The structure described by La5Ti4O15 crystallizes in the trigonal P-3c1 space group. There are three inequivalent La sites. In the first La site, La(1) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. In the second La site, La(2) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form distorted LaO12 cuboctahedra that share corners with nine equivalent La(2)O12 cuboctahedra, faces with three equivalent La(3)O12 cuboctahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Ti(2)O6 octahedra. In the third La site, La(3) is bonded to six equivalent O(2) and six equivalent O(3) atoms to form LaO12 cuboctahedra that share corners with six equivalent La(3)O12 cuboctahedra, faces with six equivalent La(2)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Ti(2)O6 octahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Ti(2)O6 octahedra,  a faceface with one La(3)O12 cuboctahedra, and faces with three equivalent La(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 14°. In the second Ti site, Ti(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form TiO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, faces with three equivalent La(3)O12 cuboctahedra, and faces with four equivalent La(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-14°. There are three inequivalent O sites. In the first O site, O(3) is bonded in a distorted linear geometry to two equivalent La(2), two equivalent La(3), and two equivalent Ti(2) atoms. In the second O site, O(1) is bonded in a 4-coordinate geometry to one La(2), two equivalent La(1), and one Ti(1) atom. In the third O site, O(2) is bonded in a 2-coordinate geometry to one La(3), two equivalent La(2), one Ti(1), and one Ti(2) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_La5Ti4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.558
_cell_length_b   5.558
_cell_length_c   22.461
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   600.959
_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
  La  La0  1  0.333  0.667  0.715  1.0
  La  La1  1  0.667  0.333  0.785  1.0
  La  La2  1  0.667  0.333  0.285  1.0
  La  La3  1  0.333  0.667  0.215  1.0
  La  La4  1  0.333  0.667  0.891  1.0
  La  La5  1  0.667  0.333  0.609  1.0
  La  La6  1  0.667  0.333  0.109  1.0
  La  La7  1  0.333  0.667  0.391  1.0
  La  La8  1  0.000  0.000  0.500  1.0
  La  La9  1  0.000  0.000  0.000  1.0
  Ti  Ti10  1  0.000  0.000  0.657  1.0
  Ti  Ti11  1  0.000  0.000  0.843  1.0
  Ti  Ti12  1  0.000  0.000  0.343  1.0
  Ti  Ti13  1  0.000  0.000  0.157  1.0
  Ti  Ti14  1  0.333  0.667  0.551  1.0
  Ti  Ti15  1  0.667  0.333  0.949  1.0
  Ti  Ti16  1  0.667  0.333  0.449  1.0
  Ti  Ti17  1  0.333  0.667  0.051  1.0
  O  O18  1  0.117  0.772  0.804  1.0
  O  O19  1  0.228  0.345  0.804  1.0
  O  O20  1  0.655  0.883  0.804  1.0
  O  O21  1  0.345  0.228  0.696  1.0
  O  O22  1  0.883  0.655  0.696  1.0
  O  O23  1  0.772  0.117  0.696  1.0
  O  O24  1  0.883  0.228  0.196  1.0
  O  O25  1  0.772  0.655  0.196  1.0
  O  O26  1  0.345  0.117  0.196  1.0
  O  O27  1  0.655  0.772  0.304  1.0
  O  O28  1  0.117  0.345  0.304  1.0
  O  O29  1  0.228  0.883  0.304  1.0
  O  O30  1  0.204  0.877  0.599  1.0
  O  O31  1  0.123  0.327  0.599  1.0
  O  O32  1  0.673  0.796  0.599  1.0
  O  O33  1  0.327  0.123  0.901  1.0
  O  O34  1  0.796  0.673  0.901  1.0
  O  O35  1  0.877  0.204  0.901  1.0
  O  O36  1  0.500  0.000  0.000  1.0
  O  O37  1  0.000  0.500  0.000  1.0
  O  O38  1  0.500  0.500  0.000  1.0
  O  O39  1  0.500  0.000  0.500  1.0
  O  O40  1  0.500  0.500  0.500  1.0
  O  O41  1  0.000  0.500  0.500  1.0
  O  O42  1  0.123  0.796  0.099  1.0
  O  O43  1  0.204  0.327  0.099  1.0
  O  O44  1  0.673  0.877  0.099  1.0
  O  O45  1  0.327  0.204  0.401  1.0
  O  O46  1  0.877  0.673  0.401  1.0
  O  O47  1  0.796  0.123  0.401  1.0
[/CIF]
.
