The crystal structure described by K4NaNb5O15 crystallizes in the monoclinic Pm space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded to one O(2), one O(3), two equivalent O(13), two equivalent O(17), two equivalent O(23), two equivalent O(27), and two equivalent O(8) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(2)O12 cuboctahedra, corners with two equivalent K(1)O12 cuboctahedra, corners with four equivalent K(5)O12 cuboctahedra, corners with four equivalent K(6)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent Nb(7)O6 octahedra, faces with two equivalent Nb(8)O6 octahedra, and faces with four equivalent Nb(3)O6 octahedra. In the second K site, K(2) is bonded to one O(3), one O(4), two equivalent O(14), two equivalent O(18), two equivalent O(24), two equivalent O(28), and two equivalent O(9) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(1)O12 cuboctahedra,  a cornercorner with one K(3)O12 cuboctahedra, corners with two equivalent K(2)O12 cuboctahedra, corners with four equivalent K(6)O12 cuboctahedra, corners with four equivalent K(7)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent Nb(8)O6 octahedra, faces with two equivalent Nb(9)O6 octahedra, and faces with four equivalent Nb(4)O6 octahedra. In the third K site, K(3) is bonded to one O(4), one O(5), two equivalent O(10), two equivalent O(15), two equivalent O(19), two equivalent O(25), and two equivalent O(29) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(2)O12 cuboctahedra, corners with two equivalent K(3)O12 cuboctahedra, corners with four equivalent K(7)O12 cuboctahedra, corners with four equivalent K(8)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, faces with two equivalent Nb(10)O6 octahedra, faces with two equivalent Nb(9)O6 octahedra, and faces with four equivalent Nb(5)O6 octahedra. In the fourth K site, K(4) is bonded to one O(6), one O(7), two equivalent O(1), two equivalent O(11), two equivalent O(16), two equivalent O(21), and two equivalent O(26) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(5)O12 cuboctahedra,  a cornercorner with one K(8)O12 cuboctahedra, corners with two equivalent K(4)O12 cuboctahedra, faces with two equivalent K(4)O12 cuboctahedra, faces with two equivalent Nb(1)O6 octahedra, faces with two equivalent Nb(2)O6 octahedra, and faces with four equivalent Nb(6)O6 octahedra. In the fifth K site, K(5) is bonded to one O(7), one O(8), two equivalent O(12), two equivalent O(17), two equivalent O(2), two equivalent O(22), and two equivalent O(27) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(4)O12 cuboctahedra,  a cornercorner with one K(6)O12 cuboctahedra, corners with two equivalent K(5)O12 cuboctahedra, corners with four equivalent K(1)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent Nb(2)O6 octahedra, faces with two equivalent Nb(3)O6 octahedra, and faces with four equivalent Nb(7)O6 octahedra. In the sixth K site, K(6) is bonded to one O(8), one O(9), two equivalent O(13), two equivalent O(18), two equivalent O(23), two equivalent O(28), and two equivalent O(3) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(5)O12 cuboctahedra,  a cornercorner with one K(7)O12 cuboctahedra, corners with two equivalent K(6)O12 cuboctahedra, corners with four equivalent K(1)O12 cuboctahedra, corners with four equivalent K(2)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent Nb(3)O6 octahedra, faces with two equivalent Nb(4)O6 octahedra, and faces with four equivalent Nb(8)O6 octahedra. In the seventh K site, K(7) is bonded to one O(10), one O(9), two equivalent O(14), two equivalent O(19), two equivalent O(24), two equivalent O(29), and two equivalent O(4) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(6)O12 cuboctahedra,  a cornercorner with one K(8)O12 cuboctahedra, corners with two equivalent K(7)O12 cuboctahedra, corners with four equivalent K(2)O12 cuboctahedra, 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 two equivalent K(7)O12 cuboctahedra, faces with two equivalent Nb(4)O6 octahedra, faces with two equivalent Nb(5)O6 octahedra, and faces with four equivalent Nb(9)O6 octahedra. In the eighth K site, K(8) is bonded to one O(10), one O(6), two equivalent O(15), two equivalent O(20), two equivalent O(25), two equivalent O(30), and two equivalent O(5) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(4)O12 cuboctahedra,  a cornercorner with one K(7)O12 cuboctahedra, corners with two equivalent K(8)O12 cuboctahedra, corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, faces with two equivalent Nb(1)O6 octahedra, faces with two equivalent Nb(5)O6 octahedra, and faces with four equivalent Nb(10)O6 octahedra. