The crystal structure described by K4Nb15O24 crystallizes in the monoclinic C2/m space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to two equivalent O(6), two equivalent O(9), four equivalent O(2), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. In the second K site, K(2) is bonded to two equivalent O(4), two equivalent O(8), four equivalent O(2), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. In the third K site, K(3) is bonded to one O(4), one O(6), one O(8), one O(9), four equivalent O(1), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with two equivalent K(1)O12 cuboctahedra, corners with two equivalent K(2)O12 cuboctahedra,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. There are five inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(9) atom to form NbO5 square pyramids that share corners with two equivalent Nb(1)O5 square pyramids, corners with three equivalent Nb(3)O5 square pyramids,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, and faces with two equivalent K(3)O12 cuboctahedra. In the second Nb site, Nb(2) is bonded in a square co-planar geometry to one O(1), one O(2), one O(5), and one O(7) atom. In the third Nb site, Nb(3) is bonded to one O(1), one O(2), one O(3), one O(6), and one O(8) atom to form NbO5 square pyramids that share corners with two equivalent Nb(3)O5 square pyramids, corners with three equivalent Nb(1)O5 square pyramids,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, and faces with two equivalent K(3)O12 cuboctahedra. In the fourth Nb site, Nb(4) is bonded in a square co-planar geometry to two equivalent O(4) and two equivalent O(5) atoms. In the fifth Nb site, Nb(5) is bonded in a square co-planar geometry to one O(5), one O(6), one O(7), and one O(8) atom. There are nine inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to two equivalent K(3), one Nb(1), one Nb(2), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one K(1), one K(2), one Nb(1), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), two equivalent K(3), one Nb(1), and one Nb(3) atom. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one K(2), one K(3), one Nb(4), and two equivalent Nb(1) atoms. In the fifth O site, O(5) is bonded in a square co-planar geometry to one Nb(4), one Nb(5), and two equivalent Nb(2) atoms. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one K(1), one K(3), one Nb(5), and two equivalent Nb(3) atoms. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Nb(5) and two equivalent Nb(2) atoms. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one K(2), one K(3), one Nb(5), and two equivalent Nb(3) atoms. In the ninth O site, O(9) is bonded in a distorted linear geometry to one K(1), one K(3), and two equivalent Nb(1) atoms. is represented by the CIF file [CIF]
data_K4Nb15O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.342
_cell_length_b   9.342
_cell_length_c   9.415
_cell_angle_alpha   66.472
_cell_angle_beta   66.472
_cell_angle_gamma   52.585
_symmetry_Int_Tables_number   1
_cell_volume   584.390
_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  0.000  0.000  0.000  1.0
  K  K1  1  0.500  0.500  0.000  1.0
  K  K2  1  0.748  0.748  0.003  1.0
  K  K3  1  0.252  0.252  0.997  1.0
  Nb  Nb4  1  0.826  0.308  0.232  1.0
  Nb  Nb5  1  0.883  0.370  0.500  1.0
  Nb  Nb6  1  0.937  0.438  0.751  1.0
  Nb  Nb7  1  0.500  0.500  0.500  1.0
  Nb  Nb8  1  0.747  0.747  0.500  1.0
  Nb  Nb9  1  0.308  0.826  0.232  1.0
  Nb  Nb10  1  0.562  0.063  0.249  1.0
  Nb  Nb11  1  0.370  0.883  0.500  1.0
  Nb  Nb12  1  0.630  0.117  0.500  1.0
  Nb  Nb13  1  0.438  0.937  0.751  1.0
  Nb  Nb14  1  0.692  0.174  0.768  1.0
  Nb  Nb15  1  0.253  0.253  0.500  1.0
  Nb  Nb16  1  0.063  0.562  0.249  1.0
  Nb  Nb17  1  0.117  0.630  0.500  1.0
  Nb  Nb18  1  0.174  0.692  0.768  1.0
  O  O19  1  0.940  0.434  0.248  1.0
  O  O20  1  0.814  0.308  0.753  1.0
  O  O21  1  0.870  0.379  0.001  1.0
  O  O22  1  0.563  0.563  0.247  1.0
  O  O23  1  0.624  0.624  0.500  1.0
  O  O24  1  0.812  0.812  0.247  1.0
  O  O25  1  0.874  0.874  0.500  1.0
  O  O26  1  0.686  0.686  0.752  1.0
  O  O27  1  0.935  0.935  0.760  1.0
  O  O28  1  0.379  0.870  0.001  1.0
  O  O29  1  0.621  0.130  0.999  1.0
  O  O30  1  0.434  0.940  0.248  1.0
  O  O31  1  0.692  0.186  0.247  1.0
  O  O32  1  0.308  0.814  0.753  1.0
  O  O33  1  0.566  0.060  0.752  1.0
  O  O34  1  0.188  0.188  0.753  1.0
  O  O35  1  0.437  0.437  0.753  1.0
  O  O36  1  0.065  0.065  0.240  1.0
  O  O37  1  0.126  0.126  0.500  1.0
  O  O38  1  0.314  0.314  0.248  1.0
  O  O39  1  0.376  0.376  0.500  1.0
  O  O40  1  0.060  0.566  0.752  1.0
  O  O41  1  0.186  0.692  0.247  1.0
  O  O42  1  0.130  0.621  0.999  1.0
[/CIF]
.
