The material structure described by K3AlF6 crystallizes in the tetragonal I4/m space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to four equivalent F(4), four equivalent F(5), and four equivalent F(7) atoms to form KF12 cuboctahedra that share faces with two equivalent K(1)F12 cuboctahedra, faces with four equivalent Al(2)F6 octahedra, and faces with four equivalent K(4)F7 pentagonal bipyramids. In the second K site, K(2) is bonded in a 11-coordinate geometry to one F(1), one F(2), one F(4), one F(5), two equivalent F(3), two equivalent F(6), and three equivalent F(7) atoms. In the third K site, K(3) is bonded to two equivalent F(2) and four equivalent F(3) atoms to form KF6 octahedra that share corners with two equivalent Al(1)F6 octahedra and corners with four equivalent Al(2)F6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fourth K site, K(4) is bonded to one F(4), one F(5), one F(6), two equivalent F(1), and two equivalent F(7) atoms to form distorted KF7 pentagonal bipyramids that share corners with five equivalent Al(2)F6 octahedra, corners with two equivalent K(4)F7 pentagonal bipyramids,  an edgeedge with one Al(1)F6 octahedra, and faces with two equivalent K(1)F12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-14°. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent F(2) and four equivalent F(1) atoms to form AlF6 octahedra that share corners with two equivalent K(3)F6 octahedra and edges with four equivalent K(4)F7 pentagonal bipyramids. The corner-sharing octahedra are not tilted. In the second Al site, Al(2) is bonded to one F(3), one F(4), one F(5), one F(6), and two equivalent F(7) atoms to form AlF6 octahedra that share  a cornercorner with one K(3)F6 octahedra, corners with five equivalent K(4)F7 pentagonal bipyramids, and faces with two equivalent K(1)F12 cuboctahedra. The corner-sharing octahedral tilt angles are 4°. There are seven inequivalent F sites. In the first F site, F(1) is bonded in a distorted single-bond geometry to two equivalent K(2), two equivalent K(4), and one Al(1) atom. In the second F site, F(2) is bonded in a distorted linear geometry to one K(3), four equivalent K(2), and one Al(1) atom. In the third F site, F(3) is bonded in a 2-coordinate geometry to one K(3), four equivalent K(2), and one Al(2) atom. In the fourth F site, F(4) is bonded in a distorted single-bond geometry to one K(4), two equivalent K(1), two equivalent K(2), and one Al(2) atom. In the fifth F site, F(5) is bonded in a 1-coordinate geometry to one K(4), two equivalent K(1), two equivalent K(2), and one Al(2) atom. In the sixth F site, F(7) is bonded in a 6-coordinate geometry to one K(1), one K(4), three equivalent K(2), and one Al(2) atom. In the seventh F site, F(6) is bonded in a 1-coordinate geometry to one K(4), four equivalent K(2), and one Al(2) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K3AlF6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.560
_cell_length_b   10.293
_cell_length_c   10.294
_cell_angle_alpha   80.041
_cell_angle_beta   65.429
_cell_angle_gamma   65.432
_symmetry_Int_Tables_number   1
_cell_volume   750.178
_cell_formula_units_Z   5
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  0.250  0.500  0.500  1.0
  K  K1  1  0.750  0.500  0.500  1.0
  K  K2  1  0.511  0.321  0.108  1.0
  K  K3  1  0.941  0.679  0.892  1.0
  K  K4  1  0.833  0.108  0.679  1.0
  K  K5  1  0.620  0.891  0.321  1.0
