The material structure described by KNaMg14O15 crystallizes in the orthorhombic Pmm2 space group. K(1) is bonded to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Na(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-12°. Na(1) is bonded to one O(3), two equivalent O(10), and two equivalent O(7) atoms to form NaO5 square pyramids that share corners with two equivalent K(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Na(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the fifth Mg site, Mg(5) is bonded to one O(6), one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-11°. In the sixth Mg site, Mg(6) is bonded in a square co-planar geometry to one O(7), one O(9), and two equivalent O(4) atoms. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 3-12°. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form distorted MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Na(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 3-17°. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form distorted OKMg5 octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second O site, O(2) is bonded to one K(1), one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OKMg5 octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)KMg5 octahedra, corners with two equivalent O(3)NaMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. In the third O site, O(3) is bonded to one Na(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form ONaMg5 octahedra that share corners with two equivalent O(2)KMg5 octahedra, corners with two equivalent O(3)NaMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(7)Na2Mg4 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(6)K2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra,  an edgeedge with one O(7)Na2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, and edges with two equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 1-16°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(6)K2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra,  an edgeedge with one O(7)Na2Mg4 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, and edges with two equivalent O(3)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the sixth O site, O(6) is bonded to two equivalent K(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)KNaMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the seventh O site, O(7) is bonded to two equivalent Na(1), one Mg(6), one Mg(8), and two equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)NaMg5 octahedra, and edges with four equivalent O(10)KNaMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)NaMg5 octahedra, and edges with four equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. In the tenth O site, O(10) is bonded to one K(1), one Na(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form OKNaMg4 octahedra that share corners with two equivalent O(11)Mg6 octahedra, corners with four equivalent O(10)KNaMg4 octahedra,  an edgeedge with one O(1)KMg5 octahedra,  an edgeedge with one O(2)KMg5 octahedra,  an edgeedge with one O(3)NaMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(7)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 5-20°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(10)KNaMg4 octahedra, corners with four equivalent O(11)Mg6 octahedra,  an edgeedge with one O(1)KMg5 octahedra,  an edgeedge with one O(2)KMg5 octahedra,  an edgeedge with one O(3)NaMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with two equivalent O(9)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 5-20°. is represented by the CIF file [CIF]
data_KNaMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.643
_cell_length_b   8.779
_cell_length_c   4.411
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   334.694
_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  0.987  0.000  0.000  1.0
  Na  Na1  1  0.992  0.500  0.000  1.0
  Mg  Mg2  1  0.498  0.000  0.000  1.0
  Mg  Mg3  1  0.516  0.500  0.000  1.0
  Mg  Mg4  1  0.006  0.253  0.500  1.0
  Mg  Mg5  1  0.006  0.747  0.500  1.0
  Mg  Mg6  1  0.497  0.253  0.500  1.0
  Mg  Mg7  1  0.497  0.747  0.500  1.0
  Mg  Mg8  1  0.249  0.000  0.500  1.0
  Mg  Mg9  1  0.242  0.500  0.500  1.0
  Mg  Mg10  1  0.747  0.000  0.500  1.0
  Mg  Mg11  1  0.766  0.500  0.500  1.0
  Mg  Mg12  1  0.245  0.224  0.000  1.0
  Mg  Mg13  1  0.245  0.776  0.000  1.0
  Mg  Mg14  1  0.756  0.254  0.000  1.0
  Mg  Mg15  1  0.756  0.746  0.000  1.0
  O  O16  1  0.274  0.000  0.000  1.0
  O  O17  1  0.719  0.000  0.000  1.0
  O  O18  1  0.739  0.500  0.000  1.0
  O  O19  1  0.253  0.258  0.500  1.0
  O  O20  1  0.253  0.742  0.500  1.0
  O  O21  1  0.750  0.253  0.500  1.0
  O  O22  1  0.750  0.747  0.500  1.0
  O  O23  1  0.013  0.000  0.500  1.0
  O  O24  1  0.011  0.500  0.500  1.0
  O  O25  1  0.496  0.000  0.500  1.0
  O  O26  1  0.482  0.500  0.500  1.0
  O  O27  1  0.015  0.265  0.000  1.0
  O  O28  1  0.015  0.735  0.000  1.0
  O  O29  1  0.486  0.266  0.000  1.0
  O  O30  1  0.486  0.734  0.000  1.0
[/CIF]
.
