The structure described by Na4Cr13Se23 crystallizes in the monoclinic Cm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one Se(2), one Se(7), two equivalent Se(11), and two equivalent Se(4) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one Se(15), one Se(8), two equivalent Se(12), and two equivalent Se(19) atoms. In the third Na site, Na(3) is bonded in a 6-coordinate geometry to one Se(12), one Se(19), two equivalent Se(16), and two equivalent Se(21) atoms. In the fourth Na site, Na(4) is bonded in a rectangular see-saw-like geometry to one Se(16), one Se(21), and two equivalent Se(23) atoms. There are thirteen inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one Se(22), one Se(3), two equivalent Se(1), and two equivalent Se(5) atoms to form CrSe6 octahedra that share corners with two equivalent Cr(13)Se6 octahedra, corners with two equivalent Cr(2)Se6 octahedra, corners with two equivalent Cr(3)Se6 octahedra, corners with two equivalent Cr(4)Se6 octahedra, corners with two equivalent Cr(12)Se5 square pyramids, edges with two equivalent Cr(1)Se6 octahedra, and  a faceface with one Cr(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 48-52°. In the second Cr site, Cr(2) is bonded to one Se(23), one Se(3), two equivalent Se(1), and two equivalent Se(7) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the third Cr site, Cr(3) is bonded to one Se(4), one Se(5), two equivalent Se(2), and two equivalent Se(9) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 47-52°. In the fourth Cr site, Cr(4) is bonded to one Se(6), one Se(7), two equivalent Se(11), and two equivalent Se(3) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. In the fifth Cr site, Cr(5) is bonded to one Se(8), one Se(9), two equivalent Se(13), and two equivalent Se(4) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the sixth Cr site, Cr(6) is bonded to one Se(10), one Se(9), two equivalent Se(13), and two equivalent Se(6) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. In the seventh Cr site, Cr(7) is bonded to one Se(10), one Se(11), two equivalent Se(15), and two equivalent Se(6) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the eighth Cr site, Cr(8) is bonded to one Se(12), one Se(13), two equivalent Se(17), and two equivalent Se(8) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the ninth Cr site, Cr(9) is bonded to one Se(14), one Se(15), two equivalent Se(10), and two equivalent Se(19) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the tenth Cr site, Cr(10) is bonded to one Se(16), one Se(17), two equivalent Se(12), and two equivalent Se(20) atoms to form CrSe6 octahedra that share edges with two equivalent Cr(10)Se6 octahedra, edges with two equivalent Cr(8)Se6 octahedra, and edges with two equivalent Cr(12)Se5 square pyramids. In the eleventh Cr site, Cr(11) is bonded to one Se(18), one Se(19), two equivalent Se(14), and two equivalent Se(21) atoms to form edge-sharing CrSe6 octahedra. In the twelfth Cr site, Cr(12) is bonded to one Se(20), two equivalent Se(16), and two equivalent Se(22) atoms to form CrSe5 square pyramids that share corners with two equivalent Cr(1)Se6 octahedra, edges with two equivalent Cr(10)Se6 octahedra, and edges with two equivalent Cr(12)Se5 square pyramids. The corner-sharing octahedral tilt angles are 50°. In the thirteenth Cr site, Cr(13) is bonded to one Se(1), one Se(21), two equivalent Se(18), and two equivalent Se(23) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 48°. There are twenty-three inequivalent Se sites. In the first Se