The crystal structure described by BaV13O18 crystallizes in the triclinic P1 space group. Ba(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), one O(15), one O(16), one O(17), one O(18), one O(7), one O(8), and one O(9) atom to form BaO12 cuboctahedra that share  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with three equivalent V(1)O6 octahedra, corners with three equivalent V(2)O6 octahedra, corners with three equivalent V(3)O6 octahedra, corners with three equivalent V(4)O6 octahedra, corners with three equivalent V(5)O6 octahedra, corners with three equivalent V(6)O6 octahedra,  a faceface with one V(10)O6 octahedra,  a faceface with one V(11)O6 octahedra,  a faceface with one V(12)O6 octahedra,  a faceface with one V(7)O6 octahedra,  a faceface with one V(8)O6 octahedra,  a faceface with one V(9)O6 octahedra, and faces with two equivalent V(13)O6 octahedra. The corner-sharing octahedral tilt angles range from 42-52°. There are thirteen inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(16), one O(18), one O(3), one O(6), and one O(7) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-13°. In the second V site, V(2) is bonded to one O(1), one O(13), one O(15), one O(2), one O(4), and one O(8) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the third V site, V(3) is bonded to one O(14), one O(17), one O(2), one O(3), one O(5), and one O(9) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. In the fourth V site, V(4) is bonded to one O(10), one O(14), one O(15), one O(3), one O(4), and one O(6) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-13°. In the fifth V site, V(5) is bonded to one O(1), one O(11), one O(17), one O(18), one O(4), and one O(5) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-9°. In the sixth V site, V(6) is bonded to one O(12), one O(13), one O(16), one O(2), one O(5), and one O(6) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. In the seventh V site, V(7) is bonded to one O(10), one O(16), one O(4), one O(5), one O(7), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(8)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 7-14°. In the eighth V site, V(8) is bonded to one O(11), one O(15), one O(5), one O(6), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the ninth V site, V(9) is bonded to one O(12), one O(17), one O(4), one O(6), one O(8), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-17°. In the tenth V site, V(10) is bonded to one O(1), one O(10), one O(12), one O(14), one O(2), and one O(7) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-17°. In the eleventh V site, V(11) is bonded to one O(10), one O(11), one O(18), one O(2), one O(3), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the twelfth V site, V(12) is bonded to one O(1), one O(11), one O(12), one O(13), one O(3), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the thirteenth V site, V(13) is bonded to one O(13), one O(14), one O(15), one O(16), one O(17), and one O(18) atom to form VO6 octahedra that share  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-9°. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded to one V(1), one V(10), one V(12), one V(2), and one V(5) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the second O site, O(2) is bonded to one V(10), one V(11), one V(2), one V(3), and one V(6) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the third O site, O(3) is bonded to one V(1), one V(11), one V(12), one V(3), and one V(4) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the fourth O site, O(4) is bonded to one V(2), one V(4), one V(5), one V(7), and one V(9) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the fifth O site, O(5) is bonded to one V(3), one V(5), one V(6), one V(7), and one V(8) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the sixth O site, O(6) is bonded to one V(1), one V(4), one V(6), one V(8), and one V(9) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(10), one V(7), and one V(8) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(11), one V(2), one V(8), and one V(9) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(12), one V(3), one V(7), and one V(9) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(11), one V(4), and one V(7) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(11), one V(12), one V(5), and one V(8) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(12), one V(6), and one V(9) atom. In the thirteenth O site, O(13) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(12), one V(13), one V(2), and one V(6) atom. In the fourteenth O site, O(14) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(13), one V(3), and one V(4) atom. In the fifteenth O site, O(15) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(13), one V(2), one V(4), and one V(8) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(13), one V(6), and one V(7) atom. In the seventeenth O site, O(17) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(13), one V(3), one V(5), and one V(9) atom. In the eighteenth O site, O(18) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(11), one V(13), and one V(5) atom. is represented by the CIF card [CIF]