The structure described by La5Ti4O15 crystallizes in the trigonal P-3c1 space group. There are three inequivalent La sites. In the first La site, La(1) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. In the second La site, La(2) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form distorted LaO12 cuboctahedra that share corners with nine equivalent La(2)O12 cuboctahedra, faces with three equivalent La(3)O12 cuboctahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Ti(2)O6 octahedra. In the third La site, La(3) is bonded to six equivalent O(2) and six equivalent O(3) atoms to form LaO12 cuboctahedra that share corners with six equivalent La(3)O12 cuboctahedra, faces with six equivalent La(2)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Ti(2)O6 octahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Ti(2)O6 octahedra,  a faceface with one La(3)O12 cuboctahedra, and faces with three equivalent La(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 14°. In the second Ti site, Ti(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form TiO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, faces with three equivalent La(3)O12 cuboctahedra, and faces with four equivalent La(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-14°. There are three inequivalent O sites. In the first O site, O(3) is bonded in a distorted linear geometry to two equivalent La(2), two equivalent La(3), and two equivalent Ti(2) atoms. In the second O site, O(1) is bonded in a 4-coordinate geometry to one La(2), two equivalent La(1), and one Ti(1) atom. In the third O site, O(2) is bonded in a 2-coordinate geometry to one La(3), two equivalent La(2), one Ti(1), and one Ti(2) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_La5Ti4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.558
_cell_length_b   5.558
_cell_length_c   22.461
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   600.959
_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
  La  La0  1  0.333  0.667  0.715  1.0
  La  La1  1  0.667  0.333  0.785  1.0
  La  La2  1  0.667  0.333  0.285  1.0
  La  La3  1  0.333  0.667  0.215  1.0
  La  La4  1  0.333  0.667  0.891  1.0
  La  La5  1  0.667  0.333  0.609  1.0
  La  La6  1  0.667  0.333  0.109  1.0
  La  La7  1  0.333  0.667  0.391  1.0
  La  La8  1  0.000  0.000  0.500  1.0
  La  La9  1  0.000  0.000  0.000  1.0
  Ti  Ti10  1  0.000  0.000  0.657  1.0
  Ti  Ti11  1  0.000  0.000  0.843  1.0
  Ti  Ti12  1  0.000  0.000  0.343  1.0
  Ti  Ti13  1  0.000  0.000  0.157  1.0
  Ti  Ti14  1  0.333  0.667  0.551  1.0
  Ti  Ti15  1  0.667  0.333  0.949  1.0
  Ti  Ti16  1  0.667  0.333  0.449  1.0
  Ti  Ti17  1  0.333  0.667  0.051  1.0
  O  O18  1  0.117  0.772  0.804  1.0
  O  O19  1  0.228  0.345  0.804  1.0
  O  O20  1  0.655  0.883  0.804  1.0
  O  O21  1  0.345  0.228  0.696  1.0
  O  O22  1  0.883  0.655  0.696  1.0
  O  O23  1  0.772  0.117  0.696  1.0
  O  O24  1  0.883  0.228  0.196  1.0
  O  O25  1  0.772  0.655  0.196  1.0
  O  O26  1  0.345  0.117  0.196  1.0
  O  O27  1  0.655  0.772  0.304  1.0
  O  O28  1  0.117  0.345  0.304  1.0
  O  O29  1  0.228  0.883  0.304  1.0
  O  O30  1  0.204  0.877  0.599  1.0
  O  O31  1  0.123  0.327  0.599  1.0
  O  O32  1  0.673  0.796  0.599  1.0
  O  O33  1  0.327  0.123  0.901  1.0
  O  O34  1  0.796  0.673  0.901  1.0
  O  O35  1  0.877  0.204  0.901  1.0
  O  O36  1  0.500  0.000  0.000  1.0
  O  O37  1  0.000  0.500  0.000  1.0
  O  O38  1  0.500  0.500  0.000  1.0
  O  O39  1  0.500  0.000  0.500  1.0
  O  O40  1  0.500  0.500  0.500  1.0
  O  O41  1  0.000  0.500  0.500  1.0
  O  O42  1  0.123  0.796  0.099  1.0
  O  O43  1  0.204  0.327  0.099  1.0
  O  O44  1  0.673  0.877  0.099  1.0
  O  O45  1  0.327  0.204  0.401  1.0
  O  O46  1  0.877  0.673  0.401  1.0
  O  O47  1  0.796  0.123  0.401  1.0
[/CIF]
.