The material described by Li4Mn13O24 is beta indium sulfide-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(2), one O(4), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra,  a cornercorner with one Mn(9)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and corners with two equivalent Mn(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-65°. In the second Li site, Li(2) is bonded to one O(10), one O(16), one O(18), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(11)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(4)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra, corners with two equivalent Mn(8)O6 octahedra, and corners with two equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-65°. In the third Li site, Li(3) is bonded to one O(15), one O(19), one O(7), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(4)O6 octahedra,  a cornercorner with one Mn(5)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, and corners with two equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. In the fourth Li site, Li(4) is bonded to one O(14), one O(17), one O(21), and one O(23) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra,  a cornercorner with one Mn(8)O6 octahedra,  a cornercorner with one Mn(9)O6 octahedra, corners with two equivalent Mn(11)O6 octahedra, and corners with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. There are thirteen inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(15), one O(2), one O(3), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(9)O6 octahedra. In the second Mn site, Mn(2) is bonded to one O(18), one O(2), one O(22), one O(23), one O(3), and one O(7) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra, and edges with two equivalent Mn(6)O6 octahedra. In the third Mn site, Mn(3) is bonded to one O(11), one O(14), one O(15), one O(4), one O(5), and one O(6) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(7)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to one O(17), one O(19), one O(21), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra, and  an edgeedge with one Mn(7)O6 octahedra. In the fifth Mn site, Mn(5) is bonded to one O(22), one O(24), one O(4), one O(5), one O(7), and one O(8) atom to form MnO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Mn(13)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(8)O6 octahedra. In the sixth Mn site, Mn(6) is bonded to one O(1), one O(18), one O(2), one O(23), one O(24), and one O(7) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. In the seventh Mn site, Mn(7) is bonded to one O(11), one O(14), one O(5), one O(6), one O(8), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. In the eighth Mn site, Mn(8) is bonded to one O(10), one O(13), one O(16), one O(22), one O(23), and one O(24) atom to form MnO6 octahedra that share  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mn(13)O4 tetrahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra, and  an edgeedge with one Mn(9)O6 octahedra. In the ninth Mn site, Mn(9) is bonded to one O(10), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(8)O6 octahedra. In the tenth Mn site, Mn(10) is bonded to one O(12), one O(13), one O(16), one O(17), one O(19), and one O(20) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(12)O6 octahedra. In the eleventh Mn site, Mn(11) is bonded to one O(1), one O(17), one O(18), one O(20), one O(21), and one O(3) atom to form MnO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra, and  an edgeedge with one Mn(6)O6 octahedra. In the twelfth Mn site, Mn(12) is bonded to one O(10), one O(12), one O(13), one O(19), one O(20), and one O(21) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(10)O6 octahedra. In the thirteenth Mn site, Mn(13) is bonded to one O(11), one O(20), one O(22), and one O(24) atom to form corner-sharing MnO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-62°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(1), one Mn(11), and one Mn(6) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), one Mn(2), and one Mn(6) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Mn(1), one Mn(11), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(3), one Mn(4), and one Mn(5) atom. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Mn(3), one Mn(5), and one Mn(7) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Mn(3), one Mn(4), and one Mn(7) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(2), one Mn(5), and one Mn(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(4), one Mn(5), and one Mn(7) atom. In the ninth O site, O(9) is bonded to one Li(3), one Mn(1), one Mn(7), and one Mn(9) atom to form a mixture of distorted corner and edge-sharing OLiMn3 trigonal pyramids. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(12), one Mn(8), and one Mn(9) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mn(1), one Mn(13), one Mn(3), and one Mn(7) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(10), one Mn(12), and one Mn(9) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Mn(10), one Mn(12), and one Mn(8) atom. In the fourteenth O site, O(14) is bonded to one Li(4), one Mn(3), one Mn(7), and one Mn(9) atom to form a mixture of corner and edge-sharing OLiMn3 tetrahedra. In the fifteenth O site, O(15) is bonded to one Li(3), one Mn(1), one Mn(3), and one Mn(9) atom to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(10), one Mn(8), and one Mn(9) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one Li(4), one Mn(10), one Mn(11), and one Mn(4) atom. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(11), one Mn(2), and one Mn(6) atom. In the nineteenth O site, O(19) is bonded to one Li(3), one Mn(10), one Mn(12), and one Mn(4) atom to form a mixture of corner and edge-sharing OLiMn3 tetrahedra. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Mn(10), one Mn(11), one Mn(12), and one Mn(13) atom. In the twenty-first O site, O(21) is bonded to one Li(4), one Mn(11), one Mn(12), and one Mn(4) atom to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. In the twenty-second O site, O(22) is bonded in a distorted rectangular see-saw-like geometry to one Mn(13), one Mn(2), one Mn(5), and one Mn(8) atom. In the twenty-third O site, O(23) is bonded to one Li(4), one Mn(2), one Mn(6), and one Mn(8) atom to form distorted corner-sharing OLiMn3 trigonal pyramids. In the twenty-fourth O site, O(24) is bonded in a distorted rectangular see-saw-like geometry to one Mn(13), one Mn(5), one Mn(6), and one Mn(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Mn13O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.030
_cell_length_b   8.344
_cell_length_c   10.291
_cell_angle_alpha   113.567
_cell_angle_beta   105.443
_cell_angle_gamma   90.473
_symmetry_Int_Tables_number   1
_cell_volume   453.611
_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
  Li  Li0  1  0.075  0.207  0.663  1.0
  Li  Li1  1  0.416  0.544  0.336  1.0
  Li  Li2  1  0.590  0.457  0.668  1.0
  Li  Li3  1  0.918  0.787  0.330  1.0
  Mn  Mn4  1  0.168  0.661  0.834  1.0
  Mn  Mn5  1  0.002  0.499  0.000  1.0
  Mn  Mn6  1  0.827  0.831  0.660  1.0
  Mn  Mn7  1  0.487  0.991  0.489  1.0
  Mn  Mn8  1  0.665  0.166  0.824  1.0
  Mn  Mn9  1  0.501  0.498  0.998  1.0
  Mn  Mn10  1  0.331  0.832  0.659  1.0
  Mn  Mn11  1  0.845  0.344  0.176  1.0
  Mn  Mn12  1  0.008  0.501  0.507  1.0
  Mn  Mn13  1  0.674  0.171  0.339  1.0
  Mn  Mn14  1  0.330  0.826  0.164  1.0
  Mn  Mn15  1  0.170  0.174  0.341  1.0
  Mn  Mn16  1  0.255  0.121  1.000  1.0
  O  O17  1  0.460  0.728  0.997  1.0
  O  O18  1  0.159  0.436  0.848  1.0
  O  O19  1  0.037  0.733  0.001  1.0
  O  O20  1  0.788  0.064  0.647  1.0
  O  O21  1  0.640  0.919  0.797  1.0
  O  O22  1  0.482  0.770  0.504  1.0
  O  O23  1  0.697  0.412  0.851  1.0
  O  O24  1  0.336  0.057  0.644  1.0
  O  O25  1  0.306  0.597  0.669  1.0
  O  O26  1  0.162  0.418  0.357  1.0
  O  O27  1  0.179  0.891  0.818  1.0
  O  O28  1  0.998  0.273  0.501  1.0
  O  O29  1  0.857  0.124  0.203  1.0
  O  O30  1  0.016  0.746  0.522  1.0
  O  O31  1  0.872  0.599  0.674  1.0
  O  O32  1  0.712  0.424  0.351  1.0
  O  O33  1  0.624  0.915  0.326  1.0
  O  O34  1  0.307  0.583  0.148  1.0
  O  O35  1  0.488  0.220  0.477  1.0
  O  O36  1  0.341  0.065  0.176  1.0
  O  O37  1  0.196  0.924  0.329  1.0
  O  O38  1  0.990  0.268  0.006  1.0
  O  O39  1  0.841  0.562  0.150  1.0
  O  O40  1  0.521  0.262  0.991  1.0
[/CIF]
.