data_BaV13O18
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.906
_cell_length_b   8.011
_cell_length_c   8.121
_cell_angle_alpha   112.590
_cell_angle_beta   109.515
_cell_angle_gamma   110.927
_symmetry_Int_Tables_number   1
_cell_volume   371.442
_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  1.000  0.996  0.997  1.0
  V  V1  1  0.354  0.768  0.398  1.0
  V  V2  1  0.758  0.394  0.341  1.0
  V  V3  1  0.403  0.344  0.766  1.0
  V  V4  1  0.647  0.231  0.604  1.0
  V  V5  1  0.232  0.600  0.654  1.0
  V  V6  1  0.598  0.658  0.236  1.0
  V  V7  1  0.115  0.431  0.920  1.0
  V  V8  1  0.434  0.927  0.123  1.0
  V  V9  1  0.928  0.127  0.431  1.0
  V  V10  1  0.886  0.571  0.081  1.0
  V  V11  1  0.567  0.076  0.877  1.0
  V  V12  1  0.078  0.879  0.572  1.0
  V  V13  1  0.499  0.498  0.499  1.0
  O  O14  1  0.059  0.608  0.386  1.0
  O  O15  1  0.603  0.385  0.059  1.0
  O  O16  1  0.383  0.051  0.610  1.0
  O  O17  1  0.933  0.390  0.614  1.0
  O  O18  1  0.395  0.621  0.946  1.0
  O  O19  1  0.622  0.950  0.392  1.0
  O  O20  1  0.175  0.736  0.114  1.0
  O  O21  1  0.723  0.100  0.154  1.0
  O  O22  1  0.101  0.162  0.720  1.0
  O  O23  1  0.830  0.263  0.886  1.0
  O  O24  1  0.276  0.903  0.842  1.0
  O  O25  1  0.898  0.841  0.287  1.0
  O  O26  1  0.778  0.682  0.511  1.0
  O  O27  1  0.683  0.516  0.780  1.0
  O  O28  1  0.480  0.212  0.327  1.0
  O  O29  1  0.323  0.480  0.213  1.0
  O  O30  1  0.220  0.315  0.485  1.0
  O  O31  1  0.517  0.784  0.676  1.0
[/CIF]
.
The crystal structure described by BaV13O18 crystallizes in the triclinic P1 space group. Ba(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), one O(15), one O(16), one O(17), one O(18), one O(7), one O(8), and one O(9) atom to form BaO12 cuboctahedra that share  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra, corners with three equivalent V(1)O6 octahedra, corners with three equivalent V(2)O6 octahedra, corners with three equivalent V(3)O6 octahedra, corners with three equivalent V(4)O6 octahedra, corners with three equivalent V(5)O6 octahedra, corners with three equivalent V(6)O6 octahedra,  a faceface with one V(10)O6 octahedra,  a faceface with one V(11)O6 octahedra,  a faceface with one V(12)O6 octahedra,  a faceface with one V(7)O6 octahedra,  a faceface with one V(8)O6 octahedra,  a faceface with one V(9)O6 octahedra, and faces with two equivalent V(13)O6 octahedra. The corner-sharing octahedral tilt angles range from 42-52°. There are thirteen inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(16), one O(18), one O(3), one O(6), and one O(7) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-13°. In the second V site, V(2) is bonded to one O(1), one O(13), one O(15), one O(2), one O(4), and one O(8) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the third V site, V(3) is bonded to one O(14), one O(17), one O(2), one O(3), one O(5), and one O(9) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. In the fourth V site, V(4) is bonded to one O(10), one O(14), one O(15), one O(3), one O(4), and one O(6) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-13°. In the fifth V site, V(5) is bonded to one O(1), one O(11), one O(17), one O(18), one O(4), and one O(5) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-9°. In the sixth V site, V(6) is bonded to one O(12), one O(13), one O(16), one O(2), one O(5), and one O(6) atom to form VO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(13)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  an edgeedge with one V(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. In the seventh V site, V(7) is bonded to one O(10), one O(16), one O(4), one O(5), one O(7), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(2)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(8)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 7-14°. In the eighth V site, V(8) is bonded to one O(11), one O(15), one O(5), one O(6), one O(7), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. In the ninth V site, V(9) is bonded to one O(12), one O(17), one O(4), one O(6), one O(8), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(1)O6 octahedra,  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(13)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-17°. In the tenth V site, V(10) is bonded to one O(1), one O(10), one O(12), one O(14), one O(2), and one O(7) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(5)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(7)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-17°. In the eleventh V site, V(11) is bonded to one O(10), one O(11), one O(18), one O(2), one O(3), and one