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 8-coordinate geometry to one O(1), one O(6), two equivalent O(11), two equivalent O(21), and two equivalent O(30) atoms. In the second Na site, Na(2) is bonded in a 8-coordinate geometry to one O(2), one O(7), two equivalent O(12), two equivalent O(22), and two equivalent O(26) atoms. There are ten inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(11), one O(20), one O(21), one O(30), and two equivalent O(6) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, faces with two equivalent K(4)O12 cuboctahedra, and faces with two equivalent K(8)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the second Nb site, Nb(2) is bonded to one O(12), one O(16), one O(22), one O(26), and two equivalent O(7) atoms to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, faces with two equivalent K(4)O12 cuboctahedra, and faces with two equivalent K(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-18°. In the third Nb site, Nb(3) is bonded to one O(13), one O(17), one O(23), one O(27), and two equivalent O(8) atoms to form NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, and faces with four equivalent K(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-14°. In the fourth Nb site, Nb(4) is bonded to one O(14), one O(18), one O(24), one O(28), and two equivalent O(9) atoms to form NbO6 octahedra that share corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the fifth Nb site, Nb(5) is bonded to one O(15), one O(19), one O(25), one O(29), and two equivalent O(10) atoms to form NbO6 octahedra that share corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, and faces with four equivalent K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the sixth Nb site, Nb(6) is bonded to one O(11), one O(16), one O(21), one O(26), and two equivalent O(1) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, and faces with four equivalent K(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the seventh Nb site, Nb(7) is bonded to one O(12), one O(17), one O(22), one O(27), and two equivalent O(2) atoms to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, faces with two equivalent K(1)O12 cuboctahedra, and faces with four equivalent K(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-16°. In the eighth Nb site, Nb(8) is bonded to one O(13), one O(18), one O(23), one O(28), and two equivalent O(3) atoms to form NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, and faces with four equivalent K(6)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the ninth Nb site, Nb(9) is bonded to one O(14), one O(19), one O(24), one O(29), and two equivalent O(4) atoms to form NbO6 octahedra that share corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, and faces with four equivalent K(7)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the tenth Nb site, Nb(10) is bonded to one O(15), one O(20), one O(25), one O(30), and two equivalent O(5) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, faces with two equivalent K(3)O12 cuboctahedra, and faces with four equivalent K(8)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-18°. There are thirty inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent K(4), one Na(1), and two equivalent Nb(6) atoms. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(5), one Na(2), and two equivalent Nb(7) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one K(1), one K(2), two equivalent K(6), and two equivalent Nb(8) atoms. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(2), one K(3), two equivalent K(7), and two equivalent Nb(9) atoms. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(8), and two equivalent Nb(10) atoms. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(4), one K(8), one Na(1), and two equivalent Nb(1) atoms. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one K(4), one K(5), one Na(2), and two equivalent Nb(2) atoms. