The crystal structure described by K4Mg2H16S4O23 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 10-coordinate geometry to one H(16), one H(4), one S(1), one O(1), one O(10), one O(18), one O(20), one O(22), one O(6), and one O(7) atom. In the second K site, K(2) is bonded in a 11-coordinate geometry to one H(11), one H(16), one H(7), one O(12), one O(14), one O(15), one O(19), one O(20), one O(4), one O(7), and one O(8) atom. In the third K site, K(3) is bonded in a 6-coordinate geometry to one H(1), one O(17), one O(19), one O(23), one O(3), and one O(9) atom. In the fourth K site, K(4) is bonded in a 8-coordinate geometry to one H(1), one H(13), one O(13), one O(15), one O(17), one O(22), one O(3), and one O(5) atom. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(15), one O(2), one O(21), and one O(6) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one S(2)O4 tetrahedra and  a cornercorner with one S(3)O4 tetrahedra. In the second Mg site, Mg(2) is bonded to one O(10), one O(13), one O(14), one O(16), one O(8), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one S(4)O4 tetrahedra. There are sixteen inequivalent H sites. In the first H site, H(1) is bonded in a single-bond geometry to one K(3), one K(4), and one O(23) atom. In the second H site, H(2) is bonded in a linear geometry to one O(1) and one O(4) atom. In the third H site, H(3) is bonded in a single-bond geometry to one O(9) atom. In the fourth H site, H(4) is bonded in a single-bond geometry to one K(1) and one O(6) atom. In the fifth H site, H(5) is bonded in a single-bond geometry to one O(9) atom. In the sixth H site, H(6) is bonded in a single-bond geometry to one O(6) atom. In the seventh H site, H(7) is bonded in a single-bond geometry to one K(2) and one O(10) atom. In the eighth H site, H(8) is bonded in a single-bond geometry to one O(10) atom. In the ninth H site, H(9) is bonded in a single-bond geometry to one O(13) atom. In the tenth H site, H(10) is bonded in a single-bond geometry to one O(13) atom. In the eleventh H site, H(11) is bonded in a single-bond geometry to one K(2) and one O(15) atom. In the twelfth H site, H(12) is bonded in a single-bond geometry to one O(14) atom. In the thirteenth H site, H(13) is bonded in a single-bond geometry to one K(4) and one O(15) atom. In the fourteenth H site, H(14) is bonded in a single-bond geometry to one O(14) atom. In the fifteenth H site, H(15) is bonded in a single-bond geometry to one O(23) atom. In the sixteenth H site, H(16) is bonded in a single-bond geometry to one K(1), one K(2), and one O(1) atom. There are four inequivalent S sites. In the first S site, S(1) is bonded in a trigonal non-coplanar geometry to one K(1), one O(4), one O(7), and one O(8) atom. In the second S site, S(2) is bonded to one O(11), one O(2), one O(3), and one O(5) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O5 trigonal bipyramid. In the third S site, S(3) is bonded to one O(12), one O(18), one O(20), and one O(21) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O5 trigonal bipyramid. In the fourth S site, S(4) is bonded to one O(16), one O(17), one O(19), and one O(22) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 22°. There are twenty-three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one K(1), one Mg(1), one H(16), and one H(2) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Mg(1) and one S(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one K(3), one K(4), and one S(2) atom. In the fourth O site, O(4) is bonded in a distorted water-like geometry to one K(2), one H(2), and one S(1) atom. In the fifth O site, O(5) is bonded in a single-bond geometry to one K(4) and one S(2) atom. In the sixth O site, O(6) is bonded in a distorted water-like geometry to one K(1), one Mg(1), one H(4), and one H(6) atom. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one K(1), one K(2), and one S(1) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one K(2), one Mg(2), and one S(1) atom. In the ninth O site, O(9) is bonded in a distorted water-like geometry to one K(3), one Mg(2), one H(3), and one H(5) atom. In the tenth O site, O(10) is bonded in a distorted water-like geometry to one K(1), one Mg(2), one H(7), and one H(8) atom. In the eleventh O site, O(11) is bonded in a single-bond geometry to one S(2) atom. In the twelfth O site, O(12) is bonded in a single-bond geometry to one K(2) and one S(3) atom. In the thirteenth O site, O(13) is bonded in a distorted water-like geometry to one K(4), one Mg(2), one H(10), and one H(9) atom. In the fourteenth O site, O(14) is bonded in a distorted water-like geometry to one K(2), one Mg(2), one H(12), and one H(14) atom. In the fifteenth O site, O(15) is bonded in a distorted water-like geometry to one K(2), one K(4), one Mg(1), one H(11), and one H(13) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Mg(2) and one S(4) atom. In the seventeenth O site, O(17) is bonded in a distorted single-bond geometry to one K(3), one K(4), and one S(4) atom. In the eighteenth O site, O(18) is bonded in a single-bond geometry to one K(1) and one S(3) atom. In the nineteenth O site, O(19) is bonded in a single-bond geometry to one K(2), one K(3), and one S(4) atom. In the twentieth O site, O(20) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(3) atom. In the twenty-first O site, O(21) is bonded in a bent 120 degrees geometry to one Mg(1) and one S(3) atom. In the twenty-second O site, O(22) is bonded in a distorted single-bond geometry to one K(1), one K(4), and one S(4) atom. In the twenty-third O site, O(23) is bonded in a water-like geometry to one K(3), one H(1), and one H(15) atom. is represented by the CIF file [CIF]
data_K4Mg2H16S4O23
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.749
_cell_length_b   7.918
_cell_length_c   9.936
_cell_angle_alpha   83.724
_cell_angle_beta   84.393
_cell_angle_gamma   80.585
_symmetry_Int_Tables_number   1
_cell_volume   595.815
_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  0.387  0.921  0.721  1.0
  K  K1  1  0.912  0.419  0.720  1.0
  K  K2  1  0.081  0.609  0.295  1.0
  K  K3  1  0.584  0.101  0.242  1.0
  Mg  Mg4  1  0.998  0.996  0.949  1.0
  Mg  Mg5  1  0.513  0.506  0.500  1.0
  H  H6  1  0.913  0.926  0.271  1.0
  H  H7  1  0.973  0.891  0.690  1.0
  H  H8  1  0.343  0.825  0.381  1.0
  H  H9  1  0.324  0.793  0.022  1.0
  H  H10  1  0.451  0.728  0.263  1.0
  H  H11  1  0.208  0.668  0.973  1.0
  H  H12  1  0.183  0.654  0.621  1.0
  H  H13  1  0.286  0.552  0.738  1.0
  H  H14  1  0.726  0.446  0.259  1.0
  H  H15  1  0.825  0.343  0.380  1.0
  H  H16  1  0.799  0.326  0.021  1.0
  H  H17  1  0.550  0.267  0.743  1.0
  H  H18  1  0.665  0.222  0.966  1.0
  H  H19  1  0.662  0.186  0.620  1.0
  H  H20  1  0.041  0.066  0.274  1.0
  H  H21  1  0.054  0.071  0.683  1.0
  S  S22  1  0.743  0.769  0.610  1.0
  S  S23  1  0.729  0.737  0.103  1.0
  S  S24  1  0.261  0.263  0.895  1.0
  S  S25  1  0.243  0.246  0.404  1.0
  O  O26  1  0.995  0.991  0.746  1.0
  O  O27  1  0.824  0.834  0.991  1.0
  O  O28  1  0.771  0.787  0.235  1.0
  O  O29  1  0.949  0.752  0.612  1.0
  O  O30  1  0.534  0.783  0.096  1.0
  O  O31  1  0.208  0.788  0.990  1.0
  O  O32  1  0.677  0.713  0.753  1.0
  O  O33  1  0.721  0.623  0.526  1.0
  O  O34  1  0.392  0.709  0.356  1.0
  O  O35  1  0.304  0.621  0.649  1.0
  O  O36  1  0.784  0.547  0.099  1.0
  O  O37  1  0.212  0.450  0.909  1.0
  O  O38  1  0.706  0.374  0.347  1.0
  O  O39  1  0.619  0.296  0.656  1.0
  O  O40  1  0.787  0.214  0.992  1.0
  O  O41  1  0.338  0.354  0.476  1.0
  O  O42  1  0.275  0.290  0.255  1.0
  O  O43  1  0.454  0.207  0.905  1.0
  O  O44  1  0.051  0.287  0.446  1.0
  O  O45  1  0.217  0.228  0.759  1.0
  O  O46  1  0.159  0.157  1.000  1.0
  O  O47  1  0.312  0.061  0.442  1.0
  O  O48  1  0.008  0.958  0.317  1.0
[/CIF]
.