site, Se(1) is bonded to one Cr(13), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted SeCr5 square pyramids that share  a cornercorner with one Se(21)Na3Cr3 pentagonal pyramid, corners with two equivalent Se(7)NaCr3 trigonal pyramids, edges with two equivalent Se(1)Cr5 square pyramids, edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids, and  an edgeedge with one Se(7)NaCr3 trigonal pyramid. In the second Se site, Se(2) is bonded in a distorted trigonal non-coplanar geometry to one Na(1) and two equivalent Cr(3) atoms. In the third Se site, Se(3) is bonded in a rectangular see-saw-like geometry to one Cr(1), one Cr(2), and two equivalent Cr(4) atoms. In the fourth Se site, Se(4) is bonded to two equivalent Na(1), one Cr(3), and two equivalent Cr(5) atoms to form SeNa2Cr3 square pyramids that share corners with two equivalent Se(13)Cr5 square pyramids, corners with two equivalent Se(11)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(7)NaCr3 trigonal pyramids,  an edgeedge with one Se(13)Cr5 square pyramid, edges with two equivalent Se(4)Na2Cr3 square pyramids, and  an edgeedge with one Se(11)Na2Cr3 trigonal bipyramid. In the fifth Se site, Se(5) is bonded in a trigonal planar geometry to one Cr(3) and two equivalent Cr(1) atoms. In the sixth Se site, Se(6) is bonded to one Cr(4), two equivalent Cr(6), and two equivalent Cr(7) atoms to form distorted SeCr5 square pyramids that share corners with two equivalent Se(13)Cr5 square pyramids,  a cornercorner with one Se(7)NaCr3 trigonal pyramid, corners with two equivalent Se(15)NaCr3 trigonal pyramids,  an edgeedge with one Se(13)Cr5 square pyramid, edges with two equivalent Se(6)Cr5 square pyramids, edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids, and  an edgeedge with one Se(15)NaCr3 trigonal pyramid. In the seventh Se site, Se(7) is bonded to one Na(1), one Cr(4), and two equivalent Cr(2) atoms to form SeNaCr3 trigonal pyramids that share  a cornercorner with one Se(6)Cr5 square pyramid, corners with two equivalent Se(1)Cr5 square pyramids, corners with two equivalent Se(4)Na2Cr3 square pyramids, corners with two equivalent Se(23)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(7)NaCr3 trigonal pyramids,  an edgeedge with one Se(1)Cr5 square pyramid, and edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids. In the eighth Se site, Se(8) is bonded in a rectangular see-saw-like geometry to one Na(2), one Cr(5), and two equivalent Cr(8) atoms. In the ninth Se site, Se(9) is bonded in a rectangular see-saw-like geometry to one Cr(5), one Cr(6), and two equivalent Cr(3) atoms. In the tenth Se site, Se(10) is bonded in a rectangular see-saw-like geometry to one Cr(6), one Cr(7), and two equivalent Cr(9) atoms. In the eleventh Se site, Se(11) is bonded to two equivalent Na(1), one Cr(7), and two equivalent Cr(4) atoms to form distorted SeNa2Cr3 trigonal bipyramids that share corners with two equivalent Se(4)Na2Cr3 square pyramids, corners with two equivalent Se(15)NaCr3 trigonal pyramids,  an edgeedge with one Se(4)Na2Cr3 square pyramid, edges with two equivalent Se(6)Cr5 square pyramids, edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids, and edges with two equivalent Se(7)NaCr3 trigonal pyramids. In the twelfth Se site, Se(12) is bonded to one Na(3), two equivalent Na(2), one Cr(8), and two equivalent Cr(10) atoms to form SeNa3Cr3 octahedra that share corners with two equivalent Se(21)Na3Cr3 pentagonal pyramids,  a cornercorner with one Se(13)Cr5 square pyramid, corners with two equivalent Se(15)NaCr3 trigonal