The structure described by BaAl5O9 crystallizes in the hexagonal P6_3/mmc space group. Ba(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form AlO6 octahedra that share corners with four equivalent Al(2)O4 tetrahedra and edges with four equivalent Al(1)O6 octahedra. In the second Al site, Al(2) is bonded to one O(1) and three equivalent O(2) atoms to form AlO4 tetrahedra that share corners with six equivalent Al(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 57°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to three equivalent Ba(1) and two equivalent Al(2) atoms. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Ba(1), one Al(2), and two equivalent Al(1) atoms. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Al(1) atoms. is represented by the CIF file [CIF]
data_BaAl5O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.707
_cell_length_b   5.707
_cell_length_c   13.496
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   380.691
_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  0.333  0.667  0.250  1.0
  Ba  Ba1  1  0.667  0.333  0.750  1.0
  Al  Al2  1  0.500  0.500  0.500  1.0
  Al  Al3  1  0.500  0.000  0.500  1.0
  Al  Al4  1  0.000  0.500  0.500  1.0
  Al  Al5  1  0.500  0.500  0.000  1.0
  Al  Al6  1  0.500  0.000  0.000  1.0
  Al  Al7  1  0.000  0.500  0.000  1.0
  Al  Al8  1  0.000  0.000  0.121  1.0
  Al  Al9  1  0.000  0.000  0.879  1.0
  Al  Al10  1  0.000  0.000  0.621  1.0
  Al  Al11  1  0.000  0.000  0.379  1.0
  O  O12  1  0.000  0.000  0.250  1.0
  O  O13  1  0.000  0.000  0.750  1.0
  O  O14  1  0.172  0.828  0.080  1.0
  O  O15  1  0.172  0.343  0.080  1.0
  O  O16  1  0.657  0.828  0.080  1.0
  O  O17  1  0.828  0.172  0.920  1.0
  O  O18  1  0.828  0.657  0.920  1.0
  O  O19  1  0.343  0.172  0.920  1.0
  O  O20  1  0.828  0.172  0.580  1.0
  O  O21  1  0.828  0.657  0.580  1.0
  O  O22  1  0.343  0.172  0.580  1.0
  O  O23  1  0.172  0.828  0.420  1.0
  O  O24  1  0.172  0.343  0.420  1.0
  O  O25  1  0.657  0.828  0.420  1.0
  O  O26  1  0.333  0.667  0.934  1.0
  O  O27  1  0.667  0.333  0.066  1.0
  O  O28  1  0.667  0.333  0.434  1.0
  O  O29  1  0.333  0.667  0.566  1.0
[/CIF]
.
The structure described by BaAl5O9 crystallizes in the hexagonal P6_3/mmc space group. Ba(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form AlO6 octahedra that share corners with four equivalent Al(2)O4 tetrahedra and edges with four equivalent Al(1)O6 octahedra. In the second Al site, Al(2) is bonded to one O(1) and three equivalent O(2) atoms to form AlO4 tetrahedra that share corners with six equivalent Al(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 57°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a linear geometry to three equivalent Ba(1) and two equivalent Al(2) atoms. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Ba(1), one Al(2), and two equivalent Al(1) atoms. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Al(1) atoms. is represented by the CIF file [CIF]
data_BaAl5O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.707
_cell_length_b   5.707
_cell_length_c   13.496
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   380.691
_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  0.333  0.667  0.250  1.0
  Ba  Ba1  1  0.667  0.333  0.750  1.0
  Al  Al2  1  0.500  0.500  0.500  1.0
  Al  Al3  1  0.500  0.000  0.500  1.0
  Al  Al4  1  0.000  0.500  0.500  1.0
  Al  Al5  1  0.500  0.500  0.000  1.0
  Al  Al6  1  0.500  0.000  0.000  1.0
  Al  Al7  1  0.000  0.500  0.000  1.0
  Al  Al8  1  0.000  0.000  0.121  1.0
  Al  Al9  1  0.000  0.000  0.879  1.0
  Al  Al10  1  0.000  0.000  0.621  1.0
  Al  Al11  1  0.000  0.000  0.379  1.0
  O  O12  1  0.000  0.000  0.250  1.0
  O  O13  1  0.000  0.000  0.750  1.0
  O  O14  1  0.172  0.828  0.080  1.0
  O  O15  1  0.172  0.343  0.080  1.0
  O  O16  1  0.657  0.828  0.080  1.0
  O  O17  1  0.828  0.172  0.920  1.0
  O  O18  1  0.828  0.657  0.920  1.0
  O  O19  1  0.343  0.172  0.920  1.0
  O  O20  1  0.828  0.172  0.580  1.0
  O  O21  1  0.828  0.657  0.580  1.0
  O  O22  1  0.343  0.172  0.580  1.0
  O  O23  1  0.172  0.828  0.420  1.0
  O  O24  1  0.172  0.343  0.420  1.0
  O  O25  1  0.657  0.828  0.420  1.0
  O  O26  1  0.333  0.667  0.934  1.0
  O  O27  1  0.667  0.333  0.066  1.0
  O  O28  1  0.667  0.333  0.434  1.0
  O  O29  1  0.333  0.667  0.566  1.0
[/CIF]
.