The structure described by Na5V3O12 crystallizes in the orthorhombic C222_1 space group. There are three inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form distorted NaO6 octahedra that share corners with six equivalent V(2)O4 tetrahedra and edges with two equivalent Na(3)O6 octahedra. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one O(3), one O(6), two equivalent O(1), and two equivalent O(5) atoms. In the third Na site, Na(3) is bonded to one O(2), one O(3), one O(5), one O(6), and two equivalent O(4) atoms to form distorted NaO6 octahedra that share corners with three equivalent V(1)O4 tetrahedra, corners with three equivalent V(2)O4 tetrahedra,  an edgeedge with one Na(1)O6 octahedra, and  an edgeedge with one Na(3)O6 octahedra. There are two inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(2) and two equivalent O(4) atoms to form VO4 tetrahedra that share corners with six equivalent Na(3)O6 octahedra and corners with two equivalent V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-57°. In the second V site, V(2) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form VO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Na(3)O6 octahedra, and  a cornercorner with one V(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 29-74°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Na(1), two equivalent Na(2), and one V(2) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Na(3), one V(1), and one V(2) atom. In the third O site, O(3) is bonded to one Na(1), one Na(2), one Na(3), and one V(2) atom to form distorted corner-sharing ONa3V tetrahedra. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(1) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Na(1), one Na(3), two equivalent Na(2), and one V(2) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Na(2) and one Na(3) atom. is represented by the CIF file [CIF]
data_Na5V3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.653
_cell_length_b   5.653
_cell_length_c   21.300
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.387
_symmetry_Int_Tables_number   1
_cell_volume   598.881
_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
  Na  Na0  1  0.515  0.515  0.000  1.0
  Na  Na1  1  0.485  0.485  0.500  1.0
  Na  Na2  1  0.205  0.846  0.943  1.0
  Na  Na3  1  0.846  0.205  0.057  1.0
  Na  Na4  1  0.795  0.154  0.443  1.0
  Na  Na5  1  0.154  0.795  0.557  1.0
  Na  Na6  1  0.537  0.476  0.833  1.0
  Na  Na7  1  0.476  0.537  0.167  1.0
  Na  Na8  1  0.463  0.524  0.333  1.0
  Na  Na9  1  0.524  0.463  0.667  1.0
  V  V10  1  0.895  0.105  0.750  1.0
  V  V11  1  0.105  0.895  0.250  1.0
  V  V12  1  0.852  0.135  0.903  1.0
  V  V13  1  0.135  0.852  0.097  1.0
  V  V14  1  0.148  0.865  0.403  1.0
  V  V15  1  0.865  0.148  0.597  1.0
  O  O16  1  0.666  0.206  0.956  1.0
  O  O17  1  0.206  0.666  0.044  1.0
  O  O18  1  0.334  0.794  0.456  1.0
  O  O19  1  0.794  0.334  0.544  1.0
  O  O20  1  0.766  0.189  0.822  1.0
  O  O21  1  0.189  0.766  0.178  1.0
  O  O22  1  0.234  0.811  0.322  1.0
  O  O23  1  0.811  0.234  0.678  1.0
  O  O24  1  0.785  0.808  0.914  1.0
  O  O25  1  0.808  0.785  0.086  1.0
  O  O26  1  0.215  0.192  0.414  1.0
  O  O27  1  0.192  0.215  0.586  1.0
  O  O28  1  0.766  0.772  0.745  1.0
  O  O29  1  0.772  0.766  0.255  1.0
  O  O30  1  0.234  0.228  0.245  1.0
  O  O31  1  0.228  0.234  0.755  1.0
  O  O32  1  0.662  0.811  0.584  1.0
  O  O33  1  0.811  0.662  0.416  1.0
  O  O34  1  0.338  0.189  0.084  1.0
  O  O35  1  0.189  0.338  0.916  1.0
  O  O36  1  0.312  0.769  0.841  1.0
  O  O37  1  0.769  0.312  0.159  1.0
  O  O38  1  0.688  0.231  0.341  1.0
  O  O39  1  0.231  0.688  0.659  1.0
[/CIF]
.
