The crystal structure described by NaCr6O11 crystallizes in the hexagonal P6_3/mmc space group. Na(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form NaO12 cuboctahedra that share corners with six equivalent Na(1)O12 cuboctahedra, edges with six equivalent Cr(1)O6 octahedra, edges with three equivalent Cr(2)O5 trigonal bipyramids, and faces with six equivalent Cr(3)O6 octahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(2)O5 trigonal bipyramids, edges with two equivalent Na(1)O12 cuboctahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the second Cr site, Cr(2) is bonded to two equivalent O(3) and three equivalent O(1) atoms to form CrO5 trigonal bipyramids that share corners with six equivalent Cr(1)O6 octahedra, corners with six equivalent Cr(3)O6 octahedra, and edges with three equivalent Na(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 41-56°. In the third Cr site, Cr(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form CrO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O5 trigonal bipyramids, faces with three equivalent Na(1)O12 cuboctahedra, and  a faceface with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(1), one Cr(2), and two equivalent Cr(3) atoms. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Na(1), one Cr(3), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Cr(2) and three equivalent Cr(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaCr6O11
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.824
_cell_length_b   5.824
_cell_length_c   13.000
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   381.883
_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  0.333  0.667  0.250  1.0
  Na  Na1  1  0.667  0.333  0.750  1.0
  Cr  Cr2  1  0.000  0.500  0.000  1.0
  Cr  Cr3  1  0.333  0.667  0.750  1.0
  Cr  Cr4  1  0.000  0.000  0.146  1.0
  Cr  Cr5  1  0.000  0.000  0.354  1.0
  Cr  Cr6  1  0.000  0.000  0.646  1.0
  Cr  Cr7  1  0.000  0.000  0.854  1.0
  Cr  Cr8  1  0.500  0.000  0.000  1.0
  Cr  Cr9  1  0.500  0.500  0.000  1.0
  Cr  Cr10  1  0.500  0.500  0.500  1.0
  Cr  Cr11  1  0.667  0.333  0.250  1.0
  Cr  Cr12  1  0.500  0.000  0.500  1.0
  Cr  Cr13  1  0.000  0.500  0.500  1.0
  O  O14  1  0.154  0.846  0.750  1.0
  O  O15  1  0.176  0.824  0.422  1.0
  O  O16  1  0.176  0.824  0.078  1.0
  O  O17  1  0.333  0.667  0.913  1.0
  O  O18  1  0.333  0.667  0.587  1.0
  O  O19  1  0.154  0.309  0.750  1.0
  O  O20  1  0.176  0.351  0.422  1.0
  O  O21  1  0.176  0.351  0.078  1.0
  O  O22  1  0.309  0.154  0.250  1.0
  O  O23  1  0.649  0.824  0.078  1.0
  O  O24  1  0.649  0.824  0.422  1.0
  O  O25  1  0.351  0.176  0.922  1.0
  O  O26  1  0.351  0.176  0.578  1.0
  O  O27  1  0.691  0.846  0.750  1.0
  O  O28  1  0.846  0.691  0.250  1.0
  O  O29  1  0.667  0.333  0.087  1.0
  O  O30  1  0.824  0.649  0.578  1.0
  O  O31  1  0.667  0.333  0.413  1.0
  O  O32  1  0.824  0.649  0.922  1.0
  O  O33  1  0.824  0.176  0.578  1.0
  O  O34  1  0.824  0.176  0.922  1.0
  O  O35  1  0.846  0.154  0.250  1.0
[/CIF]
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The crystal structure described by NaCr6O11 crystallizes in the hexagonal P6_3/mmc space group. Na(1) is bonded to six equivalent O(1) and six equivalent O(2) atoms to form NaO12 cuboctahedra that share corners with six equivalent Na(1)O12 cuboctahedra, edges with six equivalent Cr(1)O6 octahedra, edges with three equivalent Cr(2)O5 trigonal bipyramids, and faces with six equivalent Cr(3)O6 octahedra. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and four equivalent O(2) atoms to form CrO6 octahedra that share corners with four equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(2)O5 trigonal bipyramids, edges with two equivalent Na(1)O12 cuboctahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the second Cr site, Cr(2) is bonded to two equivalent O(3) and three equivalent O(1) atoms to form CrO5 trigonal bipyramids that share corners with six equivalent Cr(1)O6 octahedra, corners with six equivalent Cr(3)O6 octahedra, and edges with three equivalent Na(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 41-56°. In the third Cr site, Cr(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form CrO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O5 trigonal bipyramids, faces with three equivalent Na(1)O12 cuboctahedra, and  a faceface with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to two equivalent Na(1), one Cr(2), and two equivalent Cr(3) atoms. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Na(1), one Cr(3), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Cr(2) and three equivalent Cr(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaCr6O11
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.824
_cell_length_b   5.824
_cell_length_c   13.000
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   381.883
_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  0.333  0.667  0.250  1.0
  Na  Na1  1  0.667  0.333  0.750  1.0
  Cr  Cr2  1  0.000  0.500  0.000  1.0
  Cr  Cr3  1  0.333  0.667  0.750  1.0
  Cr  Cr4  1  0.000  0.000  0.146  1.0
  Cr  Cr5  1  0.000  0.000  0.354  1.0
  Cr  Cr6  1  0.000  0.000  0.646  1.0
  Cr  Cr7  1  0.000  0.000  0.854  1.0
  Cr  Cr8  1  0.500  0.000  0.000  1.0
  Cr  Cr9  1  0.500  0.500  0.000  1.0
  Cr  Cr10  1  0.500  0.500  0.500  1.0
  Cr  Cr11  1  0.667  0.333  0.250  1.0
  Cr  Cr12  1  0.500  0.000  0.500  1.0
  Cr  Cr13  1  0.000  0.500  0.500  1.0
  O  O14  1  0.154  0.846  0.750  1.0
  O  O15  1  0.176  0.824  0.422  1.0
  O  O16  1  0.176  0.824  0.078  1.0
  O  O17  1  0.333  0.667  0.913  1.0
  O  O18  1  0.333  0.667  0.587  1.0
  O  O19  1  0.154  0.309  0.750  1.0
  O  O20  1  0.176  0.351  0.422  1.0
  O  O21  1  0.176  0.351  0.078  1.0
  O  O22  1  0.309  0.154  0.250  1.0
  O  O23  1  0.649  0.824  0.078  1.0
  O  O24  1  0.649  0.824  0.422  1.0
  O  O25  1  0.351  0.176  0.922  1.0
  O  O26  1  0.351  0.176  0.578  1.0
  O  O27  1  0.691  0.846  0.750  1.0
  O  O28  1  0.846  0.691  0.250  1.0
  O  O29  1  0.667  0.333  0.087  1.0
  O  O30  1  0.824  0.649  0.578  1.0
  O  O31  1  0.667  0.333  0.413  1.0
  O  O32  1  0.824  0.649  0.922  1.0
  O  O33  1  0.824  0.176  0.578  1.0
  O  O34  1  0.824  0.176  0.922  1.0
  O  O35  1  0.846  0.154  0.250  1.0
[/CIF]
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