The compound described by K4MgMn4O8 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 3-coordinate geometry to one O(3), one O(6), and two equivalent O(5) atoms. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(2), two equivalent O(4), and two equivalent O(7) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(4), one O(5), two equivalent O(2), and two equivalent O(6) atoms. In the fourth K site, K(4) is bonded in a 5-coordinate geometry to one O(1), two equivalent O(3), and two equivalent O(8) atoms. Mg(1) is bonded to one O(3), one O(8), and two equivalent O(1) atoms to form distorted MgO4 tetrahedra that share  a cornercorner with one Mn(4)O5 square pyramid, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mn(1)O5 trigonal bipyramids,  an edgeedge with one Mn(1)O5 trigonal bipyramid, and edges with two equivalent Mn(3)O5 trigonal bipyramids. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(6), two equivalent O(1), and two equivalent O(5) atoms to form distorted MnO5 trigonal bipyramids that share corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Mn(2)O5 square pyramids,  an edgeedge with one Mg(1)O4 tetrahedra, and edges with two equivalent Mn(1)O5 trigonal bipyramids. In the second Mn site, Mn(2) is bonded to one O(5), two equivalent O(2), and two equivalent O(6) atoms to form edge-sharing MnO5 square pyramids. In the third Mn site, Mn(3) is bonded to one O(7), two equivalent O(3), and two equivalent O(8) atoms to form distorted MnO5 trigonal bipyramids that share edges with two equivalent Mn(4)O5 square pyramids, edges with two equivalent Mg(1)O4 tetrahedra, and edges with two equivalent Mn(3)O5 trigonal bipyramids. In the fourth Mn site, Mn(4) is bonded to one O(8), two equivalent O(4), and two equivalent O(7) atoms to form distorted MnO5 square pyramids that share  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Mn(4)O5 square pyramids, and edges with two equivalent Mn(3)O5 trigonal bipyramids. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one K(4), two equivalent Mg(1), and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(3), and two equivalent Mn(2) atoms. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(4), one Mg(1), and two equivalent Mn(3) atoms. In the fourth O site, O(4) is bonded to one K(3), two equivalent K(2), and two equivalent Mn(4) atoms to form distorted OK3Mn2 square pyramids that share corners with two equivalent O(8)K2MgMn3 octahedra, corners with four equivalent O(7)K2Mn3 trigonal bipyramids, edges with two equivalent O(4)K3Mn2 square pyramids, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 74°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(1), one Mn(2), and two equivalent Mn(1) atoms. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(3), one Mn(1), and two equivalent Mn(2) atoms. In the seventh O site, O(7) is bonded to two equivalent K(2), one Mn(3), and two equivalent Mn(4) atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four equivalent O(4)K3Mn2 square pyramids, edges with two equivalent O(8)K2MgMn3 octahedra, edges with two equivalent O(4)K3Mn2 square pyramids, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. In the eighth O site, O(8) is bonded to two equivalent K(4), one Mg(1), one Mn(4), and two equivalent Mn(3) atoms to form distorted OK2MgMn3 octahedra that share corners with two equivalent O(4)K3Mn2 square pyramids, edges with two equivalent O(8)K2MgMn3 octahedra, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4MgMn4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.086
_cell_length_b   6.584
_cell_length_c   13.682
_cell_angle_alpha   79.037
_cell_angle_beta   89.797
_cell_angle_gamma   89.978
_symmetry_Int_Tables_number   1
_cell_volume   272.898
_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  0.243  0.436  0.099  1.0
  K  K1  1  0.250  0.068  0.658  1.0
  K  K2  1  0.749  0.501  0.843  1.0
  K  K3  1  0.752  0.021  0.365  1.0
  Mg  Mg4  1  0.255  0.654  0.281  1.0
  Mn  Mn5  1  0.246  0.952  0.096  1.0
  Mn  Mn6  1  0.749  0.009  0.908  1.0
  Mn  Mn7  1  0.752  0.449  0.428  1.0
  Mn  Mn8  1  0.250  0.595  0.592  1.0
  O  O9  1  0.755  0.770  0.198  1.0
  O  O10  1  0.250  0.165  0.837  1.0
  O  O11  1  0.253  0.353  0.336  1.0
  O  O12  1  0.749  0.740  0.641  1.0
  O  O13  1  0.746  0.155  0.039  1.0
  O  O14  1  0.249  0.814  0.958  1.0
  O  O15  1  0.750  0.396  0.581  1.0
  O  O16  1  0.252  0.692  0.425  1.0
[/CIF]
.