The structure described by Na5V3O12 crystallizes in the orthorhombic C222_1 space group. There are three inequivalent Na sites. In the first Na site, Na(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form distorted NaO6 octahedra that share corners with six equivalent V(2)O4 tetrahedra and edges with two equivalent Na(3)O6 octahedra. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one O(3), one O(6), two equivalent O(1), and two equivalent O(5) atoms. In the third Na site, Na(3) is bonded to one O(2), one O(3), one O(5), one O(6), and two equivalent O(4) atoms to form distorted NaO6 octahedra that share corners with three equivalent V(1)O4 tetrahedra, corners with three equivalent V(2)O4 tetrahedra,  an edgeedge with one Na(1)O6 octahedra, and  an edgeedge with one Na(3)O6 octahedra. There are two inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(2) and two equivalent O(4) atoms to form VO4 tetrahedra that share corners with six equivalent Na(3)O6 octahedra and corners with two equivalent V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 48-57°. In the second V site, V(2) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form VO4 tetrahedra that share corners with three equivalent Na(1)O6 octahedra, corners with three equivalent Na(3)O6 octahedra, and  a cornercorner with one V(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 29-74°. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Na(1), two equivalent Na(2), and one V(2) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Na(3), one V(1), and one V(2) atom. In the third O site, O(3) is bonded to one Na(1), one Na(2), one Na(3), and one V(2) atom to form distorted corner-sharing ONa3V tetrahedra. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to two equivalent Na(3) and one V(1) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Na(1), one Na(3), two equivalent Na(2), and one V(2) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Na(2) and one Na(3) atom. is represented by the CIF file [CIF]
data_Na5V3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.653
_cell_length_b   5.653
_cell_length_c   21.300
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.387
_symmetry_Int_Tables_number   1
_cell_volume   598.881
_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
  Na  Na0  1  0.515  0.515  0.000  1.0
  Na  Na1  1  0.485  0.485  0.500  1.0
  Na  Na2  1  0.205  0.846  0.943  1.0
  Na  Na3  1  0.846  0.205  0.057  1.0
  Na  Na4  1  0.795  0.154  0.443  1.0
  Na  Na5  1  0.154  0.795  0.557  1.0
  Na  Na6  1  0.537  0.476  0.833  1.0
  Na  Na7  1  0.476  0.537  0.167  1.0
  Na  Na8  1  0.463  0.524  0.333  1.0
  Na  Na9  1  0.524  0.463  0.667  1.0
  V  V10  1  0.895  0.105  0.750  1.0
  V  V11  1  0.105  0.895  0.250  1.0
  V  V12  1  0.852  0.135  0.903  1.0
  V  V13  1  0.135  0.852  0.097  1.0
  V  V14  1  0.148  0.865  0.403  1.0
  V  V15  1  0.865  0.148  0.597  1.0
  O  O16  1  0.666  0.206  0.956  1.0
  O  O17  1  0.206  0.666  0.044  1.0
  O  O18  1  0.334  0.794  0.456  1.0
  O  O19  1  0.794  0.334  0.544  1.0
  O  O20  1  0.766  0.189  0.822  1.0
  O  O21  1  0.189  0.766  0.178  1.0
  O  O22  1  0.234  0.811  0.322  1.0
  O  O23  1  0.811  0.234  0.678  1.0
  O  O24  1  0.785  0.808  0.914  1.0
  O  O25  1  0.808  0.785  0.086  1.0
  O  O26  1  0.215  0.192  0.414  1.0
  O  O27  1  0.192  0.215  0.586  1.0
  O  O28  1  0.766  0.772  0.745  1.0
  O  O29  1  0.772  0.766  0.255  1.0
  O  O30  1  0.234  0.228  0.245  1.0
  O  O31  1  0.228  0.234  0.755  1.0
  O  O32  1  0.662  0.811  0.584  1.0
  O  O33  1  0.811  0.662  0.416  1.0
  O  O34  1  0.338  0.189  0.084  1.0
  O  O35  1  0.189  0.338  0.916  1.0
  O  O36  1  0.312  0.769  0.841  1.0
  O  O37  1  0.769  0.312  0.159  1.0
  O  O38  1  0.688  0.231  0.341  1.0
  O  O39  1  0.231  0.688  0.659  1.0
[/CIF]
.