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one K(5), one K(6), two equivalent K(1), and two equivalent Nb(3) atoms. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to one K(6), one K(7), two equivalent K(2), and two equivalent Nb(4) atoms. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one K(7), one K(8), two equivalent K(3), and two equivalent Nb(5) atoms. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to two equivalent K(4), two equivalent Na(1), one Nb(1), and one Nb(6) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to two equivalent K(5), two equivalent Na(2), one Nb(2), and one Nb(7) atom. In the thirteenth O site, O(13) is bonded in a 6-coordinate geometry to two equivalent K(1), two equivalent K(6), one Nb(3), and one Nb(8) atom. In the fourteenth O site, O(14) is bonded in a 6-coordinate geometry to two equivalent K(2), two equivalent K(7), one Nb(4), and one Nb(9) atom. In the fifteenth O site, O(15) is bonded in a 6-coordinate geometry to two equivalent K(3), two equivalent K(8), one Nb(10), and one Nb(5) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(4), one Nb(2), and one Nb(6) atom. In the seventeenth O site, O(17) is bonded in a 6-coordinate geometry to two equivalent K(1), two equivalent K(5), one Nb(3), and one Nb(7) atom. In the eighteenth O site, O(18) is bonded in a 6-coordinate geometry to two equivalent K(2), two equivalent K(6), one Nb(4), and one Nb(8) atom. In the nineteenth O site, O(19) is bonded in a 6-coordinate geometry to two equivalent K(3), two equivalent K(7), one Nb(5), and one Nb(9) atom. In the twentieth O site, O(20) is bonded in a 4-coordinate geometry to two equivalent K(8), one Nb(1), and one Nb(10) atom. In the twenty-first O site, O(21) is bonded to two equivalent K(4), two equivalent Na(1), one Nb(1), and one Nb(6) atom to form distorted edge-sharing OK2Na2Nb2 octahedra. In the twenty-second O site, O(22) is bonded to two equivalent K(5), two equivalent Na(2), one Nb(2), and one Nb(7) atom to form distorted OK2Na2Nb2 octahedra that share corners with two equivalent O(27)K4Nb2 octahedra, edges with two equivalent O(22)K2Na2Nb2 octahedra, and  a faceface with one O(27)K4Nb2 octahedra. The corner-sharing octahedral tilt angles are 60°. In the twenty-third O site, O(23) is bonded to two equivalent K(1), two equivalent K(6), one Nb(3), and one Nb(8) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-fourth O site, O(24) is bonded to two equivalent K(2), two equivalent K(7), one Nb(4), and one Nb(9) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-fifth O site, O(25) is bonded to two equivalent K(3), two equivalent K(8), one Nb(10), and one Nb(5) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles are 59°. In the twenty-sixth O site, O(26) is bonded in a 6-coordinate geometry to two equivalent K(4), two equivalent Na(2), one Nb(2), and one Nb(6) atom. In the twenty-seventh O site, O(27) is bonded to two equivalent K(1), two equivalent K(5), one Nb(3), and one Nb(7) atom to form distorted OK4Nb2 octahedra that share corners with two equivalent O(22)K2Na2Nb2 octahedra, corners with two equivalent O(23)K4Nb2 octahedra, edges with two equivalent O(27)K4Nb2 octahedra,  a faceface with one O(22)K2Na2Nb2 octahedra, and  a faceface with one O(23)K4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-eighth O site, O(28) is bonded to two equivalent K(2), two equivalent K(6), one Nb(4), and one Nb(8) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-ninth O site, O(29) is bonded to two equivalent K(3), two equivalent K(7), one Nb(5), and one Nb(9) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the thirtieth O site, O(30) is bonded in a 6-coordinate geometry to two equivalent K(8), two equivalent Na(1), one Nb(1), and one Nb(10) atom. is represented by the CIF card [CIF]
data_K4NaNb5O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.011
_cell_length_b   5.790
_cell_length_c   29.133
_cell_angle_alpha   89.250
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   676.582
_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
  K  K0  1  0.000  0.507  0.404  1.0
  K  K1  1  0.000  0.506  0.605  1.0
  K  K2  1  0.000  0.506  0.805  1.0
  K  K3  1  0.000  0.995  0.104  1.0
  K  K4  1  0.000  0.997  0.304  1.0
  K  K5  1  0.000  0.997  0.504  1.0