The material structure described by KNaMg14O15 crystallizes in the orthorhombic Pmm2 space group. K(1) is bonded to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Na(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-12°. Na(1) is bonded to one O(3), two equivalent O(10), and two equivalent O(7) atoms to form NaO5 square pyramids that share corners with two equivalent K(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Na(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles are 12°. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the second Mg site, Mg(2) is bonded to one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the fifth Mg site, Mg(5) is bonded to one O(6), one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-11°. In the sixth Mg site, Mg(6) is bonded in a square co-planar geometry to one O(7), one O(9), and two equivalent O(4) atoms. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 3-12°. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form distorted MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Na(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 3-17°. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form distorted OKMg5 octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second O site, O(2) is bonded to one K(1), one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OKMg5 octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with two equivalent O(2)KMg5 octahedra, corners with two equivalent O(3)NaMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. In the third O site, O(3) is bonded to one Na(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(8) atoms to form ONaMg5 octahedra that share corners with two equivalent O(2)KMg5 octahedra, corners with two equivalent O(3)NaMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(7)Na2Mg4 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 12°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(6)K2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra,  an edgeedge with one O(7)Na2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, and edges with two equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 1-16°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(6)K2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra,  an edgeedge with one O(7)Na2Mg4 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(10)KNaMg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, and edges with two equivalent O(3)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-7°. In the sixth O site, O(6) is bonded to two equivalent K(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)KNaMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the seventh O site, O(7) is bonded to two equivalent Na(1), one Mg(6), one Mg(8), and two equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)NaMg5 octahedra, and edges with four equivalent O(10)KNaMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(6)K2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)KMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, corners with two equivalent O(7)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)NaMg5 octahedra, and edges with four equivalent O(11)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. In the tenth O site, O(10) is bonded to one K(1), one Na(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form OKNaMg4 octahedra that share corners with two equivalent O(11)Mg6 octahedra, corners with four equivalent O(10)KNaMg4 octahedra,  an edgeedge with one O(1)KMg5 octahedra,  an edgeedge with one O(2)KMg5 octahedra,  an edgeedge with one O(3)NaMg5 octahedra, edges with two equivalent O(6)K2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(7)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 5-20°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(10)KNaMg4 octahedra, corners with four equivalent O(11)Mg6 octahedra,  an edgeedge with one O(1)KMg5 octahedra,  an edgeedge with one O(2)KMg5 octahedra,  an edgeedge with one O(3)NaMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with two equivalent O(9)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 5-20°. is represented by the CIF file [CIF]
data_KNaMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.643
_cell_length_b   8.779
_cell_length_c   4.411
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   334.694
_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  0.987  0.000  0.000  1.0
  Na  Na1  1  0.992  0.500  0.000  1.0
  Mg  Mg2  1  0.498  0.000  0.000  1.0
  Mg  Mg3  1  0.516  0.500  0.000  1.0
  Mg  Mg4  1  0.006  0.253  0.500  1.0
  Mg  Mg5  1  0.006  0.747  0.500  1.0
  Mg  Mg6  1  0.497  0.253  0.500  1.0
  Mg  Mg7  1  0.497  0.747  0.500  1.0
  Mg  Mg8  1  0.249  0.000  0.500  1.0
  Mg  Mg9  1  0.242  0.500  0.500  1.0
  Mg  Mg10  1  0.747  0.000  0.500  1.0
  Mg  Mg11  1  0.766  0.500  0.500  1.0
  Mg  Mg12  1  0.245  0.224  0.000  1.0
  Mg  Mg13  1  0.245  0.776  0.000  1.0
  Mg  Mg14  1  0.756  0.254  0.000  1.0
  Mg  Mg15  1  0.756  0.746  0.000  1.0
  O  O16  1  0.274  0.000  0.000  1.0
  O  O17  1  0.719  0.000  0.000  1.0
  O  O18  1  0.739  0.500  0.000  1.0
  O  O19  1  0.253  0.258  0.500  1.0
  O  O20  1  0.253  0.742  0.500  1.0
  O  O21  1  0.750  0.253  0.500  1.0
  O  O22  1  0.750  0.747  0.500  1.0
  O  O23  1  0.013  0.000  0.500  1.0
  O  O24  1  0.011  0.500  0.500  1.0
  O  O25  1  0.496  0.000  0.500  1.0
  O  O26  1  0.482  0.500  0.500  1.0
  O  O27  1  0.015  0.265  0.000  1.0
  O  O28  1  0.015  0.735  0.000  1.0
  O  O29  1  0.486  0.266  0.000  1.0
  O  O30  1  0.486  0.734  0.000  1.0
[/CIF]
.