pyramids, edges with two equivalent Se(12)Na3Cr3 octahedra, and edges with two equivalent Se(16)Na3Cr3 octahedra. In the thirteenth Se site, Se(13) is bonded to one Cr(8), two equivalent Cr(5), and two equivalent Cr(6) atoms to form distorted SeCr5 square pyramids that share  a cornercorner with one Se(12)Na3Cr3 octahedra, corners with two equivalent Se(6)Cr5 square pyramids, corners with two equivalent Se(4)Na2Cr3 square pyramids,  an edgeedge with one Se(6)Cr5 square pyramid,  an edgeedge with one Se(4)Na2Cr3 square pyramid, and edges with two equivalent Se(13)Cr5 square pyramids. The corner-sharing octahedral tilt angles are 2°. In the fourteenth Se site, Se(14) is bonded in a distorted T-shaped geometry to one Cr(9) and two equivalent Cr(11) atoms. In the fifteenth Se site, Se(15) is bonded to one Na(2), one Cr(9), and two equivalent Cr(7) atoms to form SeNaCr3 trigonal pyramids that share corners with two equivalent Se(12)Na3Cr3 octahedra, corners with two equivalent Se(6)Cr5 square pyramids, corners with two equivalent Se(11)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(15)NaCr3 trigonal pyramids, and  an edgeedge with one Se(6)Cr5 square pyramid. The corner-sharing octahedral tilt angles are 39°. In the sixteenth Se site, Se(16) is bonded to one Na(4), two equivalent Na(3), one Cr(10), and two equivalent Cr(12) atoms to form SeNa3Cr3 octahedra that share corners with two equivalent Se(21)Na3Cr3 pentagonal pyramids, corners with two equivalent Se(23)Na2Cr3 trigonal bipyramids, edges with two equivalent Se(12)Na3Cr3 octahedra, edges with two equivalent Se(16)Na3Cr3 octahedra, and  a faceface with one Se(21)Na3Cr3 pentagonal pyramid. In the seventeenth Se site, Se(17) is bonded in a distorted T-shaped geometry to one Cr(10) and two equivalent Cr(8) atoms. In the eighteenth Se site, Se(18) is bonded in a distorted T-shaped geometry to one Cr(11) and two equivalent Cr(13) atoms. In the nineteenth Se site, Se(19) is bonded in a 6-coordinate geometry to one Na(3), two equivalent Na(2), one Cr(11), and two equivalent Cr(9) atoms. In the twentieth Se site, Se(20) is bonded in a distorted T-shaped geometry to one Cr(12) and two equivalent Cr(10) atoms. In the twenty-first Se site, Se(21) is bonded to one Na(4), two equivalent Na(3), one Cr(13), and two equivalent Cr(11) atoms to form distorted SeNa3Cr3 pentagonal pyramids that share corners with two equivalent Se(12)Na3Cr3 octahedra, corners with two equivalent Se(16)Na3Cr3 octahedra,  a cornercorner with one Se(1)Cr5 square pyramid, edges with two equivalent Se(21)Na3Cr3 pentagonal pyramids, edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids, and  a faceface with one Se(16)Na3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 41-44°. In the twenty-second Se site, Se(22) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(12) atoms. In the twenty-third Se site, Se(23) is bonded to two equivalent Na(4), one Cr(2), and two equivalent Cr(13) atoms to form distorted SeNa2Cr3 trigonal bipyramids that share corners with two equivalent Se(16)Na3Cr3 octahedra, corners with two equivalent Se(7)NaCr3 trigonal pyramids, edges with two equivalent Se(21)Na3Cr3 pentagonal pyramids, edges with two equivalent Se(1)Cr5 square pyramids, and edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 42°. is represented by the CIF file [CIF]
data_Na4Cr13Se23
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.088
_cell_length_b   13.088
_cell_length_c   18.881
_cell_angle_alpha   85.466
_cell_angle_beta   85.466
_cell_angle_gamma   16.183
_symmetry_Int_Tables_number   1