The crystal structure described by K4Nb15O24 crystallizes in the monoclinic C2/m space group. There are three inequivalent K sites. In the first K site, K(1) is bonded to two equivalent O(6), two equivalent O(9), four equivalent O(2), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. In the second K site, K(2) is bonded to two equivalent O(4), two equivalent O(8), four equivalent O(2), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. In the third K site, K(3) is bonded to one O(4), one O(6), one O(8), one O(9), four equivalent O(1), and four equivalent O(3) atoms to form KO12 cuboctahedra that share corners with two equivalent K(1)O12 cuboctahedra, corners with two equivalent K(2)O12 cuboctahedra,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with four equivalent Nb(1)O5 square pyramids, and faces with four equivalent Nb(3)O5 square pyramids. There are five inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(9) atom to form NbO5 square pyramids that share corners with two equivalent Nb(1)O5 square pyramids, corners with three equivalent Nb(3)O5 square pyramids,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, and faces with two equivalent K(3)O12 cuboctahedra. In the second Nb site, Nb(2) is bonded in a square co-planar geometry to one O(1), one O(2), one O(5), and one O(7) atom. In the third Nb site, Nb(3) is bonded to one O(1), one O(2), one O(3), one O(6), and one O(8) atom to form NbO5 square pyramids that share corners with two equivalent Nb(3)O5 square pyramids, corners with three equivalent Nb(1)O5 square pyramids,  a faceface with one K(1)O12 cuboctahedra,  a faceface with one K(2)O12 cuboctahedra, and faces with two equivalent K(3)O12 cuboctahedra. In the fourth Nb site, Nb(4) is bonded in a square co-planar geometry to two equivalent O(4) and two equivalent O(5) atoms. In the fifth Nb site, Nb(5) is bonded in a square co-planar geometry to one O(5), one O(6), one O(7), and one O(8) atom. There are nine inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to two equivalent K(3), one Nb(1), one Nb(2), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one K(1), one K(2), one Nb(1), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted linear geometry to one K(1), one K(2), two equivalent K(3), one Nb(1), and one Nb(3) atom. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one K(2), one K(3), one Nb(4), and two equivalent Nb(1) atoms. In the fifth O site, O(5) is bonded in a square co-planar geometry to one Nb(4), one Nb(5), and two equivalent Nb(2) atoms. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one K(1), one K(3), one Nb(5), and two equivalent Nb(3) atoms. In the seventh O site, O(7) is bonded in a T-shaped geometry to one Nb(5) and two equivalent Nb(2) atoms. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one K(2), one K(3), one Nb(5), and two equivalent Nb(3) atoms. In the ninth O site, O(9) is bonded in a distorted linear geometry to one K(1), one K(3), and two equivalent Nb(1) atoms. is represented by the CIF file [CIF]
data_K4Nb15O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.342
_cell_length_b   9.342
_cell_length_c   9.415
_cell_angle_alpha   66.472
_cell_angle_beta   66.472
_cell_angle_gamma   52.585
_symmetry_Int_Tables_number   1
_cell_volume   584.390
_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  0.000  0.000  0.000  1.0
  K  K1  1  0.500  0.500  0.000  1.0
  K  K2  1  0.748  0.748  0.003  1.0
  K  K3  1  0.252  0.252  0.997  1.0
  Nb  Nb4  1  0.826  0.308  0.232  1.0
  Nb  Nb5  1  0.883  0.370  0.500  1.0
  Nb  Nb6  1  0.937  0.438  0.751  1.0
  Nb  Nb7  1  0.500  0.500  0.500  1.0
  Nb  Nb8  1  0.747  0.747  0.500  1.0
  Nb  Nb9  1  0.308  0.826  0.232  1.0
  Nb  Nb10  1  0.562  0.063  0.249  1.0
  Nb  Nb11  1  0.370  0.883  0.500  1.0
  Nb  Nb12  1  0.630  0.117  0.500  1.0
  Nb  Nb13  1  0.438  0.937  0.751  1.0
  Nb  Nb14  1  0.692  0.174  0.768  1.0
  Nb  Nb15  1  0.253  0.253  0.500  1.0
  Nb  Nb16  1  0.063  0.562  0.249  1.0
  Nb  Nb17  1  0.117  0.630  0.500  1.0
  Nb  Nb18  1  0.174  0.692  0.768  1.0
  O  O19  1  0.940  0.434  0.248  1.0
  O  O20  1  0.814  0.308  0.753  1.0
  O  O21  1  0.870  0.379  0.001  1.0
  O  O22  1  0.563  0.563  0.247  1.0
  O  O23  1  0.624  0.624  0.500  1.0
  O  O24  1  0.812  0.812  0.247  1.0
  O  O25  1  0.874  0.874  0.500  1.0
  O  O26  1  0.686  0.686  0.752  1.0
  O  O27  1  0.935  0.935  0.760  1.0
  O  O28  1  0.379  0.870  0.001  1.0
  O  O29  1  0.621  0.130  0.999  1.0
  O  O30  1  0.434  0.940  0.248  1.0
  O  O31  1  0.692  0.186  0.247  1.0
  O  O32  1  0.308  0.814  0.753  1.0
  O  O33  1  0.566  0.060  0.752  1.0
  O  O34  1  0.188  0.188  0.753  1.0
  O  O35  1  0.437  0.437  0.753  1.0
  O  O36  1  0.065  0.065  0.240  1.0
  O  O37  1  0.126  0.126  0.500  1.0
  O  O38  1  0.314  0.314  0.248  1.0
  O  O39  1  0.376  0.376  0.500  1.0
  O  O40  1  0.060  0.566  0.752  1.0
  O  O41  1  0.186  0.692  0.247  1.0
  O  O42  1  0.130  0.621  0.999  1.0
[/CIF]
.