  K  K6  1  0.000  0.997  0.705  1.0
  K  K7  1  0.000  0.995  0.905  1.0
  Na  Na8  1  0.000  0.516  0.009  1.0
  Na  Na9  1  0.000  0.517  0.209  1.0
  Nb  Nb10  1  0.500  0.008  0.007  1.0
  Nb  Nb11  1  0.500  0.009  0.206  1.0
  Nb  Nb12  1  0.500  0.007  0.407  1.0
  Nb  Nb13  1  0.500  0.006  0.607  1.0
  Nb  Nb14  1  0.500  0.006  0.808  1.0
  Nb  Nb15  1  0.500  0.499  0.107  1.0
  Nb  Nb16  1  0.500  0.502  0.306  1.0
  Nb  Nb17  1  0.500  0.501  0.507  1.0
  Nb  Nb18  1  0.500  0.500  0.708  1.0
  Nb  Nb19  1  0.500  0.498  0.909  1.0
  O  O20  1  0.000  0.499  0.098  1.0
  O  O21  1  0.000  0.499  0.297  1.0
  O  O22  1  0.000  0.499  0.499  1.0
  O  O23  1  0.000  0.499  0.699  1.0
  O  O24  1  0.000  0.499  0.900  1.0
  O  O25  1  0.000  0.997  1.000  1.0
  O  O26  1  0.000  0.998  0.199  1.0
  O  O27  1  0.000  0.003  0.399  1.0
  O  O28  1  0.000  0.002  0.599  1.0
  O  O29  1  0.000  0.002  0.800  1.0
  O  O30  1  0.500  0.270  0.045  1.0
  O  O31  1  0.500  0.270  0.245  1.0
  O  O32  1  0.500  0.256  0.447  1.0
  O  O33  1  0.500  0.256  0.648  1.0
  O  O34  1  0.500  0.256  0.848  1.0
  O  O35  1  0.500  0.232  0.146  1.0
  O  O36  1  0.500  0.242  0.347  1.0
  O  O37  1  0.500  0.242  0.548  1.0
  O  O38  1  0.500  0.241  0.748  1.0
  O  O39  1  0.500  0.232  0.947  1.0
  O  O40  1  0.500  0.769  0.053  1.0
  O  O41  1  0.500  0.769  0.252  1.0
  O  O42  1  0.500  0.764  0.451  1.0
  O  O43  1  0.500  0.764  0.652  1.0
  O  O44  1  0.500  0.764  0.853  1.0
  O  O45  1  0.500  0.722  0.154  1.0
  O  O46  1  0.500  0.733  0.351  1.0
  O  O47  1  0.500  0.734  0.552  1.0
  O  O48  1  0.500  0.734  0.752  1.0
  O  O49  1  0.500  0.723  0.955  1.0
[/CIF]
.
The crystal structure described by K4NaNb5O15 crystallizes in the monoclinic Pm space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded to one O(2), one O(3), two equivalent O(13), two equivalent O(17), two equivalent O(23), two equivalent O(27), and two equivalent O(8) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(2)O12 cuboctahedra, corners with two equivalent K(1)O12 cuboctahedra, corners with four equivalent K(5)O12 cuboctahedra, corners with four equivalent K(6)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent Nb(7)O6 octahedra, faces with two equivalent Nb(8)O6 octahedra, and faces with four equivalent Nb(3)O6 octahedra. In the second K site, K(2) is bonded to one O(3), one O(4), two equivalent O(14), two equivalent O(18), two equivalent O(24), two equivalent O(28), and two equivalent O(9) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(1)O12 cuboctahedra,  a cornercorner with one K(3)O12 cuboctahedra, corners with two equivalent K(2)O12 cuboctahedra, corners with four equivalent K(6)O12 cuboctahedra, corners with four equivalent K(7)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent Nb(8)O6 octahedra, faces with two equivalent Nb(9)O6 octahedra, and faces with four equivalent Nb(4)O6 octahedra. In the third K site, K(3) is bonded to one O(4), one O(5), two equivalent O(10), two equivalent O(15), two equivalent O(19), two equivalent O(25), and two equivalent O(29) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(2)O12 cuboctahedra, corners with two equivalent K(3)O12 cuboctahedra, corners with four equivalent K(7)O12 cuboctahedra, corners with four equivalent K(8)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, faces with two equivalent Nb(10)O6 octahedra, faces with two equivalent Nb(9)O6 octahedra, and faces with four equivalent Nb(5)O6 octahedra. In the fourth K site, K(4) is bonded to one O(6), one O(7), two equivalent O(1), two equivalent O(11), two equivalent O(16), two equivalent O(21), and two equivalent O(26) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(5)O12 cuboctahedra,  a cornercorner with one K(8)O12 cuboctahedra, corners with two equivalent K(4)O12 cuboctahedra, faces with two equivalent K(4)O12 cuboctahedra, faces with two equivalent Nb(1)O6 octahedra, faces with two equivalent Nb(2)O6 octahedra, and faces with four equivalent Nb(6)O6 octahedra. In the fifth K site, K(5) is bonded to one O(7), one O(8), two equivalent O(12), two equivalent O(17), two equivalent O(2), two equivalent O(22), and two equivalent O(27) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(4)O12 cuboctahedra,  