The crystal structure described by K4Mg(MoO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent K sites. In the first K site, K(1) is bonded to two equivalent O(1), two equivalent O(11), and two equivalent O(2) atoms to form KO6 octahedra that share corners with two equivalent K(4)O6 octahedra, corners with two equivalent Mo(1)O4 tetrahedra, corners with two equivalent Mo(2)O4 tetrahedra, and corners with two equivalent Mo(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(11), one O(12), one O(2), one O(3), one O(7), and one O(8) atom. In the third K site, K(3) is bonded in a 7-coordinate geometry to one O(12), one O(3), one O(7), two equivalent O(10), and two equivalent O(4) atoms. In the fourth K site, K(4) is bonded to one O(1), one O(10), one O(3), one O(7), and two equivalent O(6) atoms to form KO6 octahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one Mo(3)O4 tetrahedra, corners with two equivalent Mo(1)O4 tetrahedra, corners with three equivalent Mo(2)O4 tetrahedra, and  an edgeedge with one K(4)O6 octahedra. The corner-sharing octahedral tilt angles are 73°. In the fifth K site, K(5) is bonded in a 6-coordinate geometry to two equivalent O(11), two equivalent O(2), and two equivalent O(5) atoms. Mg(1) is bonded to one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form MgO5 trigonal bipyramids that share  a cornercorner with one Mo(2)O4 tetrahedra, corners with two equivalent Mo(1)O4 tetrahedra, and corners with two equivalent Mo(3)O4 tetrahedra. There are three inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one O(1), one O(12), one O(3), and one O(5) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra, corners with two equivalent K(4)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 44-63°. In the second Mo site, Mo(2) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra, corners with three equivalent K(4)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 33-57°. In the third Mo site, Mo(3) is bonded to one O(10), one O(11), one O(8), and one O(9) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one K(4)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one K(1), one K(4), and one Mo(1) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), one K(5), and one Mo(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent K(3), one Mg(1), and one Mo(2) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one K(5), one Mg(1), and one Mo(1) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to two equivalent K(4) and one Mo(2) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(2) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), and one Mo(3) atom. In the ninth O site, O(9) is bonded in a distorted bent 120 degrees geometry to one Mg(1) and one Mo(3) atom. In the tenth O site, O(10) is bonded to one K(4), two equivalent K(3), and one Mo(3) atom to form distorted edge-sharing OK3Mo trigonal pyramids. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), one K(5), and one Mo(3) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Mg(1), and one Mo(1) atom. is represented by the CIF file [CIF]
data_K4Mg(MoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.998
_cell_length_b   10.077
_cell_length_c   10.157
_cell_angle_alpha   92.969
_cell_angle_beta   106.525
_cell_angle_gamma   106.775
_symmetry_Int_Tables_number   1
_cell_volume   743.327
_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  0.500  0.500  1.0
  K  K1  1  0.783  0.739  0.275  1.0
  K  K2  1  0.217  0.261  0.725  1.0
  K  K3  1  0.749  0.028  0.975  1.0
  K  K4  1  0.251  0.972  0.025  1.0
  K  K5  1  0.356  0.932  0.613  1.0
  K  K6  1  0.644  0.068  0.387  1.0
  K  K7  1  0.500  0.500  0.500  1.0
  Mg  Mg8  1  0.832  0.627  0.945  1.0
  Mg  Mg9  1  0.168  0.373  0.055  1.0
  Mo  Mo10  1  0.769  0.318  0.760  1.0
  Mo  Mo11  1  0.231  0.682  0.240  1.0
  Mo  Mo12  1  0.877  0.860  0.684  1.0
  Mo  Mo13  1  0.123  0.140  0.316  1.0
  Mo  Mo14  1  0.384  0.651  0.890  1.0
  Mo  Mo15  1  0.616  0.349  0.110  1.0
  O  O16  1  0.787  0.284  0.592  1.0
  O  O17  1  0.213  0.716  0.408  1.0
  O  O18  1  0.833  0.715  0.554  1.0
  O  O19  1  0.167  0.285  0.446  1.0
  O  O20  1  0.558  0.199  0.767  1.0
  O  O21  1  0.442  0.801  0.233  1.0
  O  O22  1  0.882  0.807  0.855  1.0
  O  O23  1  0.118  0.193  0.145  1.0
  O  O24  1  0.765  0.498  0.768  1.0
  O  O25  1  0.235  0.502  0.232  1.0
  O  O26  1  0.701  0.940  0.631  1.0
  O  O27  1  0.299  0.060  0.369  1.0
  O  O28  1  0.095  0.987  0.705  1.0
  O  O29  1  0.905  0.013  0.295  1.0
  O  O30  1  0.613  0.654  0.992  1.0
  O  O31  1  0.387  0.346  0.008  1.0
  O  O32  1  0.215  0.574  0.974  1.0
  O  O33  1  0.785  0.426  0.026  1.0
  O  O34  1  0.393  0.828  0.870  1.0
  O  O35  1  0.607  0.172  0.130  1.0
  O  O36  1  0.320  0.552  0.722  1.0
  O  O37  1  0.680  0.448  0.278  1.0
  O  O38  1  0.964  0.280  0.879  1.0
  O  O39  1  0.036  0.720  0.121  1.0
[/CIF]
.
