The crystal structure described by KMg14GaO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. K(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) 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 Ga(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-14°. Ga(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form GaO6 octahedra that share corners with two equivalent Ga(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with two equivalent O(2)Mg5Ga octahedra, corners with four equivalent O(1)KMg5 octahedra, edges with two equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ga(1) atom to form OMg5Ga octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(6)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)K2Mg4 octahedra,  an edgeedge with one O(6)Mg4Ga2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, and edges with four equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the fourth O site, O(4) is bonded to two equivalent K(1) and four equivalent Mg(2) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)KMg5 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with two equivalent O(6)Mg4Ga2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(6)Mg4Ga2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_KMg14GaO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.603
_cell_length_b   8.603
_cell_length_c   4.393
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   325.086
_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
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.249  0.500  1.0
  Mg  Mg4  1  0.000  0.751  0.500  1.0
  Mg  Mg5  1  0.500  0.247  0.500  1.0
  Mg  Mg6  1  0.500  0.753  0.500  1.0
  Mg  Mg7  1  0.249  0.000  0.500  1.0
  Mg  Mg8  1  0.247  0.500  0.500  1.0
  Mg  Mg9  1  0.751  0.000  0.500  1.0
  Mg  Mg10  1  0.753  0.500  0.500  1.0
  Mg  Mg11  1  0.247  0.247  0.000  1.0
  Mg  Mg12  1  0.247  0.753  0.000  1.0
  Mg  Mg13  1  0.753  0.247  0.000  1.0
  Mg  Mg14  1  0.753  0.753  0.000  1.0
  Ga  Ga15  1  0.500  0.500  0.000  1.0
  O  O16  1  0.277  0.000  0.000  1.0
  O  O17  1  0.266  0.500  0.000  1.0
  O  O18  1  0.723  0.000  0.000  1.0
  O  O19  1  0.734  0.500  0.000  1.0
  O  O20  1  0.251  0.251  0.500  1.0
  O  O21  1  0.251  0.749  0.500  1.0
  O  O22  1  0.749  0.251  0.500  1.0
  O  O23  1  0.749  0.749  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.277  0.000  1.0
  O  O29  1  0.000  0.723  0.000  1.0
  O  O30  1  0.500  0.266  0.000  1.0
  O  O31  1  0.500  0.734  0.000  1.0
[/CIF]
.
The crystal structure described by KMg14GaO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. K(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form KO6 octahedra that share corners with two equivalent K(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) 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 Ga(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent K(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the third Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Ga(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the fourth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one K(1)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-14°. Ga(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form GaO6 octahedra that share corners with two equivalent Ga(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one K(1), one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OKMg5 octahedra that share corners with two equivalent O(2)Mg5Ga octahedra, corners with four equivalent O(1)KMg5 octahedra, edges with two equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ga(1) atom to form OMg5Ga octahedra that share corners with two equivalent O(1)KMg5 octahedra, corners with four equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(1)KMg5 octahedra, edges with two equivalent O(6)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)K2Mg4 octahedra,  an edgeedge with one O(6)Mg4Ga2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, and edges with four equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedral tilt angles range from 1-3°. In the fourth O site, O(4) is bonded to two equivalent K(1) and four equivalent Mg(2) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)KMg5 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with two equivalent O(6)Mg4Ga2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(1)KMg5 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four equivalent Mg(3) and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(6)Mg4Ga2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_KMg14GaO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.603
_cell_length_b   8.603
_cell_length_c   4.393
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   325.086
_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
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.249  0.500  1.0
  Mg  Mg4  1  0.000  0.751  0.500  1.0
  Mg  Mg5  1  0.500  0.247  0.500  1.0
  Mg  Mg6  1  0.500  0.753  0.500  1.0
  Mg  Mg7  1  0.249  0.000  0.500  1.0
  Mg  Mg8  1  0.247  0.500  0.500  1.0
  Mg  Mg9  1  0.751  0.000  0.500  1.0
  Mg  Mg10  1  0.753  0.500  0.500  1.0
  Mg  Mg11  1  0.247  0.247  0.000  1.0
  Mg  Mg12  1  0.247  0.753  0.000  1.0
  Mg  Mg13  1  0.753  0.247  0.000  1.0
  Mg  Mg14  1  0.753  0.753  0.000  1.0
  Ga  Ga15  1  0.500  0.500  0.000  1.0
  O  O16  1  0.277  0.000  0.000  1.0
  O  O17  1  0.266  0.500  0.000  1.0
  O  O18  1  0.723  0.000  0.000  1.0
  O  O19  1  0.734  0.500  0.000  1.0
  O  O20  1  0.251  0.251  0.500  1.0
  O  O21  1  0.251  0.749  0.500  1.0
  O  O22  1  0.749  0.251  0.500  1.0
  O  O23  1  0.749  0.749  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.277  0.000  1.0
  O  O29  1  0.000  0.723  0.000  1.0
  O  O30  1  0.500  0.266  0.000  1.0
  O  O31  1  0.500  0.734  0.000  1.0
[/CIF]
.