a cornercorner with one K(6)O12 cuboctahedra, corners with two equivalent K(5)O12 cuboctahedra, corners with four equivalent K(1)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent Nb(2)O6 octahedra, faces with two equivalent Nb(3)O6 octahedra, and faces with four equivalent Nb(7)O6 octahedra. In the sixth K site, K(6) is bonded to one O(8), one O(9), two equivalent O(13), two equivalent O(18), two equivalent O(23), two equivalent O(28), and two equivalent O(3) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(5)O12 cuboctahedra,  a cornercorner with one K(7)O12 cuboctahedra, corners with two equivalent K(6)O12 cuboctahedra, corners with four equivalent K(1)O12 cuboctahedra, corners with four equivalent K(2)O12 cuboctahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent Nb(3)O6 octahedra, faces with two equivalent Nb(4)O6 octahedra, and faces with four equivalent Nb(8)O6 octahedra. In the seventh K site, K(7) is bonded to one O(10), one O(9), two equivalent O(14), two equivalent O(19), two equivalent O(24), two equivalent O(29), and two equivalent O(4) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(6)O12 cuboctahedra,  a cornercorner with one K(8)O12 cuboctahedra, corners with two equivalent K(7)O12 cuboctahedra, corners with four equivalent K(2)O12 cuboctahedra, 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 two equivalent K(7)O12 cuboctahedra, faces with two equivalent Nb(4)O6 octahedra, faces with two equivalent Nb(5)O6 octahedra, and faces with four equivalent Nb(9)O6 octahedra. In the eighth K site, K(8) is bonded to one O(10), one O(6), two equivalent O(15), two equivalent O(20), two equivalent O(25), two equivalent O(30), and two equivalent O(5) atoms to form KO12 cuboctahedra that share  a cornercorner with one K(4)O12 cuboctahedra,  a cornercorner with one K(7)O12 cuboctahedra, corners with two equivalent K(8)O12 cuboctahedra, corners with four equivalent K(3)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, faces with two equivalent Nb(1)O6 octahedra, faces with two equivalent Nb(5)O6 octahedra, and faces with four equivalent Nb(10)O6 octahedra. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 8-coordinate geometry to one O(1), one O(6), two equivalent O(11), two equivalent O(21), and two equivalent O(30) atoms. In the second Na site, Na(2) is bonded in a 8-coordinate geometry to one O(2), one O(7), two equivalent O(12), two equivalent O(22), and two equivalent O(26) atoms. There are ten inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(11), one O(20), one O(21), one O(30), and two equivalent O(6) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, faces with two equivalent K(4)O12 cuboctahedra, and faces with two equivalent K(8)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the second Nb site, Nb(2) is bonded to one O(12), one O(16), one O(22), one O(26), and two equivalent O(7) atoms to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, faces with two equivalent K(4)O12 cuboctahedra, and faces with two equivalent K(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-18°. In the third Nb site, Nb(3) is bonded to one O(13), one O(17), one O(23), one O(27), and two equivalent O(8) atoms to form NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, faces with two equivalent K(5)O12 cuboctahedra, faces with two equivalent K(6)O12 cuboctahedra, and faces with four equivalent K(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-14°. In the fourth Nb site, Nb(4) is bonded to one O(14), one O(18), one O(24), one O(28), and two equivalent O(9) atoms to form NbO6 octahedra that share corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(6)O12 cuboctahedra, faces with two equivalent K(7)O12 cuboctahedra, and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the fifth Nb site, Nb(5) is bonded to one O(15), one O(19), one O(25), one O(29), and two equivalent O(10) atoms to form NbO6 octahedra that share corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(7)O12 cuboctahedra, faces with two equivalent K(8)O12 cuboctahedra, and faces with four equivalent K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the sixth Nb site, Nb(6) is bonded to one O(11), one O(16), one O(21), one O(26), and two equivalent O(1) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(6)O6 