The crystal structure described by K4Li5Mn2O8 crystallizes in the triclinic P1 space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded in a 5-coordinate geometry to one O(1), one O(11), one O(14), one O(2), and one O(6) atom. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(16), one O(3), one O(4), one O(7), and two equivalent O(12) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(4), one O(5), one O(7), one O(9), and two equivalent O(13) atoms. In the fourth K site, K(4) is bonded in a 3-coordinate geometry to one O(10), one O(15), and one O(8) atom. In the fifth K site, K(5) is bonded in a 3-coordinate geometry to one O(2), one O(7), and one O(9) atom. In the sixth K site, K(6) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(13), one O(15), one O(8), and two equivalent O(4) atoms. In the seventh K site, K(7) is bonded in a 5-coordinate geometry to one O(1), one O(10), one O(14), and two equivalent O(5) atoms. In the eighth K site, K(8) is bonded in a 3-coordinate geometry to one O(15), one O(3), and one O(6) atom. There are ten inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(13), one O(14), one O(2), and one O(7) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra,  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Mn(3)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(15), one O(16), one O(4), and one O(8) atom. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(8), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Mn(2)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(8)O4 tetrahedra, and  an edgeedge with one Mn(1)O4 tetrahedra. In the fourth Li site, Li(4) is bonded to one O(14), one O(3), one O(5), and one O(7) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Mn(3)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra,  an edgeedge with one Mn(4)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. In the fifth Li site, Li(5) is bonded in a 4-coordinate geometry to one O(1), one O(11), one O(5), and one O(9) atom. In the sixth Li site, Li(6) is bonded in a 4-coordinate geometry to one O(12), one O(16), one O(6), and one O(8) atom. In the seventh Li site, Li(7) is bonded in a bent 150 degrees geometry to one O(11) and one O(6) atom. In the eighth Li site, Li(8) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Mn(2)O4 tetrahedra. In the ninth Li site, Li(9) is bonded to one O(10), one O(12), one O(14), and one O(3) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Mn(4)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid,  an edgeedge with one Mn(3)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the tenth Li site, Li(10) is bonded to one O(1), one O(13), one O(2), and one O(9) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(8)O4 tetrahedra,  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Mn(2)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(16), one O(2), one O(6), and one O(8) atom to form MnO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Li(8)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(3)O4 tetrahedra. In the second Mn site, Mn(2) is bonded to one O(1), one O(11), one O(15), and one O(9) atom to form MnO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra, and  an edgeedge with one Li(8)O4 tetrahedra. In the third Mn site, Mn(3) is bonded to one O(12), one O(13), one O(14), and one O(7) atom to form MnO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid, corners with two equivalent Li(4)O4 trigonal pyramids,  an edgeedge with one Li(9)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. In the fourth Mn site, Mn(4) is bonded to one O(10), one O(3), one O(4), and one O(5) atom to form MnO4 tetrahedra that share corners with two equivalent Li(9)O4 tetrahedra and  an edgeedge with one Li(4)O4 trigonal pyramid. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), one K(7), one Li(10), one Li(3), one Li(5), and one Mn(2) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(1), one K(5), one Li(1), one Li(10), one Li(3), and one Mn(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(2), one K(8), one Li(4), one Li(9), and one Mn(4) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(2), one K(3), two equivalent K(6), one Li(2), and one Mn(4) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(7), one Li(4), one Li(5), and one Mn(4) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(1), one K(8), one Li(6), one Li(7), and one Mn(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one K(2), one K(3), one K(5), one Li(1), one Li(4), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one K(4), one K(6), one Li(2), one Li(3), one Li(6), one Li(8), and one Mn(1) atom. In the ninth O site, O(9) is bonded in a 7-coordinate geometry to one K(3), one K(5), one Li(10), one Li(3), one Li(5), one Li(8), and one Mn(2) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one K(4), one K(6), one K(7), one Li(9), and one Mn(4) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one K(1), one Li(5), one Li(7), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one K(6), two equivalent K(2), one Li(6), one Li(9), and one Mn(3) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one K(6), two equivalent K(3), one Li(1), one Li(10), and one Mn(3) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one K(1), one K(7), one Li(1), one Li(4), one Li(9), and one Mn(3) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one K(4), one K(6), one K(8), one Li(2), one Li(8), and one Mn(2) atom. In the sixteenth O site, O(16) is bonded in a 5-coordinate geometry to one K(2), one Li(2), one Li(6), one Li(8), and one Mn(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4Li5Mn2O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.555
