The crystal structure described by Li4Mn3Sn5O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(8), and two equivalent O(11) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with two equivalent Sn(4)O6 octahedra, corners with three equivalent Sn(3)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. In the second Li site, Li(2) is bonded to one O(4), one O(5), and two equivalent O(12) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Sn(3)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-66°. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(6), and two equivalent O(9) atoms. In the fourth Li site, Li(4) is bonded to one O(1), one O(7), and two equivalent O(10) atoms to form LiO4 tetrahedra that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Sn(1)O6 octahedra, and corners with four equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(3), two equivalent O(10), and two equivalent O(12) atoms to form MnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with four equivalent Sn(4)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 55°. In the second Mn site, Mn(2) is bonded to one O(11), one O(4), one O(6), one O(7), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Sn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Sn(3)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Sn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. There are four inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one O(1), one O(6), two equivalent O(10), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the second Sn site, Sn(2) is bonded to one O(4), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Sn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Sn(3)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the third Sn site, Sn(3) is bonded to one O(5), one O(8), two equivalent O(11), and two equivalent O(12) atoms to form SnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Sn(4)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-55°. In the fourth Sn site, Sn(4) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), and one O(5) atom to form SnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Sn(4)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 50-51°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(4), one Sn(1), and two equivalent Sn(4) atoms to form distorted OLiSn3 trigonal pyramids that share  a cornercorner with one O(7)LiMn2Sn tetrahedra and corners with two equivalent O(3)LiMnSn2 tetrahedra. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Sn(4) atoms. In the third O site, O(3) is bonded to one Li(3), one Mn(1), and two equivalent Sn(4) atoms to form distorted corner-sharing OLiMnSn2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Mn(2), and one Sn(2) atom to form corner-sharing OLiMn2Sn tetrahedra. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Sn(3), and two equivalent Sn(4) atoms. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Sn(1) atom. In the seventh O site, O(7) is bonded to one Li(4), two equivalent Mn(2), and one Sn(2) atom to form distorted OLiMn2Sn tetrahedra that share corners with three equivalent O(4)LiMn2Sn tetrahedra,  a cornercorner with one O(1)LiSn3 trigonal pyramid, and  an edgeedge with one O(8)LiMn2Sn tetrahedra. In the eighth O site, O(8) is bonded to one Li(1), two equivalent Mn(2), and one Sn(3) atom to form a mixture of distorted corner and edge-sharing OLiMn2Sn tetrahedra. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(3), one Mn(2), one Sn(1), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), one Sn(1), and one Sn(4) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(2), one Sn(2), and one Sn(3) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Sn(3), and one Sn(4) atom. is represented by the CIF file [CIF]
data_Li4Mn3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.110
_cell_length_b   6.263
_cell_length_c   9.963
_cell_angle_alpha   88.277
_cell_angle_beta   89.999
_cell_angle_gamma   60.808
_symmetry_Int_Tables_number   1
_cell_volume   332.598
_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  0.663  0.673  0.896  1.0
  Li  Li1  1  0.988  0.024  0.987  1.0
  Li  Li2  1  0.999  0.002  0.494  1.0
  Li  Li3  1  0.331  0.337  0.402  1.0
  Mn  Mn4  1  0.831  0.338  0.214  1.0
  Mn  Mn5  1  0.661  0.169  0.712  1.0
  Mn  Mn6  1  0.170  0.169  0.712  1.0
  O  O7  1  0.517  0.967  0.343  1.0
  O  O8  1  0.659  0.682  0.100  1.0
  O  O9  1  0.006  0.988  0.312  1.0
  O  O10  1  0.997  0.006  0.802  1.0
  O  O11  1  0.162  0.676  0.096  1.0
  O  O12  1  0.845  0.311  0.601  1.0
  O  O13  1  0.338  0.325  0.612  1.0
  O  O14  1  0.477  0.047  0.831  1.0
  O  O15  1  0.844  0.823  0.595  1.0
  O  O16  1  0.333  0.823  0.595  1.0
  O  O17  1  0.967  0.526  0.349  1.0
  O  O18  1  0.507  0.526  0.349  1.0
  O  O19  1  0.479  0.492  0.848  1.0
  O  O20  1  0.029  0.492  0.848  1.0
  O  O21  1  0.675  0.153  0.091  1.0
  O  O22  1  0.172  0.153  0.091  1.0
  Sn  Sn23  1  0.673  0.654  0.493  1.0
  Sn  Sn24  1  0.170  0.660  0.716  1.0
  Sn  Sn25  1  0.336  0.328  0.987  1.0
  Sn  Sn26  1  0.832  0.828  0.214  1.0
  Sn  Sn27  1  0.340  0.828  0.214  1.0
[/CIF]
.