_cell_volume   898.521
_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  0.499  0.499  0.723  1.0
  Na  Na1  1  0.499  0.499  0.395  1.0
  Na  Na2  1  0.999  0.999  0.223  1.0
  Na  Na3  1  0.497  0.497  0.051  1.0
  Cr  Cr4  1  0.745  0.745  0.914  1.0
  Cr  Cr5  1  0.866  0.866  0.901  1.0
  Cr  Cr6  1  0.138  0.138  0.767  1.0
  Cr  Cr7  1  0.361  0.361  0.743  1.0
  Cr  Cr8  1  0.633  0.633  0.600  1.0
  Cr  Cr9  1  0.750  0.750  0.584  1.0
  Cr  Cr10  1  0.867  0.867  0.565  1.0
  Cr  Cr11  1  0.139  0.139  0.426  1.0
  Cr  Cr12  1  0.361  0.361  0.405  1.0
  Cr  Cr13  1  0.639  0.639  0.261  1.0
  Cr  Cr14  1  0.859  0.859  0.238  1.0
  Cr  Cr15  1  0.144  0.144  0.099  1.0
  Cr  Cr16  1  0.361  0.361  0.074  1.0
  Se  Se17  1  0.305  0.305  0.965  1.0
  Se  Se18  1  0.585  0.585  0.820  1.0
  Se  Se19  1  0.806  0.806  0.801  1.0
  Se  Se20  1  0.083  0.083  0.660  1.0
  Se  Se21  1  0.194  0.194  0.871  1.0
  Se  Se22  1  0.306  0.306  0.632  1.0
  Se  Se23  1  0.418  0.418  0.843  1.0
  Se  Se24  1  0.585  0.585  0.491  1.0
  Se  Se25  1  0.692  0.692  0.700  1.0
  Se  Se26  1  0.807  0.807  0.466  1.0
  Se  Se27  1  0.913  0.913  0.678  1.0
  Se  Se28  1  0.082  0.082  0.323  1.0
  Se  Se29  1  0.194  0.194  0.534  1.0
  Se  Se30  1  0.308  0.308  0.299  1.0
  Se  Se31  1  0.418  0.418  0.510  1.0
  Se  Se32  1  0.582  0.582  0.147  1.0
  Se  Se33  1  0.691  0.691  0.365  1.0
  Se  Se34  1  0.808  0.808  0.133  1.0
  Se  Se35  1  0.916  0.916  0.345  1.0
  Se  Se36  1  0.192  0.192  0.203  1.0
  Se  Se37  1  0.417  0.417  0.176  1.0
  Se  Se38  1  0.689  0.689  0.034  1.0
  Se  Se39  1  0.916  0.916  0.009  1.0
[/CIF]
.
The structure described by Na4Cr13Se23 crystallizes in the monoclinic Cm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to one Se(2), one Se(7), two equivalent Se(11), and two equivalent Se(4) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one Se(15), one Se(8), two equivalent Se(12), and two equivalent Se(19) atoms. In the third Na site, Na(3) is bonded in a 6-coordinate geometry to one Se(12), one Se(19), two equivalent Se(16), and two equivalent Se(21) atoms. In the fourth Na site, Na(4) is bonded in a rectangular see-saw-like geometry to one Se(16), one Se(21), and two equivalent Se(23) atoms. There are thirteen inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one Se(22), one Se(3), two equivalent Se(1), and two equivalent Se(5) atoms to form CrSe6 octahedra that share corners with two equivalent Cr(13)Se6 octahedra, corners with two equivalent Cr(2)Se6 octahedra, corners with two equivalent Cr(3)Se6 octahedra, corners with two equivalent Cr(4)Se6 octahedra, corners with two equivalent Cr(12)Se5 square pyramids, edges with two equivalent Cr(1)Se6 octahedra, and  a faceface with one Cr(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 48-52°. In the second Cr site, Cr(2) is bonded to one Se(23), one Se(3), two equivalent Se(1), and two equivalent Se(7) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the third Cr site, Cr(3) is bonded to one Se(4), one Se(5), two equivalent Se(2), and two equivalent Se(9) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 47-52°. In the fourth Cr site, Cr(4) is bonded to one Se(6), one Se(7), two equivalent Se(11), and two equivalent Se(3) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. In the fifth Cr site, Cr(5) is bonded to one Se(8), one Se(9), two equivalent Se(13), and two equivalent Se(4) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the sixth Cr site, Cr(6) is bonded to one