The structure described by Na5V12O32 crystallizes in the monoclinic Cm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(18), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form edge-sharing NaO6 octahedra. In the second Na site, Na(2) is bonded to one O(19), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form edge-sharing NaO6 octahedra. In the third Na site, Na(3) is bonded to one O(12), one O(13), one O(16), one O(17), one O(20), and one O(8) atom to form NaO6 octahedra that share  a cornercorner with one Na(4)O4 tetrahedra and edges with two equivalent Na(3)O6 octahedra. In the fourth Na site, Na(4) is bonded to one O(12), one O(2), and two equivalent O(22) atoms to form distorted corner-sharing NaO4 tetrahedra. The corner-sharing octahedral tilt angles are 70°. There are nine inequivalent V sites. In the first V site, V(1) is bonded in a 6-coordinate geometry to one O(14), one O(19), one O(2), one O(7), and two equivalent O(1) atoms. In the second V site, V(2) is bonded in a 6-coordinate geometry to one O(15), one O(18), one O(3), one O(6), and two equivalent O(1) atoms. In the third V site, V(3) is bonded in a 5-coordinate geometry to one O(21), one O(4), one O(5), one O(8), and one O(9) atom. In the fourth V site, V(4) is bonded in a 6-coordinate geometry to one O(12), one O(14), one O(2), one O(23), and two equivalent O(10) atoms. In the fifth V site, V(5) is bonded in a 6-coordinate geometry to one O(13), one O(15), one O(24), one O(3), and two equivalent O(10) atoms. In the sixth V site, V(6) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(14), one O(15), and one O(22) atom. In the seventh V site, V(7) is bonded in a 5-coordinate geometry to one O(16), one O(18), one O(4), and two equivalent O(21) atoms. In the eighth V site, V(8) is bonded in a 5-coordinate geometry to one O(17), one O(19), one O(5), and two equivalent O(21) atoms. In the ninth V site, V(9) is bonded in a 6-coordinate geometry to one O(10), one O(20), one O(22), one O(23), one O(24), and one O(8) atom. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one V(1), one V(2), and one V(6) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Na(4), one V(1), and one V(4) atom. In the third O site, O(3) is bonded in a bent 120 degrees geometry to one V(2) and one V(5) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one V(7) and two equivalent V(3) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one V(8) and two equivalent V(3) atoms. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Na(2) and one V(2) atom. In the seventh O site, O(7) is bonded in a distorted bent 150 degrees geometry to one Na(1) and one V(1) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Na(3), one V(3), and one V(9) atom. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Na(1), one Na(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one V(4), one V(5), one V(6), and one V(9) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Na(1), one Na(2), and one V(6) atom. In the twelfth O site, O(12) is bonded in a distorted tetrahedral geometry to one Na(4), two equivalent Na(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(5) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one V(1), one V(4), and two equivalent V(6) atoms. In the fifteenth O site, O(15) is bonded in a 4-coordinate geometry to one V(2), one V(5), and two equivalent V(6) atoms. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(7) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(8) atom. In the eighteenth O site, O(18) is bonded in a trigonal planar geometry to one Na(1), one V(2), and one V(7) atom. In the nineteenth O site, O(19) is bonded in a trigonal planar geometry to one Na(2), one V(1), and one V(8) atom. In the twentieth O site, O(20) is bonded in a distorted bent 150 degrees geometry to one Na(3) and one V(9) atom. In the twenty-first O site, O(21) is bonded in a distorted trigonal non-coplanar geometry to one V(3), one V(7), and one V(8) atom. In the twenty-second O site, O(22) is bonded in a trigonal non-coplanar geometry to one Na(4), one V(6), and one V(9) atom. In the twenty-third O site, O(23) is bonded in a distorted trigonal non-coplanar geometry to one V(4) and two equivalent V(9) atoms. In the twenty-fourth O site, O(24) is bonded in a 3-coordinate geometry to one V(5) and two equivalent V(9) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na5V12O32