The crystal structure described by K4Mg(MoO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent K sites. In the first K site, K(1) is bonded to two equivalent O(1), two equivalent O(11), and two equivalent O(2) atoms to form KO6 octahedra that share corners with two equivalent K(4)O6 octahedra, corners with two equivalent Mo(1)O4 tetrahedra, corners with two equivalent Mo(2)O4 tetrahedra, and corners with two equivalent Mo(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 73°. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(11), one O(12), one O(2), one O(3), one O(7), and one O(8) atom. In the third K site, K(3) is bonded in a 7-coordinate geometry to one O(12), one O(3), one O(7), two equivalent O(10), and two equivalent O(4) atoms. In the fourth K site, K(4) is bonded to one O(1), one O(10), one O(3), one O(7), and two equivalent O(6) atoms to form KO6 octahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one Mo(3)O4 tetrahedra, corners with two equivalent Mo(1)O4 tetrahedra, corners with three equivalent Mo(2)O4 tetrahedra, and  an edgeedge with one K(4)O6 octahedra. The corner-sharing octahedral tilt angles are 73°. In the fifth K site, K(5) is bonded in a 6-coordinate geometry to two equivalent O(11), two equivalent O(2), and two equivalent O(5) atoms. Mg(1) is bonded to one O(12), one O(4), one O(5), one O(8), and one O(9) atom to form MgO5 trigonal bipyramids that share  a cornercorner with one Mo(2)O4 tetrahedra, corners with two equivalent Mo(1)O4 tetrahedra, and corners with two equivalent Mo(3)O4 tetrahedra. There are three inequivalent Mo sites. In the first Mo site, Mo(1) is bonded to one O(1), one O(12), one O(3), and one O(5) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra, corners with two equivalent K(4)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 44-63°. In the second Mo site, Mo(2) is bonded to one O(2), one O(4), one O(6), and one O(7) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra, corners with three equivalent K(4)O6 octahedra, and  a cornercorner with one Mg(1)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 33-57°. In the third Mo site, Mo(3) is bonded to one O(10), one O(11), one O(8), and one O(9) atom to form MoO4 tetrahedra that share  a cornercorner with one K(1)O6 octahedra,  a cornercorner with one K(4)O6 octahedra, and corners with two equivalent Mg(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 51-56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one K(1), one K(4), and one Mo(1) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), one K(5), and one Mo(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent K(3), one Mg(1), and one Mo(2) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one K(5), one Mg(1), and one Mo(1) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to two equivalent K(4) and one Mo(2) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one K(2), one K(3), one K(4), and one Mo(2) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one K(2), one Mg(1), and one Mo(3) atom. In the ninth O site, O(9) is bonded in a distorted bent 120 degrees geometry to one Mg(1) and one Mo(3) atom. In the tenth O site, O(10) is bonded to one K(4), two equivalent K(3), and one Mo(3) atom to form distorted edge-sharing OK3Mo trigonal pyramids. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one K(1), one K(2), one K(5), and one Mo(3) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one K(2), one K(3), one Mg(1), and one Mo(1) atom. is represented by the CIF file [CIF]
data_K4Mg(MoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.998
_cell_length_b   10.077
_cell_length_c   10.157
_cell_angle_alpha   92.969
_cell_angle_beta   106.525
_cell_angle_gamma   106.775
_symmetry_Int_Tables_number   1
_cell_volume   743.327
_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  0.500  0.500  1.0
  K  K1  1  0.783  0.739  0.275  1.0
  K  K2  1  0.217  0.261  0.725  1.0
  K  K3  1  0.749  0.028  0.975  1.0
  K  K4  1  0.251  0.972  0.025  1.0
  K  K5  1  0.356  0.932  0.613  1.0
  K  K6  1  0.644  0.068  0.387  1.0
  K  K7  1  0.500  0.500  0.500  1.0
  Mg  Mg8  1  0.832  0.627  0.945  1.0
  Mg  Mg9  1  0.168  0.373  0.055  1.0
  Mo  Mo10  1  0.769  0.318  0.760  1.0
  Mo  Mo11  1  0.231  0.682  0.240  1.0
  Mo  Mo12  1  0.877  0.860  0.684  1.0
  Mo  Mo13  1  0.123  0.140  0.316  1.0
  Mo  Mo14  1  0.384  0.651  0.890  1.0
  Mo  Mo15  1  0.616  0.349  0.110  1.0
  O  O16  1  0.787  0.284  0.592  1.0
  O  O17  1  0.213  0.716  0.408  1.0
  O  O18  1  0.833  0.715  0.554  1.0
  O  O19  1  0.167  0.285  0.446  1.0
  O  O20  1  0.558  0.199  0.767  1.0
  O  O21  1  0.442  0.801  0.233  1.0
  O  O22  1  0.882  0.807  0.855  1.0
  O  O23  1  0.118  0.193  0.145  1.0
  O  O24  1  0.765  0.498  0.768  1.0
  O  O25  1  0.235  0.502  0.232  1.0
  O  O26  1  0.701  0.940  0.631  1.0
  O  O27  1  0.299  0.060  0.369  1.0
  O  O28  1  0.095  0.987  0.705  1.0
  O  O29  1  0.905  0.013  0.295  1.0
  O  O30  1  0.613  0.654  0.992  1.0
  O  O31  1  0.387  0.346  0.008  1.0
  O  O32  1  0.215  0.574  0.974  1.0
  O  O33  1  0.785  0.426  0.026  1.0
  O  O34  1  0.393  0.828  0.870  1.0
  O  O35  1  0.607  0.172  0.130  1.0
  O  O36  1  0.320  0.552  0.722  1.0
  O  O37  1  0.680  0.448  0.278  1.0
  O  O38  1  0.964  0.280  0.879  1.0
  O  O39  1  0.036  0.720  0.121  1.0
[/CIF]
.