Se(10), one Se(9), two equivalent Se(13), and two equivalent Se(6) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles range from 47-50°. In the seventh Cr site, Cr(7) is bonded to one Se(10), one Se(11), two equivalent Se(15), and two equivalent Se(6) atoms to form a mixture of edge, corner, and face-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the eighth Cr site, Cr(8) is bonded to one Se(12), one Se(13), two equivalent Se(17), and two equivalent Se(8) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the ninth Cr site, Cr(9) is bonded to one Se(14), one Se(15), two equivalent Se(10), and two equivalent Se(19) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. In the tenth Cr site, Cr(10) is bonded to one Se(16), one Se(17), two equivalent Se(12), and two equivalent Se(20) atoms to form CrSe6 octahedra that share edges with two equivalent Cr(10)Se6 octahedra, edges with two equivalent Cr(8)Se6 octahedra, and edges with two equivalent Cr(12)Se5 square pyramids. In the eleventh Cr site, Cr(11) is bonded to one Se(18), one Se(19), two equivalent Se(14), and two equivalent Se(21) atoms to form edge-sharing CrSe6 octahedra. In the twelfth Cr site, Cr(12) is bonded to one Se(20), two equivalent Se(16), and two equivalent Se(22) atoms to form CrSe5 square pyramids that share corners with two equivalent Cr(1)Se6 octahedra, edges with two equivalent Cr(10)Se6 octahedra, and edges with two equivalent Cr(12)Se5 square pyramids. The corner-sharing octahedral tilt angles are 50°. In the thirteenth Cr site, Cr(13) is bonded to one Se(1), one Se(21), two equivalent Se(18), and two equivalent Se(23) atoms to form a mixture of edge and corner-sharing CrSe6 octahedra. The corner-sharing octahedral tilt angles are 48°. There are twenty-three inequivalent Se sites. In the first Se site, Se(1) is bonded to one Cr(13), two equivalent Cr(1), and two equivalent Cr(2) atoms to form distorted SeCr5 square pyramids that share  a cornercorner with one Se(21)Na3Cr3 pentagonal pyramid, corners with two equivalent Se(7)NaCr3 trigonal pyramids, edges with two equivalent Se(1)Cr5 square pyramids, edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids, and  an edgeedge with one Se(7)NaCr3 trigonal pyramid. In the second Se site, Se(2) is bonded in a distorted trigonal non-coplanar geometry to one Na(1) and two equivalent Cr(3) atoms. In the third Se site, Se(3) is bonded in a rectangular see-saw-like geometry to one Cr(1), one Cr(2), and two equivalent Cr(4) atoms. In the fourth Se site, Se(4) is bonded to two equivalent Na(1), one Cr(3), and two equivalent Cr(5) atoms to form SeNa2Cr3 square pyramids that share corners with two equivalent Se(13)Cr5 square pyramids, corners with two equivalent Se(11)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(7)NaCr3 trigonal pyramids,  an edgeedge with one Se(13)Cr5 square pyramid, edges with two equivalent Se(4)Na2Cr3 square pyramids, and  an edgeedge with one Se(11)Na2Cr3 trigonal bipyramid. In the fifth Se site, Se(5) is bonded in a trigonal planar geometry to one Cr(3) and two equivalent Cr(1) atoms. In the sixth Se site, Se(6) is bonded to one Cr(4), two equivalent Cr(6), and two equivalent Cr(7) atoms to form distorted SeCr5 square pyramids that share corners with two equivalent Se(13)Cr5 square pyramids,  a cornercorner with one Se(7)NaCr3 trigonal pyramid, corners with two equivalent Se(15)NaCr3 trigonal pyramids,  an edgeedge with one Se(13)Cr5 square pyramid, edges with two equivalent Se(6)Cr5 square pyramids, edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids, and  