_cell_length_b   8.923
_cell_length_c   10.952
_cell_angle_alpha   90.905
_cell_angle_beta   100.015
_cell_angle_gamma   90.059
_symmetry_Int_Tables_number   1
_cell_volume   534.524
_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  0.925  0.010  0.151  1.0
  K  K1  1  0.834  0.761  0.636  1.0
  K  K2  1  0.669  0.493  0.370  1.0
  K  K3  1  0.597  0.238  0.853  1.0
  K  K4  1  0.375  0.760  0.157  1.0
  K  K5  1  0.290  0.469  0.648  1.0
  K  K6  1  0.166  0.232  0.372  1.0
  K  K7  1  0.066  0.036  0.816  1.0
  Li  Li8  1  0.901  0.746  0.305  1.0
  Li  Li9  1  0.900  0.472  0.801  1.0
  Li  Li10  1  0.690  0.486  0.074  1.0
  Li  Li11  1  0.771  0.983  0.423  1.0
  Li  Li12  1  0.589  0.242  0.198  1.0
  Li  Li13  1  0.408  0.762  0.799  1.0
  Li  Li14  1  0.469  0.977  0.994  1.0
  Li  Li15  1  0.314  0.527  0.934  1.0
  Li  Li16  1  0.221  0.015  0.565  1.0
  Li  Li17  1  0.089  0.518  0.201  1.0
  Mn  Mn18  1  0.846  0.712  0.953  1.0
  Mn  Mn19  1  0.159  0.301  0.050  1.0
  Mn  Mn20  1  0.318  0.773  0.447  1.0
  Mn  Mn21  1  0.701  0.219  0.555  1.0
  O  O22  1  0.903  0.321  0.151  1.0
  O  O23  1  0.849  0.693  0.129  1.0
  O  O24  1  0.892  0.060  0.589  1.0
  O  O25  1  0.783  0.406  0.624  1.0
  O  O26  1  0.666  0.195  0.382  1.0
  O  O27  1  0.677  0.903  0.904  1.0
  O  O28  1  0.606  0.783  0.388  1.0
  O  O29  1  0.645  0.543  0.892  1.0
  O  O30  1  0.366  0.464  0.119  1.0
  O  O31  1  0.416  0.194  0.607  1.0
  O  O32  1  0.331  0.106  0.085  1.0
  O  O33  1  0.325  0.803  0.612  1.0
  O  O34  1  0.180  0.601  0.370  1.0
  O  O35  1  0.103  0.918  0.386  1.0
  O  O36  1  0.152  0.331  0.882  1.0
  O  O37  1  0.107  0.695  0.859  1.0
[/CIF]
.
The crystal structure described by K4Li5Mn2O8 crystallizes in the triclinic P1 space group. There are eight inequivalent K sites. In the first K site, K(1) is bonded in a 5-coordinate geometry to one O(1), one O(11), one O(14), one O(2), and one O(6) atom. In the second K site, K(2) is bonded in a 6-coordinate geometry to one O(16), one O(3), one O(4), one O(7), and two equivalent O(12) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(4), one O(5), one O(7), one O(9), and two equivalent O(13) atoms. In the fourth K site, K(4) is bonded in a 3-coordinate geometry to one O(10), one O(15), and one O(8) atom. In the fifth K site, K(5) is bonded in a 3-coordinate geometry to one O(2), one O(7), and one O(9) atom. In the sixth K site, K(6) is bonded in a 7-coordinate geometry to one O(10), one O(12), one O(13), one O(15), one O(8), and two equivalent O(4) atoms. In the seventh K site, K(7) is bonded in a 5-coordinate geometry to one O(1), one O(10), one O(14), and two equivalent O(5) atoms. In the eighth K site, K(8) is bonded in a 3-coordinate geometry to one O(15), one O(3), and one O(6) atom. There are ten inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(13), one O(14), one O(2), and one O(7) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(9)O4 tetrahedra,  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Mn(3)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(15), one O(16), one O(4), and one O(8) atom. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(8), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Mn(2)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid,  an edgeedge with one Li(10)O4 tetrahedra,  an edgeedge with one Li(8)O4 tetrahedra, and  an edgeedge with one Mn(1)O4 tetrahedra. In the fourth Li site, Li(4) is bonded to one O(14), one O(3), one O(5), and one O(7) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Mn(3)O4 tetrahedra,  an edgeedge with one Li(9)O4 tetrahedra,  an edgeedge with one Mn(4)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. In the fifth Li site, Li(5) is bonded in a 4-coordinate geometry to one O(1), one O(11), one O(5), and one O(9) atom. In the sixth Li site, Li(6) is bonded in a 4-coordinate geometry to one O(12), one O(16), one O(6), and one O(8) atom. In the seventh Li site, Li(7) is bonded in a bent 150 degrees geometry to one O(11) and one O(6) atom. In the eighth Li site, Li(8) is bonded to one O(15), one O(16), one O(8), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Mn(2)O4 tetrahedra. In the ninth Li site, Li(9) is bonded to one O(10), one O(12), one O(14), and one O(3) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Mn(4)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid,  an edgeedge with one Mn(3)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the tenth Li