The material described by Li4Mn13O24 is beta indium sulfide-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(2), one O(4), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra,  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra,  a cornercorner with one Mn(9)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, and corners with two equivalent Mn(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-65°. In the second Li site, Li(2) is bonded to one O(10), one O(16), one O(18), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(11)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(4)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra, corners with two equivalent Mn(8)O6 octahedra, and corners with two equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-65°. In the third Li site, Li(3) is bonded to one O(15), one O(19), one O(7), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(4)O6 octahedra,  a cornercorner with one Mn(5)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, and corners with two equivalent Mn(9)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. In the fourth Li site, Li(4) is bonded to one O(14), one O(17), one O(21), and one O(23) atom to form LiO4 tetrahedra that share  a cornercorner with one Mn(10)O6 octahedra,  a cornercorner with one Mn(12)O6 octahedra,  a cornercorner with one Mn(2)O6 octahedra,  a cornercorner with one Mn(3)O6 octahedra,  a cornercorner with one Mn(6)O6 octahedra,  a cornercorner with one Mn(7)O6 octahedra,  a cornercorner with one Mn(8)O6 octahedra,  a cornercorner with one Mn(9)O6 octahedra, corners with two equivalent Mn(11)O6 octahedra, and corners with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. There are thirteen inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(15), one O(2), one O(3), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(9)O6 octahedra. In the second Mn site, Mn(2) is bonded to one O(18), one O(2), one O(22), one O(23), one O(3), and one O(7) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra, and edges with two equivalent Mn(6)O6 octahedra. In the third Mn site, Mn(3) is bonded to one O(11), one O(14), one O(15), one O(4), one O(5), and one O(6) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(7)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to one O(17), one O(19), one O(21), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra, and  an edgeedge with one Mn(7)O6 octahedra. In the fifth Mn site, Mn(5) is bonded to one O(22), one O(24), one O(4), one O(5), one O(7), and one O(8) atom to form MnO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Mn(13)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(8)O6 octahedra. In the sixth Mn site, Mn(6) is bonded to one O(1), one O(18), one O(2), one O(23), one O(24), and one O(7) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. In the seventh Mn site, Mn(7) is bonded to one O(11), one O(14), one O(5), one O(6), one O(8), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. In the eighth Mn site, Mn(8) is bonded to one O(10), one O(13), one O(16), one O(22), one O(23), and one O(24) atom to form MnO6 octahedra that share  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mn(13)O4 tetrahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(5)O6 octahedra,  an edgeedge with one Mn(6)O6 octahedra, and  an edgeedge with one Mn(9)O6 octahedra. In the ninth Mn site, Mn(9) is bonded to one O(10), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(3)O6 octahedra,  an edgeedge with one Mn(7)O6 octahedra, and  an edgeedge with one Mn(8)O6 octahedra. In the tenth Mn site, Mn(10) is bonded to one O(12), one O(13), one O(16), one O(17), one O(19), and one O(20) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(12)O6 octahedra. In the eleventh Mn site, Mn(11) is bonded to one O(1), one O(17), one O(18), one O(20), one O(21), and one O(3) atom to form MnO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra,  an edgeedge with one Mn(10)O6 octahedra,  an edgeedge with one Mn(12)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra, and  an edgeedge with one Mn(6)O6 octahedra. In the twelfth Mn site, Mn(12) is bonded to one O(10), one O(12), one O(13), one O(19), one O(20), and one O(21) atom to form MnO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Mn(13)O4 tetrahedra,  an edgeedge with one Mn(11)O6 octahedra,  an edgeedge with one Mn(4)O6 octahedra,  an edgeedge with one Mn(8)O6 octahedra,  an edgeedge with one Mn(9)O6 octahedra, and edges with two equivalent Mn(10)O6 octahedra. In the thirteenth Mn site, Mn(13) is bonded to one O(11), one O(20), one O(22), and one O(24) atom to form corner-sharing MnO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-62°. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Mn(1), one Mn(11), and one Mn(6) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), one Mn(2), and one Mn(6) atom. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Mn(1), one Mn(11), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(3), one Mn(4), and one Mn(5) atom. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Mn(3), one Mn(5), and one Mn(7) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Mn(3), one Mn(4), and one Mn(7) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(2), one Mn(5), and one Mn(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(4), one Mn(5), and one Mn(7) atom. In the ninth O site, O(9) is bonded to one Li(3), one Mn(1), one Mn(7), and one Mn(9) atom to form a mixture of distorted corner and edge-sharing OLiMn3 trigonal pyramids. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(12), one Mn(8), and one Mn(9) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mn(1), one Mn(13), one Mn(3), and one Mn(7) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(10), one Mn(12), and one Mn(9) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Mn(10), one Mn(12), and one Mn(8) atom. In the fourteenth O site, O(14) is bonded to one Li(4), one Mn(3), one Mn(7), and one Mn(9) atom to form a mixture of corner and edge-sharing OLiMn3 tetrahedra. In the fifteenth O site, O(15) is bonded to one Li(3), one Mn(1), one Mn(3), and one Mn(9) atom to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. In the sixteenth O site, O(16) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(10), one Mn(8), and one Mn(9) atom. In the seventeenth O site, O(17) is bonded in a rectangular see-saw-like geometry to one Li(4), one Mn(10), one Mn(11), and one Mn(4) atom. In the eighteenth O site, O(18) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(11), one Mn(2), and one Mn(6) atom. In the nineteenth O site, O(19) is bonded to one Li(3), one Mn(10), one Mn(12), and one Mn(4) atom to form a mixture of corner and edge-sharing OLiMn3 tetrahedra. In the twentieth O site, O(20) is bonded in a rectangular see-saw-like geometry to one Mn(10), one Mn(11), one Mn(12), and one Mn(13) atom. In the twenty-first O site, O(21) is bonded to one Li(4), one Mn(11), one Mn(12), and one Mn(4) atom to form a mixture of distorted corner and edge-sharing OLiMn3 tetrahedra. In the twenty-second O site, O(22) is bonded in a distorted rectangular see-saw-like geometry to one Mn(13), one Mn(2), one Mn(5), and one Mn(8) atom. In the twenty-third O site, O(23) is bonded to one Li(4), one Mn(2), one Mn(6), and one Mn(8) atom to form distorted corner-sharing OLiMn3 trigonal pyramids. In the twenty-fourth O site, O(24) is bonded in a distorted rectangular see-saw-like geometry to one Mn(13), one Mn(5), one Mn(6), and one Mn(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Mn13O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.030
_cell_length_b   8.344
_cell_length_c   10.291
_cell_angle_alpha   113.567
_cell_angle_beta   105.443
_cell_angle_gamma   90.473
_symmetry_Int_Tables_number   1
_cell_volume   453.611
_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
  Li  Li0  1  0.075  0.207  0.663  1.0
  Li  Li1  1  0.416  0.544  0.336  1.0
  Li  Li2  1  0.590  0.457  0.668  1.0
  Li  Li3  1  0.918  0.787  0.330  1.0
  Mn  Mn4  1  0.168  0.661  0.834  1.0
  Mn  Mn5  1  0.002  0.499  0.000  1.0
  Mn  Mn6  1  0.827  0.831  0.660  1.0
  Mn  Mn7  1  0.487  0.991  0.489  1.0
  Mn  Mn8  1  0.665  0.166  0.824  1.0
  Mn  Mn9  1  0.501  0.498  0.998  1.0
  Mn  Mn10  1  0.331  0.832  0.659  1.0
  Mn  Mn11  1  0.845  0.344  0.176  1.0
  Mn  Mn12  1  0.008  0.501  0.507  1.0
  Mn  Mn13  1  0.674  0.171  0.339  1.0
  Mn  Mn14  1  0.330  0.826  0.164  1.0
  Mn  Mn15  1  0.170  0.174  0.341  1.0
  Mn  Mn16  1  0.255  0.121  1.000  1.0
  O  O17  1  0.460  0.728  0.997  1.0
  O  O18  1  0.159  0.436  0.848  1.0
  O  O19  1  0.037  0.733  0.001  1.0
  O  O20  1  0.788  0.064  0.647  1.0
  O  O21  1  0.640  0.919  0.797  1.0
  O  O22  1  0.482  0.770  0.504  1.0
  O  O23  1  0.697  0.412  0.851  1.0
  O  O24  1  0.336  0.057  0.644  1.0
  O  O25  1  0.306  0.597  0.669  1.0
  O  O26  1  0.162  0.418  0.357  1.0
  O  O27  1  0.179  0.891  0.818  1.0
  O  O28  1  0.998  0.273  0.501  1.0
  O  O29  1  0.857  0.124  0.203  1.0
  O  O30  1  0.016  0.746  0.522  1.0
  O  O31  1  0.872  0.599  0.674  1.0
  O  O32  1  0.712  0.424  0.351  1.0
  O  O33  1  0.624  0.915  0.326  1.0
  O  O34  1  0.307  0.583  0.148  1.0
  O  O35  1  0.488  0.220  0.477  1.0
  O  O36  1  0.341  0.065  0.176  1.0
  O  O37  1  0.196  0.924  0.329  1.0
  O  O38  1  0.990  0.268  0.006  1.0
  O  O39  1  0.841  0.562  0.150  1.0
  O  O40  1  0.521  0.262  0.991  1.0
[/CIF]
.