an edgeedge with one Se(15)NaCr3 trigonal pyramid. In the seventh Se site, Se(7) is bonded to one Na(1), one Cr(4), and two equivalent Cr(2) atoms to form SeNaCr3 trigonal pyramids that share  a cornercorner with one Se(6)Cr5 square pyramid, corners with two equivalent Se(1)Cr5 square pyramids, corners with two equivalent Se(4)Na2Cr3 square pyramids, corners with two equivalent Se(23)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(7)NaCr3 trigonal pyramids,  an edgeedge with one Se(1)Cr5 square pyramid, and edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids. In the eighth Se site, Se(8) is bonded in a rectangular see-saw-like geometry to one Na(2), one Cr(5), and two equivalent Cr(8) atoms. In the ninth Se site, Se(9) is bonded in a rectangular see-saw-like geometry to one Cr(5), one Cr(6), and two equivalent Cr(3) atoms. In the tenth Se site, Se(10) is bonded in a rectangular see-saw-like geometry to one Cr(6), one Cr(7), and two equivalent Cr(9) atoms. In the eleventh Se site, Se(11) is bonded to two equivalent Na(1), one Cr(7), and two equivalent Cr(4) atoms to form distorted SeNa2Cr3 trigonal bipyramids that share corners with two equivalent Se(4)Na2Cr3 square pyramids, corners with two equivalent Se(15)NaCr3 trigonal pyramids,  an edgeedge with one Se(4)Na2Cr3 square pyramid, edges with two equivalent Se(6)Cr5 square pyramids, edges with two equivalent Se(11)Na2Cr3 trigonal bipyramids, and edges with two equivalent Se(7)NaCr3 trigonal pyramids. In the twelfth Se site, Se(12) is bonded to one Na(3), two equivalent Na(2), one Cr(8), and two equivalent Cr(10) atoms to form SeNa3Cr3 octahedra that share corners with two equivalent Se(21)Na3Cr3 pentagonal pyramids,  a cornercorner with one Se(13)Cr5 square pyramid, corners with two equivalent Se(15)NaCr3 trigonal pyramids, edges with two equivalent Se(12)Na3Cr3 octahedra, and edges with two equivalent Se(16)Na3Cr3 octahedra. In the thirteenth Se site, Se(13) is bonded to one Cr(8), two equivalent Cr(5), and two equivalent Cr(6) atoms to form distorted SeCr5 square pyramids that share  a cornercorner with one Se(12)Na3Cr3 octahedra, corners with two equivalent Se(6)Cr5 square pyramids, corners with two equivalent Se(4)Na2Cr3 square pyramids,  an edgeedge with one Se(6)Cr5 square pyramid,  an edgeedge with one Se(4)Na2Cr3 square pyramid, and edges with two equivalent Se(13)Cr5 square pyramids. The corner-sharing octahedral tilt angles are 2°. In the fourteenth Se site, Se(14) is bonded in a distorted T-shaped geometry to one Cr(9) and two equivalent Cr(11) atoms. In the fifteenth Se site, Se(15) is bonded to one Na(2), one Cr(9), and two equivalent Cr(7) atoms to form SeNaCr3 trigonal pyramids that share corners with two equivalent Se(12)Na3Cr3 octahedra, corners with two equivalent Se(6)Cr5 square pyramids, corners with two equivalent Se(11)Na2Cr3 trigonal bipyramids, corners with two equivalent Se(15)NaCr3 trigonal pyramids, and  an edgeedge with one Se(6)Cr5 square pyramid. The corner-sharing octahedral tilt angles are 39°. In the sixteenth Se site, Se(16) is bonded to one Na(4), two equivalent Na(3), one Cr(10), and two equivalent Cr(12) atoms to form SeNa3Cr3 octahedra that share corners with two equivalent Se(21)Na3Cr3 pentagonal pyramids, corners with two equivalent Se(23)Na2Cr3 trigonal bipyramids, edges with two equivalent Se(12)Na3Cr3 octahedra, edges with two equivalent Se(16)Na3Cr3 octahedra, and  a faceface with one Se(21)Na3Cr3 pentagonal pyramid. In the seventeenth Se site, Se(17) is bonded in a distorted