The compound described by K4MgMn4O8 crystallizes in the triclinic P1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded in a 3-coordinate geometry to one O(3), one O(6), and two equivalent O(5) atoms. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(2), two equivalent O(4), and two equivalent O(7) atoms. In the third K site, K(3) is bonded in a 6-coordinate geometry to one O(4), one O(5), two equivalent O(2), and two equivalent O(6) atoms. In the fourth K site, K(4) is bonded in a 5-coordinate geometry to one O(1), two equivalent O(3), and two equivalent O(8) atoms. Mg(1) is bonded to one O(3), one O(8), and two equivalent O(1) atoms to form distorted MgO4 tetrahedra that share  a cornercorner with one Mn(4)O5 square pyramid, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mn(1)O5 trigonal bipyramids,  an edgeedge with one Mn(1)O5 trigonal bipyramid, and edges with two equivalent Mn(3)O5 trigonal bipyramids. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(6), two equivalent O(1), and two equivalent O(5) atoms to form distorted MnO5 trigonal bipyramids that share corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Mn(2)O5 square pyramids,  an edgeedge with one Mg(1)O4 tetrahedra, and edges with two equivalent Mn(1)O5 trigonal bipyramids. In the second Mn site, Mn(2) is bonded to one O(5), two equivalent O(2), and two equivalent O(6) atoms to form edge-sharing MnO5 square pyramids. In the third Mn site, Mn(3) is bonded to one O(7), two equivalent O(3), and two equivalent O(8) atoms to form distorted MnO5 trigonal bipyramids that share edges with two equivalent Mn(4)O5 square pyramids, edges with two equivalent Mg(1)O4 tetrahedra, and edges with two equivalent Mn(3)O5 trigonal bipyramids. In the fourth Mn site, Mn(4) is bonded to one O(8), two equivalent O(4), and two equivalent O(7) atoms to form distorted MnO5 square pyramids that share  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Mn(4)O5 square pyramids, and edges with two equivalent Mn(3)O5 trigonal bipyramids. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one K(4), two equivalent Mg(1), and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(3), and two equivalent Mn(2) atoms. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(4), one Mg(1), and two equivalent Mn(3) atoms. In the fourth O site, O(4) is bonded to one K(3), two equivalent K(2), and two equivalent Mn(4) atoms to form distorted OK3Mn2 square pyramids that share corners with two equivalent O(8)K2MgMn3 octahedra, corners with four equivalent O(7)K2Mn3 trigonal bipyramids, edges with two equivalent O(4)K3Mn2 square pyramids, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 74°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one K(3), two equivalent K(1), one Mn(2), and two equivalent Mn(1) atoms. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one K(1), two equivalent K(3), one Mn(1), and two equivalent Mn(2) atoms. In the seventh O site, O(7) is bonded to two equivalent K(2), one Mn(3), and two equivalent Mn(4) atoms to form distorted OK2Mn3 trigonal bipyramids that share corners with four equivalent O(4)K3Mn2 square pyramids, edges with two equivalent O(8)K2MgMn3 octahedra, edges with two equivalent O(4)K3Mn2 square pyramids, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. In the eighth O site, O(8) is bonded to two equivalent K(4), one Mg(1), one Mn(4), and two equivalent Mn(3) atoms to form distorted OK2MgMn3 octahedra that share corners with two equivalent O(4)K3Mn2 square pyramids, edges with two equivalent O(8)K2MgMn3 octahedra, and edges with two equivalent O(7)K2Mn3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4MgMn4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.086
_cell_length_b   6.584
_cell_length_c   13.682
_cell_angle_alpha   79.037
_cell_angle_beta   89.797
_cell_angle_gamma   89.978
_symmetry_Int_Tables_number   1
_cell_volume   272.898
_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  0.243  0.436  0.099  1.0
  K  K1  1  0.250  0.068  0.658  1.0
  K  K2  1  0.749  0.501  0.843  1.0
  K  K3  1  0.752  0.021  0.365  1.0
  Mg  Mg4  1  0.255  0.654  0.281  1.0
  Mn  Mn5  1  0.246  0.952  0.096  1.0
  Mn  Mn6  1  0.749  0.009  0.908  1.0
  Mn  Mn7  1  0.752  0.449  0.428  1.0
  Mn  Mn8  1  0.250  0.595  0.592  1.0
  O  O9  1  0.755  0.770  0.198  1.0
  O  O10  1  0.250  0.165  0.837  1.0
  O  O11  1  0.253  0.353  0.336  1.0
  O  O12  1  0.749  0.740  0.641  1.0
  O  O13  1  0.746  0.155  0.039  1.0
  O  O14  1  0.249  0.814  0.958  1.0
  O  O15  1  0.750  0.396  0.581  1.0
  O  O16  1  0.252  0.692  0.425  1.0
[/CIF]
.