  K  K6  1  0.489  0.679  0.892  1.0
  K  K7  1  0.059  0.321  0.108  1.0
  K  K8  1  0.167  0.892  0.321  1.0
  K  K9  1  0.380  0.109  0.679  1.0
  K  K10  1  0.500  0.000  0.000  1.0
  K  K11  1  0.088  0.649  0.175  1.0
  K  K12  1  0.912  0.351  0.825  1.0
  K  K13  1  0.737  0.175  0.351  1.0
  K  K14  1  0.263  0.825  0.649  1.0
  Al  Al15  1  0.000  0.000  0.000  1.0
  Al  Al16  1  0.593  0.603  0.212  1.0
  Al  Al17  1  0.407  0.397  0.788  1.0
  Al  Al18  1  0.196  0.212  0.397  1.0
  Al  Al19  1  0.804  0.788  0.603  1.0
  F  F20  1  0.876  0.186  0.062  1.0
  F  F21  1  0.124  0.814  0.938  1.0
  F  F22  1  0.062  0.062  0.814  1.0
  F  F23  1  0.938  0.938  0.186  1.0
  F  F24  1  0.790  1.000  1.000  1.0
  F  F25  1  0.210  0.000  0.000  1.0
  F  F26  1  0.548  0.776  0.128  1.0
  F  F27  1  0.452  0.224  0.872  1.0
  F  F28  1  0.323  0.128  0.224  1.0
  F  F29  1  0.677  0.872  0.776  1.0
  F  F30  1  0.462  0.692  0.385  1.0
  F  F31  1  0.538  0.308  0.615  1.0
  F  F32  1  0.153  0.385  0.308  1.0
  F  F33  1  0.847  0.615  0.692  1.0
  F  F34  1  0.636  0.433  0.296  1.0
  F  F35  1  0.364  0.567  0.704  1.0
  F  F36  1  0.068  0.296  0.567  1.0
  F  F37  1  0.932  0.704  0.433  1.0
  F  F38  1  0.722  0.521  0.035  1.0
  F  F39  1  0.278  0.479  0.965  1.0
  F  F40  1  0.243  0.035  0.479  1.0
  F  F41  1  0.757  0.965  0.521  1.0
  F  F42  1  0.382  0.603  0.208  1.0
  F  F43  1  0.193  0.396  0.792  1.0
  F  F44  1  0.985  0.208  0.396  1.0
  F  F45  1  0.590  0.792  0.604  1.0
  F  F46  1  0.618  0.397  0.792  1.0
  F  F47  1  0.807  0.604  0.208  1.0
  F  F48  1  0.015  0.792  0.604  1.0
  F  F49  1  0.410  0.208  0.396  1.0
[/CIF]
.
The material structure described by K3AlF6 crystallizes in the tetragonal I4/m space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to four equivalent F(4), four equivalent F(5), and four equivalent F(7) atoms to form KF12 cuboctahedra that share faces with two equivalent K(1)F12 cuboctahedra, faces with four equivalent Al(2)F6 octahedra, and faces with four equivalent K(4)F7 pentagonal bipyramids. In the second K site, K(2) is bonded in a 11-coordinate geometry to one F(1), one F(2), one F(4), one F(5), two equivalent F(3), two equivalent F(6), and three equivalent F(7) atoms. In the third K site, K(3) is bonded to two equivalent F(2) and four equivalent F(3) atoms to form KF6 octahedra that share corners with two equivalent Al(1)F6 octahedra and corners with four equivalent Al(2)F6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fourth K site, K(4) is bonded to one F(4), one F(5), one F(6), two equivalent F(1), and two equivalent F(7) atoms to form distorted KF7 pentagonal bipyramids that share corners with five equivalent Al(2)F6 octahedra, corners with two equivalent K(4)F7 pentagonal bipyramids,  an edgeedge with one Al(1)F6 octahedra, and faces with two equivalent K(1)F12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-14°. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent F(2) and four equivalent F(1) atoms to form AlF6 octahedra that share corners with two equivalent K(3)F6 octahedra and edges with four equivalent K(4)F7 pentagonal bipyramids. The corner-sharing octahedra are not tilted. In the second Al site, Al(2) is bonded to one F(3), one F(4), one F(5), one F(6), and two equivalent F(7) atoms to form AlF6 octahedra that share  a cornercorner with one K(3)F6 octahedra, corners with five equivalent K(4)F7 pentagonal bipyramids, and faces with two equivalent K(1)F12 cuboctahedra. The corner-sharing octahedral tilt angles are 4°. There are seven inequivalent F sites. In the first F site, F(1) is bonded in a distorted single-bond geometry to two equivalent K(2), two equivalent K(4), and one Al(1) atom. In the second F site, F(2) is bonded in a distorted linear geometry to one K(3), four equivalent K(2), and one Al(1) atom. In the third F site, F(3) is bonded in a 2-coordinate geometry to one K(3), four equivalent K(2), and one Al(2) atom. In the fourth F site, F(4) is bonded in a distorted single-bond geometry to one K(4), two equivalent K(1), two equivalent K(2), and one Al(2) atom. In the fifth F site, F(5) is bonded in a 1-coordinate geometry to one K(4), two equivalent K(1), two equivalent K(2), and one Al(2) atom. In the sixth F site, F(7) is bonded in a 6-coordinate geometry to one K(1), one K(4), three equivalent K(2), and one Al(2) atom. In the seventh F site, F(6) is bonded in a 1-coordinate geometry to one K(4), four equivalent K(2), and one Al(2) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K3AlF6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.560
_cell_length_b   10.293
_cell_length_c   10.294
_cell_angle_alpha   80.041
_cell_angle_beta   65.429
_cell_angle_gamma   65.432
_symmetry_Int_Tables_number   1
_cell_volume   750.178
_cell_formula_units_Z   5
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  0.250  0.500  0.500  1.0
  K  K1  1  0.750  0.500  0.500  1.0
  K  K2  1  0.511  0.321  0.108  1.0
  K  K3  1  0.941  0.679  0.892  1.0
  K  K4  1  0.833  0.108  0.679  1.0
  K  K5  1  0.620  0.891  0.321  1.0
  K  K6  1  0.489  0.679  0.892  1.0
  K  K7  1  0.059  0.321  0.108  1.0
  K  K8  1  0.167  0.892  0.321  1.0
  K  K9  1  0.380  0.109  0.679  1.0
  K  K10  1  0.500  0.000  0.000  1.0
  K  K11  1  0.088  0.649  0.175  1.0
  K  K12  1  0.912  0.351  0.825  1.0
  K  K13  1  0.737  0.175  0.351  1.0
  K  K14  1  0.263  0.825  0.649  1.0
  Al  Al15  1  0.000  0.000  0.000  1.0
  Al  Al16  1  0.593  0.603  0.212  1.0
  Al  Al17  1  0.407  0.397  0.788  1.0
  Al  Al18  1  0.196  0.212  0.397  1.0
  Al  Al19  1  0.804  0.788  0.603  1.0
  F  F20  1  0.876  0.186  0.062  1.0
  F  F21  1  0.124  0.814  0.938  1.0
  F  F22  1  0.062  0.062  0.814  1.0
  F  F23  1  0.938  0.938  0.186  1.0
  F  F24  1  0.790  1.000  1.000  1.0
  F  F25  1  0.210  0.000  0.000  1.0
  F  F26  1  0.548  0.776  0.128  1.0
  F  F27  1  0.452  0.224  0.872  1.0
  F  F28  1  0.323  0.128  0.224  1.0
  F  F29  1  0.677  0.872  0.776  1.0
  F  F30  1  0.462  0.692  0.385  1.0
  F  F31  1  0.538  0.308  0.615  1.0
  F  F32  1  0.153  0.385  0.308  1.0
  F  F33  1  0.847  0.615  0.692  1.0
  F  F34  1  0.636  0.433  0.296  1.0
  F  F35  1  0.364  0.567  0.704  1.0
  F  F36  1  0.068  0.296  0.567  1.0
  F  F37  1  0.932  0.704  0.433  1.0
  F  F38  1  0.722  0.521  0.035  1.0
  F  F39  1  0.278  0.479  0.965  1.0
  F  F40  1  0.243  0.035  0.479  1.0
  F  F41  1  0.757  0.965  0.521  1.0
  F  F42  1  0.382  0.603  0.208  1.0
  F  F43  1  0.193  0.396  0.792  1.0
  F  F44  1  0.985  0.208  0.396  1.0
  F  F45  1  0.590  0.792  0.604  1.0
  F  F46  1  0.618  0.397  0.792  1.0
  F  F47  1  0.807  0.604  0.208  1.0
  F  F48  1  0.015  0.792  0.604  1.0
  F  F49  1  0.410  0.208  0.396  1.0
[/CIF]
.