O(8) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(6)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(12)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(8)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-10°. In the twelfth V site, V(12) is bonded to one O(1), one O(11), one O(12), one O(13), one O(3), and one O(9) atom to form VO6 octahedra that share  a cornercorner with one Ba(1)O12 cuboctahedra,  a cornercorner with one V(13)O6 octahedra,  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(10)O6 octahedra,  an edgeedge with one V(11)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra,  an edgeedge with one V(9)O6 octahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the thirteenth V site, V(13) is bonded to one O(13), one O(14), one O(15), one O(16), one O(17), and one O(18) atom to form VO6 octahedra that share  a cornercorner with one V(10)O6 octahedra,  a cornercorner with one V(11)O6 octahedra,  a cornercorner with one V(12)O6 octahedra,  a cornercorner with one V(7)O6 octahedra,  a cornercorner with one V(8)O6 octahedra,  a cornercorner with one V(9)O6 octahedra,  an edgeedge with one V(1)O6 octahedra,  an edgeedge with one V(2)O6 octahedra,  an edgeedge with one V(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra,  an edgeedge with one V(6)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 6-9°. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded to one V(1), one V(10), one V(12), one V(2), and one V(5) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the second O site, O(2) is bonded to one V(10), one V(11), one V(2), one V(3), and one V(6) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the third O site, O(3) is bonded to one V(1), one V(11), one V(12), one V(3), and one V(4) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the fourth O site, O(4) is bonded to one V(2), one V(4), one V(5), one V(7), and one V(9) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the fifth O site, O(5) is bonded to one V(3), one V(5), one V(6), one V(7), and one V(8) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the sixth O site, O(6) is bonded to one V(1), one V(4), one V(6), one V(8), and one V(9) atom to form a mixture of corner and edge-sharing OV5 square pyramids. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(10), one V(7), and one V(8) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(11), one V(2), one V(8), and one V(9) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(12), one V(3), one V(7), and one V(9) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(11), one V(4), and one V(7) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(11), one V(12), one V(5), and one V(8) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(12), one V(6), and one V(9) atom. In the thirteenth O site, O(13) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(12), one V(13), one V(2), and one V(6) atom. In the fourteenth O site, O(14) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(10), one V(13), one V(3), and one V(4) atom. In the fifteenth O site, O(15) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(13), one V(2), one V(4), and one V(8) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(13), one V(6), and one V(7) atom. In the seventeenth O site, O(17) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(13), one V(3), one V(5), and one V(9) atom. In the eighteenth O site, O(18) is bonded in a distorted rectangular see-saw-like geometry to one Ba(1), one V(1), one V(11), one V(13), and one V(5) atom. is represented by the CIF card [CIF]
data_BaV13O18
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.906
_cell_length_b   8.011
_cell_length_c   8.121
_cell_angle_alpha   112.590
_cell_angle_beta   109.515
_cell_angle_gamma   110.927
_symmetry_Int_Tables_number   1
_cell_volume   371.442
_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  1.000  0.996  0.997  1.0
  V  V1  1  0.354  0.768  0.398  1.0
  V  V2  1  0.758  0.394  0.341  1.0
  V  V3  1  0.403  0.344  0.766  1.0
  V  V4  1  0.647  0.231  0.604  1.0
  V  V5  1  0.232  0.600  0.654  1.0
  V  V6  1  0.598  0.658  0.236  1.0
  V  V7  1  0.115  0.431  0.920  1.0
  V  V8  1  0.434  0.927  0.123  1.0
  V  V9  1  0.928  0.127  0.431  1.0
  V  V10  1  0.886  0.571  0.081  1.0
  V  V11  1  0.567  0.076  0.877  1.0
  V  V12  1  0.078  0.879  0.572  1.0
  V  V13  1  0.499  0.498  0.499  1.0
  O  O14  1  0.059  0.608  0.386  1.0
  O  O15  1  0.603  0.385  0.059  1.0
  O  O16  1  0.383  0.051  0.610  1.0
  O  O17  1  0.933  0.390  0.614  1.0
  O  O18  1  0.395  0.621  0.946  1.0
  O  O19  1  0.622  0.950  0.392  1.0
  O  O20  1  0.175  0.736  0.114  1.0
  O  O21  1  0.723  0.100  0.154  1.0
  O  O22  1  0.101  0.162  0.720  1.0
  O  O23  1  0.830  0.263  0.886  1.0
  O  O24  1  0.276  0.903  0.842  1.0
  O  O25  1  0.898  0.841  0.287  1.0
  O  O26  1  0.778  0.682  0.511  1.0
  O  O27  1  0.683  0.516  0.780  1.0
  O  O28  1  0.480  0.212  0.327  1.0
  O  O29  1  0.323  0.480  0.213  1.0
  O  O30  1  0.220  0.315  0.485  1.0
  O  O31  1  0.517  0.784  0.676  1.0
[/CIF]
.