The material structure described by NaV5O8 crystallizes in the monoclinic C2 space group. Na(1) is bonded in a 4-coordinate geometry to two equivalent O(3) and two equivalent O(4) atoms. There are six inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. In the second V site, V(2) is bonded to one O(1), one O(8), two equivalent O(3), and two equivalent O(7) atoms to form a mixture of distorted edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the third V site, V(3) is bonded to one O(2), one O(7), two equivalent O(4), and two equivalent O(8) atoms to form a mixture of distorted edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the fourth V site, V(4) is bonded to two equivalent O(4) and four equivalent O(2) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the fifth V site, V(5) is bonded to one O(1), two equivalent O(7), and three equivalent O(5) atoms to form a mixture of edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the sixth V site, V(6) is bonded to one O(2), two equivalent O(8), and three equivalent O(6) atoms to form a mixture of edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. There are eight inequivalent O sites. In the first O site, O(5) is bonded in a 3-coordinate geometry to three equivalent V(5) atoms. In the second O site, O(6) is bonded in a distorted T-shaped geometry to three equivalent V(6) atoms. In the third O site, O(7) is bonded to one V(3), two equivalent V(2), and two equivalent V(5) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(4)Na2V3 trigonal bipyramids,  a cornercorner with one O(2)V4 trigonal pyramid,  an edgeedge with one O(3)Na2V3 trigonal bipyramid, edges with two equivalent O(7)V5 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and edges with two equivalent O(1)V4 trigonal pyramids. In the fourth O site, O(8) is bonded to one V(2), two equivalent V(3), and two equivalent V(6) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(4)Na2V3 trigonal bipyramids,  a cornercorner with one O(1)V4 trigonal pyramid,  an edgeedge with one O(4)Na2V3 trigonal bipyramid, edges with two equivalent O(7)V5 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and edges with two equivalent O(2)V4 trigonal pyramids. In the fifth O site, O(1) is bonded to one V(2), one V(5), and two equivalent V(1) atoms to form OV4 trigonal pyramids that share  a cornercorner with one O(8)V5 trigonal bipyramid, corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with four equivalent O(1)V4 trigonal pyramids, edges with two equivalent O(3)Na2V3 trigonal bipyramids, edges with two equivalent O(7)V5 trigonal bipyramids, and  an edgeedge with one O(1)V4 trigonal pyramid. In the sixth O site, O(2) is bonded to one V(3), one V(6), and two equivalent V(4) atoms to form OV4 trigonal pyramids that share  a cornercorner with one O(7)V5 trigonal bipyramid, corners with two equivalent O(4)Na2V3 trigonal bipyramids, corners with four equivalent O(2)V4 trigonal pyramids, edges with two equivalent O(4)Na2V3 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and  an edgeedge with one O(2)V4 trigonal pyramid. In the seventh O site, O(3) is bonded to two equivalent Na(1), one V(1), and two equivalent V(2) atoms to form distorted ONa2V3 trigonal bipyramids that share  a cornercorner with one O(3)Na2V3 trigonal bipyramid, corners with two equivalent O(4)Na2V3 trigonal bipyramids, corners with two equivalent O(7)V5 trigonal bipyramids, corners with two equivalent O(8)V5 trigonal bipyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(4)Na2V3 trigonal bipyramid,  an edgeedge with one O(7)V5 trigonal bipyramid, edges with two equivalent O(3)Na2V3 trigonal bipyramids, and edges with two equivalent O(1)V4 trigonal pyramids. In the eighth O site, O(4) is bonded to two equivalent Na(1), one V(4), and two equivalent V(3) atoms to form distorted ONa2V3 trigonal bipyramids that share  a cornercorner with one O(4)Na2V3 trigonal bipyramid, corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(7)V5 trigonal bipyramids, corners with two equivalent O(8)V5 trigonal bipyramids, corners with two equivalent O(2)V4 trigonal pyramids,  an edgeedge with one O(3)Na2V3 trigonal bipyramid,  an edgeedge with one O(8)V5 trigonal bipyramid, edges with two equivalent O(4)Na2V3 trigonal bipyramids, and edges with two equivalent O(2)V4 trigonal pyramids. is represented by the CIF file [CIF]
data_NaV5O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.072
_cell_length_b   7.257
_cell_length_c   7.856
_cell_angle_alpha   106.189
_cell_angle_beta   101.266
_cell_angle_gamma   90.010
_symmetry_Int_Tables_number   1
_cell_volume   164.671
_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  0.001  1.000  0.000  1.0
  O  O1  1  0.082  0.624  0.164  1.0
  O  O2  1  0.917  0.376  0.836  1.0
  O  O3  1  0.577  0.300  0.149  1.0
  O  O4  1  0.428  0.700  0.851  1.0
  O  O5  1  0.663  0.983  0.349  1.0
  O  O6  1  0.314  0.017  0.651  1.0
  O  O7  1  0.734  0.640  0.460  1.0
  O  O8  1  0.274  0.360  0.540  1.0
  V  V9  1  0.501  0.500  0.000  1.0
  V  V10  1  0.157  0.427  0.307  1.0
  V  V11  1  0.850  0.573  0.693  1.0
  V  V12  1  0.203  0.832  0.404  1.0
  V  V13  1  0.798  0.168  0.596  1.0
[/CIF]
.