octahedra, and faces with four equivalent K(4)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-18°. In the seventh Nb site, Nb(7) is bonded to one O(12), one O(17), one O(22), one O(27), and two equivalent O(2) atoms to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(7)O6 octahedra, faces with two equivalent K(1)O12 cuboctahedra, and faces with four equivalent K(5)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 1-16°. In the eighth Nb site, Nb(8) is bonded to one O(13), one O(18), one O(23), one O(28), and two equivalent O(3) atoms to form NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(8)O6 octahedra, faces with two equivalent K(1)O12 cuboctahedra, faces with two equivalent K(2)O12 cuboctahedra, and faces with four equivalent K(6)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the ninth Nb site, Nb(9) is bonded to one O(14), one O(19), one O(24), one O(29), and two equivalent O(4) atoms to form NbO6 octahedra that share corners with two equivalent Nb(4)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, corners with two equivalent Nb(9)O6 octahedra, faces with two equivalent K(2)O12 cuboctahedra, faces with two equivalent K(3)O12 cuboctahedra, and faces with four equivalent K(7)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 2-14°. In the tenth Nb site, Nb(10) is bonded to one O(15), one O(20), one O(25), one O(30), and two equivalent O(5) atoms to form NbO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(10)O6 octahedra, corners with two equivalent Nb(5)O6 octahedra, faces with two equivalent K(3)O12 cuboctahedra, and faces with four equivalent K(8)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-18°. There are thirty inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to two equivalent K(4), one Na(1), and two equivalent Nb(6) atoms. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(5), one Na(2), and two equivalent Nb(7) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one K(1), one K(2), two equivalent K(6), and two equivalent Nb(8) atoms. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(2), one K(3), two equivalent K(7), and two equivalent Nb(9) atoms. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(8), and two equivalent Nb(10) atoms. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one K(4), one K(8), one Na(1), and two equivalent Nb(1) atoms. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one K(4), one K(5), one Na(2), and two equivalent Nb(2) atoms. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one K(5), one K(6), two equivalent K(1), and two equivalent Nb(3) atoms. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to one K(6), one K(7), two equivalent K(2), and two equivalent Nb(4) atoms. In the tenth O site, O(10) is bonded in a 2-coordinate geometry to one K(7), one K(8), two equivalent K(3), and two equivalent Nb(5) atoms. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to two equivalent K(4), two equivalent Na(1), one Nb(1), and one Nb(6) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to two equivalent K(5), two equivalent Na(2), one Nb(2), and one Nb(7) atom. In the thirteenth O site, O(13) is bonded in a 6-coordinate geometry to two equivalent K(1), two equivalent K(6), one Nb(3), and one Nb(8) atom. In the fourteenth O site, O(14) is bonded in a 6-coordinate geometry to two equivalent K(2), two equivalent K(7), one Nb(4), and one Nb(9) atom. In the fifteenth O site, O(15) is bonded in a 6-coordinate geometry to two equivalent K(3), two equivalent K(8), one Nb(10), and one Nb(5) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to two equivalent K(4), one Nb(2), and one Nb(6) atom. In the seventeenth O site, O(17) is bonded in a 6-coordinate geometry to two equivalent K(1), two equivalent K(5), one Nb(3), and one Nb(7) atom. In the eighteenth O site, O(18) is bonded in a 6-coordinate geometry to two equivalent K(2), two equivalent K(6), one Nb(4), and one Nb(8) atom. In the nineteenth O site, O(19) is bonded in a 6-coordinate geometry to two equivalent K(3), two equivalent K(7), one Nb(5), and one Nb(9) atom. In the twentieth O site, O(20) is bonded in a 4-coordinate geometry to two equivalent K(8), one Nb(1), and one Nb(10) atom. In the twenty-first O site, O(21) is bonded to two equivalent K(4), two