T-shaped geometry to one Cr(10) and two equivalent Cr(8) atoms. In the eighteenth Se site, Se(18) is bonded in a distorted T-shaped geometry to one Cr(11) and two equivalent Cr(13) atoms. In the nineteenth Se site, Se(19) is bonded in a 6-coordinate geometry to one Na(3), two equivalent Na(2), one Cr(11), and two equivalent Cr(9) atoms. In the twentieth Se site, Se(20) is bonded in a distorted T-shaped geometry to one Cr(12) and two equivalent Cr(10) atoms. In the twenty-first Se site, Se(21) is bonded to one Na(4), two equivalent Na(3), one Cr(13), and two equivalent Cr(11) atoms to form distorted SeNa3Cr3 pentagonal pyramids that share corners with two equivalent Se(12)Na3Cr3 octahedra, corners with two equivalent Se(16)Na3Cr3 octahedra,  a cornercorner with one Se(1)Cr5 square pyramid, edges with two equivalent Se(21)Na3Cr3 pentagonal pyramids, edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids, and  a faceface with one Se(16)Na3Cr3 octahedra. The corner-sharing octahedral tilt angles range from 41-44°. In the twenty-second Se site, Se(22) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(12) atoms. In the twenty-third Se site, Se(23) is bonded to two equivalent Na(4), one Cr(2), and two equivalent Cr(13) atoms to form distorted SeNa2Cr3 trigonal bipyramids that share corners with two equivalent Se(16)Na3Cr3 octahedra, corners with two equivalent Se(7)NaCr3 trigonal pyramids, edges with two equivalent Se(21)Na3Cr3 pentagonal pyramids, edges with two equivalent Se(1)Cr5 square pyramids, and edges with two equivalent Se(23)Na2Cr3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 42°. is represented by the CIF file [CIF]
data_Na4Cr13Se23
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   13.088
_cell_length_b   13.088
_cell_length_c   18.881
_cell_angle_alpha   85.466
_cell_angle_beta   85.466
_cell_angle_gamma   16.183
_symmetry_Int_Tables_number   1
_cell_volume   898.521
_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  0.499  0.499  0.723  1.0
  Na  Na1  1  0.499  0.499  0.395  1.0
  Na  Na2  1  0.999  0.999  0.223  1.0
  Na  Na3  1  0.497  0.497  0.051  1.0
  Cr  Cr4  1  0.745  0.745  0.914  1.0
  Cr  Cr5  1  0.866  0.866  0.901  1.0
  Cr  Cr6  1  0.138  0.138  0.767  1.0
  Cr  Cr7  1  0.361  0.361  0.743  1.0
  Cr  Cr8  1  0.633  0.633  0.600  1.0
  Cr  Cr9  1  0.750  0.750  0.584  1.0
  Cr  Cr10  1  0.867  0.867  0.565  1.0
  Cr  Cr11  1  0.139  0.139  0.426  1.0
  Cr  Cr12  1  0.361  0.361  0.405  1.0
  Cr  Cr13  1  0.639  0.639  0.261  1.0
  Cr  Cr14  1  0.859  0.859  0.238  1.0
  Cr  Cr15  1  0.144  0.144  0.099  1.0
  Cr  Cr16  1  0.361  0.361  0.074  1.0
  Se  Se17  1  0.305  0.305  0.965  1.0
  Se  Se18  1  0.585  0.585  0.820  1.0
  Se  Se19  1  0.806  0.806  0.801  1.0
  Se  Se20  1  0.083  0.083  0.660  1.0
  Se  Se21  1  0.194  0.194  0.871  1.0
  Se  Se22  1  0.306  0.306  0.632  1.0
  Se  Se23  1  0.418  0.418  0.843  1.0
  Se  Se24  1  0.585  0.585  0.491  1.0
  Se  Se25  1  0.692  0.692  0.700  1.0
  Se  Se26  1  0.807  0.807  0.466  1.0
  Se  Se27  1  0.913  0.913  0.678  1.0
  Se  Se28  1  0.082  0.082  0.323  1.0
  Se  Se29  1  0.194  0.194  0.534  1.0
  Se  Se30  1  0.308  0.308  0.299  1.0
  Se  Se31  1  0.418  0.418  0.510  1.0
  Se  Se32  1  0.582  0.582  0.147  1.0
  Se  Se33  1  0.691  0.691  0.365  1.0
  Se  Se34  1  0.808  0.808  0.133  1.0
  Se  Se35  1  0.916  0.916  0.345  1.0
  Se  Se36  1  0.192  0.192  0.203  1.0
  Se  Se37  1  0.417  0.417  0.176  1.0
  Se  Se38  1  0.689  0.689  0.034  1.0
  Se  Se39  1  0.916  0.916  0.009  1.0
[/CIF]
.