The crystal structure described by K4Mg2H16S4O23 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 10-coordinate geometry to one H(16), one H(4), one S(1), one O(1), one O(10), one O(18), one O(20), one O(22), one O(6), and one O(7) atom. In the second K site, K(2) is bonded in a 11-coordinate geometry to one H(11), one H(16), one H(7), one O(12), one O(14), one O(15), one O(19), one O(20), one O(4), one O(7), and one O(8) atom. In the third K site, K(3) is bonded in a 6-coordinate geometry to one H(1), one O(17), one O(19), one O(23), one O(3), and one O(9) atom. In the fourth K site, K(4) is bonded in a 8-coordinate geometry to one H(1), one H(13), one O(13), one O(15), one O(17), one O(22), one O(3), and one O(5) atom. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(15), one O(2), one O(21), and one O(6) atom to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one S(2)O4 tetrahedra and  a cornercorner with one S(3)O4 tetrahedra. In the second Mg site, Mg(2) is bonded to one O(10), one O(13), one O(14), one O(16), one O(8), and one O(9) atom to form MgO6 octahedra that share  a cornercorner with one S(4)O4 tetrahedra. There are sixteen inequivalent H sites. In the first H site, H(1) is bonded in a single-bond geometry to one K(3), one K(4), and one O(23) atom. In the second H site, H(2) is bonded in a linear geometry to one O(1) and one O(4) atom. In the third H site, H(3) is bonded in a single-bond geometry to one O(9) atom. In the fourth H site, H(4) is bonded in a single-bond geometry to one K(1) and one O(6) atom. In the fifth H site, H(5) is bonded in a single-bond geometry to one O(9) atom. In the sixth H site, H(6) is bonded in a single-bond geometry to one O(6) atom. In the seventh H site, H(7) is bonded in a single-bond geometry to one K(2) and one O(10) atom. In the eighth H site, H(8) is bonded in a single-bond geometry to one O(10) atom. In the ninth H site, H(9) is bonded in a single-bond geometry to one O(13) atom. In the tenth H site, H(10) is bonded in a single-bond geometry to one O(13) atom. In the eleventh H site, H(11) is bonded in a single-bond geometry to one K(2) and one O(15) atom. In the twelfth H site, H(12) is bonded in a single-bond geometry to one O(14) atom. In the thirteenth H site, H(13) is bonded in a single-bond geometry to one K(4) and one O(15) atom. In the fourteenth H site, H(14) is bonded in a single-bond geometry to one O(14) atom. In the fifteenth H site, H(15) is bonded in a single-bond geometry to one O(23) atom. In the sixteenth H site, H(16) is bonded in a single-bond geometry to one K(1), one K(2), and one O(1) atom. There are four inequivalent S sites. In the first S site, S(1) is bonded in a trigonal non-coplanar geometry to one K(1), one O(4), one O(7), and one O(8) atom. In the second S site, S(2) is bonded to one O(11), one O(2), one O(3), and one O(5) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O5 trigonal bipyramid. In the third S site, S(3) is bonded to one O(12), one O(18), one O(20), and one O(21) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(1)O5 trigonal bipyramid. In the fourth S site, S(4) is bonded to one O(16), one O(17), one O(19), and one O(22) atom to form SO4 tetrahedra that share  a cornercorner with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 22°. There are twenty-three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one K(1), one Mg(1), one H(16), and one H(2) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Mg(1) and one S(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one K(3), one K(4), and one S(2) atom. In the fourth O site, O(4) is bonded in a distorted water-like geometry to one K(2), one H(2), and one S(1) atom. In the fifth O site, O(5) is bonded in a single-bond geometry to one K(4) and one S(2) atom. In the sixth O site, O(6) is bonded in a distorted water-like geometry to one K(1), one Mg(1), one H(4), and one H(6) atom. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one K(1), one K(2), and one S(1) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one K(2), one Mg(2), and one S(1) atom. In the ninth O site, O(9) is bonded in a distorted water-like geometry to one K(3), one Mg(2), one H(3), and one H(5) atom. In the tenth O site, O(10) is bonded in a distorted water-like geometry to one K(1), one Mg(2), one H(7), and one H(8) atom. In the eleventh O site, O(11) is bonded in a single-bond geometry to one S(2) atom. In the twelfth O site, O(12) is bonded in a single-bond geometry to one K(2) and one S(3) atom. In the thirteenth O site, O(13) is bonded in a distorted water-like geometry to one K(4), one Mg(2), one H(10), and one H(9) atom. In the fourteenth O site, O(14) is bonded in a distorted water-like geometry to one K(2), one Mg(2), one H(12), and one H(14) atom. In the fifteenth O site, O(15) is bonded in a distorted water-like geometry to one K(2), one K(4), one Mg(1), one H(11), and one H(13) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Mg(2) and one S(4) atom. In the seventeenth O site, O(17) is bonded in a distorted single-bond geometry to one K(3), one K(4), and one S(4) atom. In the eighteenth O site, O(18) is bonded in a single-bond geometry to one K(1) and one S(3) atom. In the nineteenth O site, O(19) is bonded in a single-bond geometry to one K(2), one K(3), and one S(4) atom. In the twentieth O site, O(20) is bonded in a distorted single-bond geometry to one K(1), one K(2), and one S(3) atom. In the twenty-first O site, O(21) is bonded in a bent 120 degrees geometry to one Mg(1) and one S(3) atom. In the twenty-second O site, O(22) is bonded in a distorted single-bond geometry to one K(1), one K(4), and one S(4) atom. In the twenty-third O site, O(23) is bonded in a water-like geometry to one K(3), one H(1), and one H(15) atom. is represented by the CIF file [CIF]
data_K4Mg2H16S4O23
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.749
_cell_length_b   7.918
_cell_length_c   9.936
_cell_angle_alpha   83.724
_cell_angle_beta   84.393
_cell_angle_gamma   80.585
_symmetry_Int_Tables_number   1
_cell_volume   595.815
_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  0.387  0.921  0.721  1.0
  K  K1  1  0.912  0.419  0.720  1.0
  K  K2  1  0.081  0.609  0.295  1.0
  K  K3  1  0.584  0.101  0.242  1.0
  Mg  Mg4  1  0.998  0.996  0.949  1.0
  Mg  Mg5  1  0.513  0.506  0.500  1.0
  H  H6  1  0.913  0.926  0.271  1.0
  H  H7  1  0.973  0.891  0.690  1.0
  H  H8  1  0.343  0.825  0.381  1.0
  H  H9  1  0.324  0.793  0.022  1.0
  H  H10  1  0.451  0.728  0.263  1.0
  H  H11  1  0.208  0.668  0.973  1.0
  H  H12  1  0.183  0.654  0.621  1.0
  H  H13  1  0.286  0.552  0.738  1.0
  H  H14  1  0.726  0.446  0.259  1.0
  H  H15  1  0.825  0.343  0.380  1.0
  H  H16  1  0.799  0.326  0.021  1.0
  H  H17  1  0.550  0.267  0.743  1.0
  H  H18  1  0.665  0.222  0.966  1.0
  H  H19  1  0.662  0.186  0.620  1.0
  H  H20  1  0.041  0.066  0.274  1.0
  H  H21  1  0.054  0.071  0.683  1.0
  S  S22  1  0.743  0.769  0.610  1.0
  S  S23  1  0.729  0.737  0.103  1.0
  S  S24  1  0.261  0.263  0.895  1.0
  S  S25  1  0.243  0.246  0.404  1.0
  O  O26  1  0.995  0.991  0.746  1.0
  O  O27  1  0.824  0.834  0.991  1.0
  O  O28  1  0.771  0.787  0.235  1.0
  O  O29  1  0.949  0.752  0.612  1.0
  O  O30  1  0.534  0.783  0.096  1.0
  O  O31  1  0.208  0.788  0.990  1.0
  O  O32  1  0.677  0.713  0.753  1.0
  O  O33  1  0.721  0.623  0.526  1.0
  O  O34  1  0.392  0.709  0.356  1.0
  O  O35  1  0.304  0.621  0.649  1.0
  O  O36  1  0.784  0.547  0.099  1.0
  O  O37  1  0.212  0.450  0.909  1.0
  O  O38  1  0.706  0.374  0.347  1.0
  O  O39  1  0.619  0.296  0.656  1.0
  O  O40  1  0.787  0.214  0.992  1.0
  O  O41  1  0.338  0.354  0.476  1.0
  O  O42  1  0.275  0.290  0.255  1.0
  O  O43  1  0.454  0.207  0.905  1.0
  O  O44  1  0.051  0.287  0.446  1.0
  O  O45  1  0.217  0.228  0.759  1.0
  O  O46  1  0.159  0.157  1.000  1.0
  O  O47  1  0.312  0.061  0.442  1.0
  O  O48  1  0.008  0.958  0.317  1.0
[/CIF]
.