equivalent Na(1), one Nb(1), and one Nb(6) atom to form distorted edge-sharing OK2Na2Nb2 octahedra. In the twenty-second O site, O(22) is bonded to two equivalent K(5), two equivalent Na(2), one Nb(2), and one Nb(7) atom to form distorted OK2Na2Nb2 octahedra that share corners with two equivalent O(27)K4Nb2 octahedra, edges with two equivalent O(22)K2Na2Nb2 octahedra, and  a faceface with one O(27)K4Nb2 octahedra. The corner-sharing octahedral tilt angles are 60°. In the twenty-third O site, O(23) is bonded to two equivalent K(1), two equivalent K(6), one Nb(3), and one Nb(8) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-fourth O site, O(24) is bonded to two equivalent K(2), two equivalent K(7), one Nb(4), and one Nb(9) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-fifth O site, O(25) is bonded to two equivalent K(3), two equivalent K(8), one Nb(10), and one Nb(5) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles are 59°. In the twenty-sixth O site, O(26) is bonded in a 6-coordinate geometry to two equivalent K(4), two equivalent Na(2), one Nb(2), and one Nb(6) atom. In the twenty-seventh O site, O(27) is bonded to two equivalent K(1), two equivalent K(5), one Nb(3), and one Nb(7) atom to form distorted OK4Nb2 octahedra that share corners with two equivalent O(22)K2Na2Nb2 octahedra, corners with two equivalent O(23)K4Nb2 octahedra, edges with two equivalent O(27)K4Nb2 octahedra,  a faceface with one O(22)K2Na2Nb2 octahedra, and  a faceface with one O(23)K4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-eighth O site, O(28) is bonded to two equivalent K(2), two equivalent K(6), one Nb(4), and one Nb(8) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twenty-ninth O site, O(29) is bonded to two equivalent K(3), two equivalent K(7), one Nb(5), and one Nb(9) atom to form a mixture of distorted edge, face, and corner-sharing OK4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the thirtieth O site, O(30) is bonded in a 6-coordinate geometry to two equivalent K(8), two equivalent Na(1), one Nb(1), and one Nb(10) atom. is represented by the CIF card [CIF]
data_K4NaNb5O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.011
_cell_length_b   5.790
_cell_length_c   29.133
_cell_angle_alpha   89.250
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   676.582
_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
  K  K0  1  0.000  0.507  0.404  1.0
  K  K1  1  0.000  0.506  0.605  1.0
  K  K2  1  0.000  0.506  0.805  1.0
  K  K3  1  0.000  0.995  0.104  1.0
  K  K4  1  0.000  0.997  0.304  1.0
  K  K5  1  0.000  0.997  0.504  1.0
  K  K6  1  0.000  0.997  0.705  1.0
  K  K7  1  0.000  0.995  0.905  1.0
  Na  Na8  1  0.000  0.516  0.009  1.0
  Na  Na9  1  0.000  0.517  0.209  1.0
  Nb  Nb10  1  0.500  0.008  0.007  1.0
  Nb  Nb11  1  0.500  0.009  0.206  1.0
  Nb  Nb12  1  0.500  0.007  0.407  1.0
  Nb  Nb13  1  0.500  0.006  0.607  1.0
  Nb  Nb14  1  0.500  0.006  0.808  1.0
  Nb  Nb15  1  0.500  0.499  0.107  1.0
  Nb  Nb16  1  0.500  0.502  0.306  1.0
  Nb  Nb17  1  0.500  0.501  0.507  1.0
  Nb  Nb18  1  0.500  0.500  0.708  1.0
  Nb  Nb19  1  0.500  0.498  0.909  1.0
  O  O20  1  0.000  0.499  0.098  1.0
  O  O21  1  0.000  0.499  0.297  1.0
  O  O22  1  0.000  0.499  0.499  1.0
  O  O23  1  0.000  0.499  0.699  1.0
  O  O24  1  0.000  0.499  0.900  1.0
  O  O25  1  0.000  0.997  1.000  1.0
  O  O26  1  0.000  0.998  0.199  1.0
  O  O27  1  0.000  0.003  0.399  1.0
  O  O28  1  0.000  0.002  0.599  1.0
  O  O29  1  0.000  0.002  0.800  1.0
  O  O30  1  0.500  0.270  0.045  1.0
  O  O31  1  0.500  0.270  0.245  1.0
  O  O32  1  0.500  0.256  0.447  1.0
  O  O33  1  0.500  0.256  0.648  1.0
  O  O34  1  0.500  0.256  0.848  1.0
  O  O35  1  0.500  0.232  0.146  1.0
  O  O36  1  0.500  0.242  0.347  1.0
  O  O37  1  0.500  0.242  0.548  1.0
  O  O38  1  0.500  0.241  0.748  1.0
  O  O39  1  0.500  0.232  0.947  1.0
  O  O40  1  0.500  0.769  0.053  1.0
  O  O41  1  0.500  0.769  0.252  1.0
  O  O42  1  0.500  0.764  0.451  1.0
  O  O43  1  0.500  0.764  0.652  1.0
  O  O44  1  0.500  0.764  0.853  1.0
  O  O45  1  0.500  0.722  0.154  1.0
  O  O46  1  0.500  0.733  0.351  1.0
  O  O47  1  0.500  0.734  0.552  1.0
  O  O48  1  0.500  0.734  0.752  1.0
  O  O49  1  0.500  0.723  0.955  1.0
[/CIF]
.