The compound described by RbKMg6O7 crystallizes in the tetragonal P4mm space group. Rb(1) is bonded to one O(1) and four equivalent O(5) atoms to form distorted RbO5 square pyramids that share  a cornercorner with one K(1)O5 square pyramid, corners with four equivalent Rb(1)O5 square pyramids, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. K(1) is bonded to one O(1) and four equivalent O(4) atoms to form KO5 square pyramids that share  a cornercorner with one Rb(1)O5 square pyramid, corners with four equivalent K(1)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(2), one O(3), and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent K(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the second Mg site, Mg(2) is bonded to one O(2), one O(3), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Rb(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the third Mg site, Mg(3) is bonded in a distorted square co-planar geometry to one O(4), one O(5), and two equivalent O(2) atoms. In the fourth Mg site, Mg(4) 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 four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Rb(1)O5 square pyramids, and edges with two equivalent K(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 2-4°. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one K(1), and four equivalent Mg(4) atoms to form OKRbMg4 octahedra that share corners with four equivalent O(1)KRbMg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Mg6 octahedra, corners with four equivalent O(2)Mg6 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(2)Mg6 octahedra, corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, edges with four equivalent O(1)KRbMg4 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(5)Rb2Mg4 octahedra, corners with four equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KRbMg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)K2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the fifth O site, O(5) is bonded to two equivalent Rb(1), one Mg(3), one Mg(4), and two equivalent Mg(2) atoms to form ORb2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Rb2Mg4 octahedra, edges with two equivalent O(1)KRbMg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. is represented by the CIF file [CIF]
data_KRbMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.022
_cell_length_b   4.929
_cell_length_c   4.929
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   194.903
_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  0.022  0.000  0.000  1.0
  Rb  Rb1  1  0.442  0.000  0.000  1.0
  Mg  Mg2  1  0.002  0.500  0.500  1.0
  Mg  Mg3  1  0.508  0.500  0.500  1.0
  Mg  Mg4  1  0.254  0.000  0.500  1.0
  Mg  Mg5  1  0.750  0.000  0.500  1.0
  Mg  Mg6  1  0.254  0.500  0.000  1.0
  Mg  Mg7  1  0.750  0.500  0.000  1.0
  O  O8  1  0.738  0.000  0.000  1.0
  O  O9  1  0.255  0.500  0.500  1.0
  O  O10  1  0.755  0.500  0.500  1.0
  O  O11  1  0.015  0.000  0.500  1.0
  O  O12  1  0.495  0.000  0.500  1.0
  O  O13  1  0.015  0.500  0.000  1.0
  O  O14  1  0.495  0.500  0.000  1.0
[/CIF]
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The compound described by RbKMg6O7 crystallizes in the tetragonal P4mm space group. Rb(1) is bonded to one O(1) and four equivalent O(5) atoms to form distorted RbO5 square pyramids that share  a cornercorner with one K(1)O5 square pyramid, corners with four equivalent Rb(1)O5 square pyramids, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. K(1) is bonded to one O(1) and four equivalent O(4) atoms to form KO5 square pyramids that share  a cornercorner with one Rb(1)O5 square pyramid, corners with four equivalent K(1)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(2), one O(3), and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent K(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the second Mg site, Mg(2) is bonded to one O(2), one O(3), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Rb(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the third Mg site, Mg(3) is bonded in a distorted square co-planar geometry to one O(4), one O(5), and two equivalent O(2) atoms. In the fourth Mg site, Mg(4) 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 four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Rb(1)O5 square pyramids, and edges with two equivalent K(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 2-4°. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Rb(1), one K(1), and four equivalent Mg(4) atoms to form OKRbMg4 octahedra that share corners with four equivalent O(1)KRbMg4 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Mg6 octahedra, corners with four equivalent O(2)Mg6 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(2)Mg6 octahedra, corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(4)K2Mg4 octahedra, edges with four equivalent O(1)KRbMg4 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to two equivalent K(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form OK2Mg4 octahedra that share corners with two equivalent O(5)Rb2Mg4 octahedra, corners with four equivalent O(4)K2Mg4 octahedra, edges with two equivalent O(1)KRbMg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)K2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the fifth O site, O(5) is bonded to two equivalent Rb(1), one Mg(3), one Mg(4), and two equivalent Mg(2) atoms to form ORb2Mg4 octahedra that share corners with two equivalent O(4)K2Mg4 octahedra, corners with four equivalent O(5)Rb2Mg4 octahedra, edges with two equivalent O(1)KRbMg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Rb2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. is represented by the CIF file [CIF]
data_KRbMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.022
_cell_length_b   4.929
_cell_length_c   4.929
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   194.903
_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  0.022  0.000  0.000  1.0
  Rb  Rb1  1  0.442  0.000  0.000  1.0
  Mg  Mg2  1  0.002  0.500  0.500  1.0
  Mg  Mg3  1  0.508  0.500  0.500  1.0
  Mg  Mg4  1  0.254  0.000  0.500  1.0
  Mg  Mg5  1  0.750  0.000  0.500  1.0
  Mg  Mg6  1  0.254  0.500  0.000  1.0
  Mg  Mg7  1  0.750  0.500  0.000  1.0
  O  O8  1  0.738  0.000  0.000  1.0
  O  O9  1  0.255  0.500  0.500  1.0
  O  O10  1  0.755  0.500  0.500  1.0
  O  O11  1  0.015  0.000  0.500  1.0
  O  O12  1  0.495  0.000  0.500  1.0
  O  O13  1  0.015  0.500  0.000  1.0
  O  O14  1  0.495  0.500  0.000  1.0
[/CIF]
.