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.319
_cell_length_b   8.319
_cell_length_c   12.377
_cell_angle_alpha   74.072
_cell_angle_beta   74.072
_cell_angle_gamma   52.023
_symmetry_Int_Tables_number   1
_cell_volume   642.916
_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
  Na  Na0  1  0.125  0.125  0.681  1.0
  Na  Na1  1  0.626  0.626  0.684  1.0
  Na  Na2  1  0.376  0.873  0.319  1.0
  Na  Na3  1  0.873  0.376  0.319  1.0
  Na  Na4  1  0.091  0.091  0.051  1.0
  V  V5  1  0.344  0.344  0.806  1.0
  V  V6  1  0.842  0.842  0.808  1.0
  V  V7  1  0.554  0.053  0.462  1.0
  V  V8  1  0.053  0.554  0.462  1.0
  V  V9  1  0.282  0.282  0.080  1.0
  V  V10  1  0.780  0.780  0.080  1.0
  V  V11  1  0.720  0.222  0.918  1.0
  V  V12  1  0.222  0.720  0.918  1.0
  V  V13  1  0.946  0.946  0.540  1.0
  V  V14  1  0.446  0.446  0.539  1.0
  V  V15  1  0.654  0.155  0.195  1.0
  V  V16  1  0.155  0.654  0.195  1.0
  O  O17  1  0.623  0.123  0.826  1.0
  O  O18  1  0.123  0.623  0.826  1.0
  O  O19  1  0.249  0.249  0.954  1.0
  O  O20  1  0.750  0.750  0.952  1.0
  O  O21  1  0.843  0.843  0.463  1.0
  O  O22  1  0.343  0.343  0.463  1.0
  O  O23  1  0.772  0.772  0.728  1.0
  O  O24  1  0.271  0.271  0.730  1.0
  O  O25  1  0.037  0.538  0.328  1.0
  O  O26  1  0.538  0.037  0.328  1.0
  O  O27  1  0.947  0.447  0.554  1.0
  O  O28  1  0.447  0.947  0.554  1.0
  O  O29  1  0.567  0.067  0.073  1.0
  O  O30  1  0.067  0.567  0.073  1.0
  O  O31  1  0.321  0.824  0.817  1.0
  O  O32  1  0.824  0.321  0.817  1.0
  O  O33  1  0.178  0.178  0.180  1.0
  O  O34  1  0.679  0.679  0.182  1.0
  O  O35  1  0.432  0.432  0.926  1.0
  O  O36  1  0.935  0.935  0.927  1.0
  O  O37  1  0.053  0.053  0.448  1.0
  O  O38  1  0.553  0.553  0.448  1.0
  O  O39  1  0.962  0.962  0.674  1.0
  O  O40  1  0.462  0.462  0.674  1.0
  O  O41  1  0.733  0.225  0.269  1.0
  O  O42  1  0.225  0.733  0.269  1.0
  O  O43  1  0.656  0.157  0.538  1.0
  O  O44  1  0.157  0.656  0.538  1.0
  O  O45  1  0.252  0.750  0.046  1.0
  O  O46  1  0.750  0.252  0.046  1.0
  O  O47  1  0.376  0.376  0.173  1.0
  O  O48  1  0.878  0.878  0.172  1.0
[/CIF]
.
The structure described by Na5V12O32 crystallizes in the monoclinic Cm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(18), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form edge-sharing NaO6 octahedra. In the second Na site, Na(2) is bonded to one O(19), one O(6), two equivalent O(11), and two equivalent O(9) atoms to form edge-sharing NaO6 octahedra. In the third Na site, Na(3) is bonded to one O(12), one O(13), one O(16), one O(17), one O(20), and one O(8) atom to form NaO6 octahedra that share  a cornercorner with one Na(4)O4 tetrahedra and edges with two equivalent Na(3)O6 octahedra. In the fourth Na site, Na(4) is bonded to one O(12), one O(2), and two equivalent O(22) atoms to form distorted corner-sharing NaO4 tetrahedra. The corner-sharing octahedral tilt angles are 70°. There are nine inequivalent V sites. In the first V site, V(1) is bonded in a 6-coordinate geometry to one O(14), one O(19), one O(2), one O(7), and two equivalent O(1) atoms. In the second V site, V(2) is bonded in a 6-coordinate geometry to one O(15), one O(18), one O(3), one O(6), and two equivalent O(1) atoms. In the third V site, V(3) is bonded in a 5-coordinate geometry to one O(21), one O(4), one O(5), one O(8), and one O(9) atom. In the fourth V site, V(4) is bonded in a 6-coordinate geometry to one O(12), one O(14), one O(2), one O(23), and two equivalent O(10) atoms. In the fifth V site, V(5) is bonded in a 6-coordinate geometry to one O(13), one O(15), one O(24), one O(3), and two equivalent O(10) atoms. In the sixth V site, V(6) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(14), one O(15), and one O(22) atom. In the seventh V site, V(7) is bonded in a 5-coordinate geometry to one O(16), one O(18), one O(4), and two equivalent O(21) atoms. In the eighth V site, V(8) is bonded in a 5-coordinate geometry to one O(17), one O(19), one O(5), and two equivalent O(21) atoms. In the ninth V site, V(9) is bonded in a 6-coordinate geometry to one O(10), one O(20), one O(22), one O(23), one O(24), and one O(8) atom. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one V(1), one V(2), and one V(6) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one Na(4), one V(1), and one V(4) atom. In the third O site, O(3) is bonded in a bent 120 degrees geometry to one V(2) and one V(5) atom. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one V(7) and two equivalent V(3) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one V(8) and two equivalent V(3) atoms. In the sixth O site, O(6) is bonded in a distorted bent 150 degrees geometry to one Na(2) and one V(2) atom. In the seventh O site, O(7) is bonded in a distorted bent 150 degrees geometry to one Na(1) and one V(1) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Na(3), one V(3), and one V(9) atom. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Na(1), one Na(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one V(4), one V(5), one V(6), and one V(9) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Na(1), one Na(2), and one V(6) atom. In the twelfth O site, O(12) is bonded in a distorted tetrahedral geometry to one Na(4), two equivalent Na(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(5) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one V(1), one V(4), and two equivalent V(6) atoms. In the fifteenth O site, O(15) is bonded in a 4-coordinate geometry to one V(2), one V(5), and two equivalent V(6) atoms. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(7) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(8) atom. In the eighteenth O site, O(18) is bonded in a trigonal planar geometry to one Na(1), one V(2), and one V(7) atom. In the nineteenth O site, O(19) is bonded in a trigonal planar geometry to one Na(2), one V(1), and one V(8) atom. In the twentieth O site, O(20) is bonded in a distorted bent 150 degrees geometry to one Na(3) and one V(9) atom. In the twenty-first O site, O(21) is bonded in a distorted trigonal non-coplanar geometry to one V(3), one V(7), and one V(8) atom. In the twenty-second O site, O(22) is bonded in a trigonal non-coplanar geometry to one Na(4), one V(6), and one V(9) atom. In the twenty-third O site, O(23) is bonded in a distorted trigonal non-coplanar geometry to one V(4) and two equivalent V(9) atoms. In the twenty-fourth O site, O(24) is bonded in a 3-coordinate geometry to one V(5) and two equivalent V(9) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Na5V12O32
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.319
_cell_length_b   8.319
_cell_length_c   12.377
_cell_angle_alpha   74.072
_cell_angle_beta   74.072
_cell_angle_gamma   52.023
_symmetry_Int_Tables_number   1
_cell_volume   642.916
_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
  Na  Na0  1  0.125  0.125  0.681  1.0
  Na  Na1  1  0.626  0.626  0.684  1.0
  Na  Na2  1  0.376  0.873  0.319  1.0
  Na  Na3  1  0.873  0.376  0.319  1.0
  Na  Na4  1  0.091  0.091  0.051  1.0
  V  V5  1  0.344  0.344  0.806  1.0
  V  V6  1  0.842  0.842  0.808  1.0
  V  V7  1  0.554  0.053  0.462  1.0
  V  V8  1  0.053  0.554  0.462  1.0
  V  V9  1  0.282  0.282  0.080  1.0
  V  V10  1  0.780  0.780  0.080  1.0
  V  V11  1  0.720  0.222  0.918  1.0
  V  V12  1  0.222  0.720  0.918  1.0
  V  V13  1  0.946  0.946  0.540  1.0
  V  V14  1  0.446  0.446  0.539  1.0
  V  V15  1  0.654  0.155  0.195  1.0
  V  V16  1  0.155  0.654  0.195  1.0
  O  O17  1  0.623  0.123  0.826  1.0
  O  O18  1  0.123  0.623  0.826  1.0
  O  O19  1  0.249  0.249  0.954  1.0
  O  O20  1  0.750  0.750  0.952  1.0
  O  O21  1  0.843  0.843  0.463  1.0
  O  O22  1  0.343  0.343  0.463  1.0
  O  O23  1  0.772  0.772  0.728  1.0
  O  O24  1  0.271  0.271  0.730  1.0
  O  O25  1  0.037  0.538  0.328  1.0
  O  O26  1  0.538  0.037  0.328  1.0
  O  O27  1  0.947  0.447  0.554  1.0
  O  O28  1  0.447  0.947  0.554  1.0
  O  O29  1  0.567  0.067  0.073  1.0
  O  O30  1  0.067  0.567  0.073  1.0
  O  O31  1  0.321  0.824  0.817  1.0
  O  O32  1  0.824  0.321  0.817  1.0
  O  O33  1  0.178  0.178  0.180  1.0
  O  O34  1  0.679  0.679  0.182  1.0
  O  O35  1  0.432  0.432  0.926  1.0
  O  O36  1  0.935  0.935  0.927  1.0
  O  O37  1  0.053  0.053  0.448  1.0
  O  O38  1  0.553  0.553  0.448  1.0
  O  O39  1  0.962  0.962  0.674  1.0
  O  O40  1  0.462  0.462  0.674  1.0
  O  O41  1  0.733  0.225  0.269  1.0
  O  O42  1  0.225  0.733  0.269  1.0
  O  O43  1  0.656  0.157  0.538  1.0
  O  O44  1  0.157  0.656  0.538  1.0
  O  O45  1  0.252  0.750  0.046  1.0
  O  O46  1  0.750  0.252  0.046  1.0
  O  O47  1  0.376  0.376  0.173  1.0
  O  O48  1  0.878  0.878  0.172  1.0
[/CIF]
.