site, Li(10) is bonded to one O(1), one O(13), one O(2), and one O(9) atom to form distorted LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(8)O4 tetrahedra,  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra,  an edgeedge with one Li(3)O4 tetrahedra,  an edgeedge with one Mn(2)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(16), one O(2), one O(6), and one O(8) atom to form MnO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra, corners with two equivalent Li(8)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(3)O4 tetrahedra. In the second Mn site, Mn(2) is bonded to one O(1), one O(11), one O(15), and one O(9) atom to form MnO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Li(10)O4 tetrahedra, and  an edgeedge with one Li(8)O4 tetrahedra. In the third Mn site, Mn(3) is bonded to one O(12), one O(13), one O(14), and one O(7) atom to form MnO4 tetrahedra that share  a cornercorner with one Li(10)O4 tetrahedra,  a cornercorner with one Li(1)O4 trigonal pyramid, corners with two equivalent Li(4)O4 trigonal pyramids,  an edgeedge with one Li(9)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. In the fourth Mn site, Mn(4) is bonded to one O(10), one O(3), one O(4), and one O(5) atom to form MnO4 tetrahedra that share corners with two equivalent Li(9)O4 tetrahedra and  an edgeedge with one Li(4)O4 trigonal pyramid. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), one K(7), one Li(10), one Li(3), one Li(5), and one Mn(2) atom. In the second O site, O(2) is bonded in a 4-coordinate geometry to one K(1), one K(5), one Li(1), one Li(10), one Li(3), and one Mn(1) atom. In the third O site, O(3) is bonded in a 5-coordinate geometry to one K(2), one K(8), one Li(4), one Li(9), and one Mn(4) atom. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to one K(2), one K(3), two equivalent K(6), one Li(2), and one Mn(4) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(7), one Li(4), one Li(5), and one Mn(4) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one K(1), one K(8), one Li(6), one Li(7), and one Mn(1) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one K(2), one K(3), one K(5), one Li(1), one Li(4), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a 4-coordinate geometry to one K(4), one K(6), one Li(2), one Li(3), one Li(6), one Li(8), and one Mn(1) atom. In the ninth O site, O(9) is bonded in a 7-coordinate geometry to one K(3), one K(5), one Li(10), one Li(3), one Li(5), one Li(8), and one Mn(2) atom. In the tenth O site, O(10) is bonded in a 5-coordinate geometry to one K(4), one K(6), one K(7), one Li(9), and one Mn(4) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one K(1), one Li(5), one Li(7), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one K(6), two equivalent K(2), one Li(6), one Li(9), and one Mn(3) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one K(6), two equivalent K(3), one Li(1), one Li(10), and one Mn(3) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one K(1), one K(7), one Li(1), one Li(4), one Li(9), and one Mn(3) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one K(4), one K(6), one K(8), one Li(2), one Li(8), and one Mn(2) atom. In the sixteenth O site, O(16) is bonded in a 5-coordinate geometry to one K(2), one Li(2), one Li(6), one Li(8), and one Mn(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4Li5Mn2O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.555
_cell_length_b   8.923
_cell_length_c   10.952
_cell_angle_alpha   90.905
_cell_angle_beta   100.015
_cell_angle_gamma   90.059
_symmetry_Int_Tables_number   1
_cell_volume   534.524
_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  0.925  0.010  0.151  1.0
  K  K1  1  0.834  0.761  0.636  1.0
  K  K2  1  0.669  0.493  0.370  1.0
  K  K3  1  0.597  0.238  0.853  1.0
  K  K4  1  0.375  0.760  0.157  1.0
  K  K5  1  0.290  0.469  0.648  1.0
  K  K6  1  0.166  0.232  0.372  1.0
  K  K7  1  0.066  0.036  0.816  1.0
  Li  Li8  1  0.901  0.746  0.305  1.0
  Li  Li9  1  0.900  0.472  0.801  1.0
  Li  Li10  1  0.690  0.486  0.074  1.0
  Li  Li11  1  0.771  0.983  0.423  1.0
  Li  Li12  1  0.589  0.242  0.198  1.0
  Li  Li13  1  0.408  0.762  0.799  1.0
  Li  Li14  1  0.469  0.977  0.994  1.0
  Li  Li15  1  0.314  0.527  0.934  1.0
  Li  Li16  1  0.221  0.015  0.565  1.0
  Li  Li17  1  0.089  0.518  0.201  1.0
  Mn  Mn18  1  0.846  0.712  0.953  1.0
  Mn  Mn19  1  0.159  0.301  0.050  1.0
  Mn  Mn20  1  0.318  0.773  0.447  1.0
  Mn  Mn21  1  0.701  0.219  0.555  1.0
  O  O22  1  0.903  0.321  0.151  1.0
  O  O23  1  0.849  0.693  0.129  1.0
  O  O24  1  0.892  0.060  0.589  1.0
  O  O25  1  0.783  0.406  0.624  1.0
  O  O26  1  0.666  0.195  0.382  1.0
  O  O27  1  0.677  0.903  0.904  1.0
  O  O28  1  0.606  0.783  0.388  1.0
  O  O29  1  0.645  0.543  0.892  1.0
  O  O30  1  0.366  0.464  0.119  1.0
  O  O31  1  0.416  0.194  0.607  1.0
  O  O32  1  0.331  0.106  0.085  1.0
  O  O33  1  0.325  0.803  0.612  1.0
  O  O34  1  0.180  0.601  0.370  1.0
  O  O35  1  0.103  0.918  0.386  1.0
  O  O36  1  0.152  0.331  0.882  1.0
  O  O37  1  0.107  0.695  0.859  1.0
[/CIF]
.