The compound described by K7Nb(SO4)6 crystallizes in the trigonal R-3 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded to six equivalent O(4) atoms to form KO6 octahedra that share corners with six equivalent S(1)O4 tetrahedra and edges with six equivalent K(2)O6 octahedra. In the second K site, K(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent K(2)O6 octahedra, corners with six equivalent S(1)O4 tetrahedra,  an edgeedge with one K(1)O6 octahedra, and edges with two equivalent K(2)O6 octahedra. The corner-sharing octahedral tilt angles are 77°. Nb(1) is bonded to six equivalent O(3) atoms to form NbO6 octahedra that share corners with six equivalent S(1)O4 tetrahedra. S(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one Nb(1)O6 octahedra, and corners with six equivalent K(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-65°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to two equivalent K(2) and one S(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to two equivalent K(2) and one S(1) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Nb(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one K(1), two equivalent K(2), and one S(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K7Nb(SO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.465
_cell_length_b   9.465
_cell_length_c   9.465
_cell_angle_alpha   109.447
_cell_angle_beta   109.447
_cell_angle_gamma   109.447
_symmetry_Int_Tables_number   1
_cell_volume   653.252
_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
  K  K0  1  0.500  0.500  0.500  1.0
  K  K1  1  0.837  0.335  0.678  1.0
  K  K2  1  0.335  0.678  0.837  1.0
  K  K3  1  0.678  0.837  0.335  1.0
  K  K4  1  0.163  0.665  0.322  1.0
  K  K5  1  0.665  0.322  0.163  1.0
  K  K6  1  0.322  0.163  0.665  1.0
  Nb  Nb7  1  0.000  0.000  0.000  1.0
  S  S8  1  0.968  0.745  0.618  1.0
  S  S9  1  0.745  0.618  0.968  1.0
  S  S10  1  0.618  0.968  0.745  1.0
  S  S11  1  0.032  0.255  0.382  1.0
  S  S12  1  0.255  0.382  0.032  1.0
  S  S13  1  0.382  0.032  0.255  1.0
  O  O14  1  0.428  0.910  0.166  1.0
  O  O15  1  0.910  0.166  0.428  1.0
  O  O16  1  0.166  0.428  0.910  1.0
  O  O17  1  0.572  0.090  0.834  1.0
  O  O18  1  0.090  0.834  0.572  1.0
  O  O19  1  0.834  0.572  0.090  1.0
  O  O20  1  0.314  0.985  0.361  1.0
  O  O21  1  0.985  0.361  0.314  1.0
  O  O22  1  0.361  0.314  0.985  1.0
  O  O23  1  0.686  0.015  0.639  1.0
  O  O24  1  0.015  0.639  0.686  1.0
  O  O25  1  0.639  0.686  0.015  1.0
  O  O26  1  0.767  0.978  0.892  1.0
  O  O27  1  0.978  0.892  0.767  1.0
  O  O28  1  0.647  0.475  0.787  1.0
  O  O29  1  0.787  0.647  0.475  1.0
  O  O30  1  0.475  0.787  0.647  1.0
  O  O31  1  0.353  0.525  0.213  1.0
  O  O32  1  0.213  0.353  0.525  1.0
  O  O33  1  0.525  0.213  0.353  1.0
  O  O34  1  0.108  0.233  0.022  1.0
  O  O35  1  0.022  0.108  0.233  1.0
  O  O36  1  0.233  0.022  0.108  1.0
  O  O37  1  0.892  0.767  0.978  1.0
[/CIF]
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The compound described by K7Nb(SO4)6 crystallizes in the trigonal R-3 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded to six equivalent O(4) atoms to form KO6 octahedra that share corners with six equivalent S(1)O4 tetrahedra and edges with six equivalent K(2)O6 octahedra. In the second K site, K(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form KO6 octahedra that share corners with two equivalent K(2)O6 octahedra, corners with six equivalent S(1)O4 tetrahedra,  an edgeedge with one K(1)O6 octahedra, and edges with two equivalent K(2)O6 octahedra. The corner-sharing octahedral tilt angles are 77°. Nb(1) is bonded to six equivalent O(3) atoms to form NbO6 octahedra that share corners with six equivalent S(1)O4 tetrahedra. S(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form SO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one Nb(1)O6 octahedra, and corners with six equivalent K(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-65°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted single-bond geometry to two equivalent K(2) and one S(1) atom. In the second O site, O(2) is bonded in a distorted single-bond geometry to two equivalent K(2) and one S(1) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Nb(1) and one S(1) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one K(1), two equivalent K(2), and one S(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K7Nb(SO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.465
_cell_length_b   9.465
_cell_length_c   9.465
_cell_angle_alpha   109.447
_cell_angle_beta   109.447
_cell_angle_gamma   109.447
_symmetry_Int_Tables_number   1
_cell_volume   653.252
_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
  K  K0  1  0.500  0.500  0.500  1.0
  K  K1  1  0.837  0.335  0.678  1.0
  K  K2  1  0.335  0.678  0.837  1.0
  K  K3  1  0.678  0.837  0.335  1.0
  K  K4  1  0.163  0.665  0.322  1.0
  K  K5  1  0.665  0.322  0.163  1.0
  K  K6  1  0.322  0.163  0.665  1.0
  Nb  Nb7  1  0.000  0.000  0.000  1.0
  S  S8  1  0.968  0.745  0.618  1.0
  S  S9  1  0.745  0.618  0.968  1.0
  S  S10  1  0.618  0.968  0.745  1.0
  S  S11  1  0.032  0.255  0.382  1.0
  S  S12  1  0.255  0.382  0.032  1.0
  S  S13  1  0.382  0.032  0.255  1.0
  O  O14  1  0.428  0.910  0.166  1.0
  O  O15  1  0.910  0.166  0.428  1.0
  O  O16  1  0.166  0.428  0.910  1.0
  O  O17  1  0.572  0.090  0.834  1.0
  O  O18  1  0.090  0.834  0.572  1.0
  O  O19  1  0.834  0.572  0.090  1.0
  O  O20  1  0.314  0.985  0.361  1.0
  O  O21  1  0.985  0.361  0.314  1.0
  O  O22  1  0.361  0.314  0.985  1.0
  O  O23  1  0.686  0.015  0.639  1.0
  O  O24  1  0.015  0.639  0.686  1.0
  O  O25  1  0.639  0.686  0.015  1.0
  O  O26  1  0.767  0.978  0.892  1.0
  O  O27  1  0.978  0.892  0.767  1.0
  O  O28  1  0.647  0.475  0.787  1.0
  O  O29  1  0.787  0.647  0.475  1.0
  O  O30  1  0.475  0.787  0.647  1.0
  O  O31  1  0.353  0.525  0.213  1.0
  O  O32  1  0.213  0.353  0.525  1.0
  O  O33  1  0.525  0.213  0.353  1.0
  O  O34  1  0.108  0.233  0.022  1.0
  O  O35  1  0.022  0.108  0.233  1.0
  O  O36  1  0.233  0.022  0.108  1.0
  O  O37  1  0.892  0.767  0.978  1.0
[/CIF]
.