.994  1.0
  O  O31  1  0.503  0.005  0.494  1.0
  O  O32  1  0.824  0.647  0.116  1.0
  O  O33  1  0.830  0.660  0.377  1.0
  O  O34  1  0.837  0.673  0.759  1.0
  O  O35  1  0.824  0.176  0.116  1.0
  O  O36  1  0.830  0.170  0.377  1.0
  O  O37  1  0.837  0.163  0.759  1.0
[/CIF]
.