The material structure described by NaV5O8 crystallizes in the monoclinic C2 space group. Na(1) is bonded in a 4-coordinate geometry to two equivalent O(3) and two equivalent O(4) atoms. There are six inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(3) and four equivalent O(1) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. In the second V site, V(2) is bonded to one O(1), one O(8), two equivalent O(3), and two equivalent O(7) atoms to form a mixture of distorted edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the third V site, V(3) is bonded to one O(2), one O(7), two equivalent O(4), and two equivalent O(8) atoms to form a mixture of distorted edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the fourth V site, V(4) is bonded to two equivalent O(4) and four equivalent O(2) atoms to form a mixture of edge and corner-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the fifth V site, V(5) is bonded to one O(1), two equivalent O(7), and three equivalent O(5) atoms to form a mixture of edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. In the sixth V site, V(6) is bonded to one O(2), two equivalent O(8), and three equivalent O(6) atoms to form a mixture of edge, corner, and face-sharing VO6 octahedra. The corner-sharing octahedral tilt angles range from 41-60°. There are eight inequivalent O sites. In the first O site, O(5) is bonded in a 3-coordinate geometry to three equivalent V(5) atoms. In the second O site, O(6) is bonded in a distorted T-shaped geometry to three equivalent V(6) atoms. In the third O site, O(7) is bonded to one V(3), two equivalent V(2), and two equivalent V(5) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(4)Na2V3 trigonal bipyramids,  a cornercorner with one O(2)V4 trigonal pyramid,  an edgeedge with one O(3)Na2V3 trigonal bipyramid, edges with two equivalent O(7)V5 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and edges with two equivalent O(1)V4 trigonal pyramids. In the fourth O site, O(8) is bonded to one V(2), two equivalent V(3), and two equivalent V(6) atoms to form distorted OV5 trigonal bipyramids that share corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(4)Na2V3 trigonal bipyramids,  a cornercorner with one O(1)V4 trigonal pyramid,  an edgeedge with one O(4)Na2V3 trigonal bipyramid, edges with two equivalent O(7)V5 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and edges with two equivalent O(2)V4 trigonal pyramids. In the fifth O site, O(1) is bonded to one V(2), one V(5), and two equivalent V(1) atoms to form OV4 trigonal pyramids that share  a cornercorner with one O(8)V5 trigonal bipyramid, corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with four equivalent O(1)V4 trigonal pyramids, edges with two equivalent O(3)Na2V3 trigonal bipyramids, edges with two equivalent O(7)V5 trigonal bipyramids, and  an edgeedge with one O(1)V4 trigonal pyramid. In the sixth O site, O(2) is bonded to one V(3), one V(6), and two equivalent V(4) atoms to form OV4 trigonal pyramids that share  a cornercorner with one O(7)V5 trigonal bipyramid, corners with two equivalent O(4)Na2V3 trigonal bipyramids, corners with four equivalent O(2)V4 trigonal pyramids, edges with two equivalent O(4)Na2V3 trigonal bipyramids, edges with two equivalent O(8)V5 trigonal bipyramids, and  an edgeedge with one O(2)V4 trigonal pyramid. In the seventh O site, O(3) is bonded to two equivalent Na(1), one V(1), and two equivalent V(2) atoms to form distorted ONa2V3 trigonal bipyramids that share  a cornercorner with one O(3)Na2V3 trigonal bipyramid, corners with two equivalent O(4)Na2V3 trigonal bipyramids, corners with two equivalent O(7)V5 trigonal bipyramids, corners with two equivalent O(8)V5 trigonal bipyramids, corners with two equivalent O(1)V4 trigonal pyramids,  an edgeedge with one O(4)Na2V3 trigonal bipyramid,  an edgeedge with one O(7)V5 trigonal bipyramid, edges with two equivalent O(3)Na2V3 trigonal bipyramids, and edges with two equivalent O(1)V4 trigonal pyramids. In the eighth O site, O(4) is bonded to two equivalent Na(1), one V(4), and two equivalent V(3) atoms to form distorted ONa2V3 trigonal bipyramids that share  a cornercorner with one O(4)Na2V3 trigonal bipyramid, corners with two equivalent O(3)Na2V3 trigonal bipyramids, corners with two equivalent O(7)V5 trigonal bipyramids, corners with two equivalent O(8)V5 trigonal bipyramids, corners with two equivalent O(2)V4 trigonal pyramids,  an edgeedge with one O(3)Na2V3 trigonal bipyramid,  an edgeedge with one O(8)V5 trigonal bipyramid, edges with two equivalent O(4)Na2V3 trigonal bipyramids, and edges with two equivalent O(2)V4 trigonal pyramids. is represented by the CIF file [CIF]
data_NaV5O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.072
_cell_length_b   7.257
_cell_length_c   7.856
_cell_angle_alpha   106.189
_cell_angle_beta   101.266
_cell_angle_gamma   90.010
_symmetry_Int_Tables_number   1
_cell_volume   164.671
_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  0.001  1.000  0.000  1.0
  O  O1  1  0.082  0.624  0.164  1.0
  O  O2  1  0.917  0.376  0.836  1.0
  O  O3  1  0.577  0.300  0.149  1.0
  O  O4  1  0.428  0.700  0.851  1.0
  O  O5  1  0.663  0.983  0.349  1.0
  O  O6  1  0.314  0.017  0.651  1.0
  O  O7  1  0.734  0.640  0.460  1.0
  O  O8  1  0.274  0.360  0.540  1.0
  V  V9  1  0.501  0.500  0.000  1.0
  V  V10  1  0.157  0.427  0.307  1.0
  V  V11  1  0.850  0.573  0.693  1.0
  V  V12  1  0.203  0.832  0.404  1.0
  V  V13  1  0.798  0.168  0.596  1.0
[/CIF]
.