The crystal structure described by Li4Mn3Sn5O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(8), and two equivalent O(11) atoms to form LiO4 tetrahedra that share  a cornercorner with one Mn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with two equivalent Sn(4)O6 octahedra, corners with three equivalent Sn(3)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. In the second Li site, Li(2) is bonded to one O(4), one O(5), and two equivalent O(12) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Sn(3)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-66°. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(3), one O(6), and two equivalent O(9) atoms. In the fourth Li site, Li(4) is bonded to one O(1), one O(7), and two equivalent O(10) atoms to form LiO4 tetrahedra that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Sn(1)O6 octahedra, and corners with four equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(3), two equivalent O(10), and two equivalent O(12) atoms to form MnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with four equivalent Sn(4)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 55°. In the second Mn site, Mn(2) is bonded to one O(11), one O(4), one O(6), one O(7), one O(8), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Sn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Sn(3)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Sn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. There are four inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one O(1), one O(6), two equivalent O(10), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the second Sn site, Sn(2) is bonded to one O(4), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Sn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Sn(3)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the third Sn site, Sn(3) is bonded to one O(5), one O(8), two equivalent O(11), and two equivalent O(12) atoms to form SnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Sn(4)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-55°. In the fourth Sn site, Sn(4) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), and one O(5) atom to form SnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Sn(4)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 50-51°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(4), one Sn(1), and two equivalent Sn(4) atoms to form distorted OLiSn3 trigonal pyramids that share  a cornercorner with one O(7)LiMn2Sn tetrahedra and corners with two equivalent O(3)LiMnSn2 tetrahedra. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Sn(4) atoms. In the third O site, O(3) is bonded to one Li(3), one Mn(1), and two equivalent Sn(4) atoms to form distorted corner-sharing OLiMnSn2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Mn(2), and one Sn(2) atom to form corner-sharing OLiMn2Sn tetrahedra. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Sn(3), and two equivalent Sn(4) atoms. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Sn(1) atom. In the seventh O site, O(7) is bonded to one Li(4), two equivalent Mn(2), and one Sn(2) atom to form distorted OLiMn2Sn tetrahedra that share corners with three equivalent O(4)LiMn2Sn tetrahedra,  a cornercorner with one O(1)LiSn3 trigonal pyramid, and  an edgeedge with one O(8)LiMn2Sn tetrahedra. In the eighth O site, O(8) is bonded to one Li(1), two equivalent Mn(2), and one Sn(3) atom to form a mixture of distorted corner and edge-sharing OLiMn2Sn tetrahedra. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(3), one Mn(2), one Sn(1), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), one Sn(1), and one Sn(4) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(2), one Sn(2), and one Sn(3) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Sn(3), and one Sn(4) atom. is represented by the CIF file [CIF]
data_Li4Mn3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.110
_cell_length_b   6.263
_cell_length_c   9.963
_cell_angle_alpha   88.277
_cell_angle_beta   89.999
_cell_angle_gamma   60.808
_symmetry_Int_Tables_number   1
_cell_volume   332.598
_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  0.663  0.673  0.896  1.0
  Li  Li1  1  0.988  0.024  0.987  1.0
  Li  Li2  1  0.999  0.002  0.494  1.0
  Li  Li3  1  0.331  0.337  0.402  1.0
  Mn  Mn4  1  0.831  0.338  0.214  1.0
  Mn  Mn5  1  0.661  0.169  0.712  1.0
  Mn  Mn6  1  0.170  0.169  0.712  1.0
  O  O7  1  0.517  0.967  0.343  1.0
  O  O8  1  0.659  0.682  0.100  1.0
  O  O9  1  0.006  0.988  0.312  1.0
  O  O10  1  0.997  0.006  0.802  1.0
  O  O11  1  0.162  0.676  0.096  1.0
  O  O12  1  0.845  0.311  0.601  1.0
  O  O13  1  0.338  0.325  0.612  1.0
  O  O14  1  0.477  0.047  0.831  1.0
  O  O15  1  0.844  0.823  0.595  1.0
  O  O16  1  0.333  0.823  0.595  1.0
  O  O17  1  0.967  0.526  0.349  1.0
  O  O18  1  0.507  0.526  0.349  1.0
  O  O19  1  0.479  0.492  0.848  1.0
  O  O20  1  0.029  0.492  0.848  1.0
  O  O21  1  0.675  0.153  0.091  1.0
  O  O22  1  0.172  0.153  0.091  1.0
  Sn  Sn23  1  0.673  0.654  0.493  1.0
  Sn  Sn24  1  0.170  0.660  0.716  1.0
  Sn  Sn25  1  0.336  0.328  0.987  1.0
  Sn  Sn26  1  0.832  0.828  0.214  1.0
  Sn  Sn27  1  0.340  0.828  0.214  1.0
[/CIF]
.