The structure described by Li4Cr3Sn5O16 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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. In the second Li site, Li(2) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(5), and two equivalent O(12) atoms. In the third Li site, Li(3) is bonded to one O(3), one O(6), and two equivalent O(9) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(4)O6 octahedra, corners with three equivalent Sn(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(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 58-61°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), two equivalent O(10), and two equivalent O(12) atoms to form CrO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, and edges with four equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the second Cr site, Cr(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 CrO6 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,  an edgeedge with one Sn(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-53°. 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 Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. 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,  an edgeedge with one Sn(3)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. 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 Cr(1)O6 octahedra, corners with four equivalent Sn(4)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 a mixture of distorted corner and edge-sharing OLiSn3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Cr(1), and two equivalent Sn(4) atoms to form distorted OLiCrSn2 trigonal pyramids that share  a cornercorner with one O(8)LiCr2Sn tetrahedra, corners with three equivalent O(3)LiCrSn2 tetrahedra, edges with two equivalent O(10)LiCrSn2 tetrahedra, and  an edgeedge with one O(1)LiSn3 trigonal pyramid. In the third O site, O(3) is bonded to one Li(3), one Cr(1), and two equivalent Sn(4) atoms to form distorted OLiCrSn2 tetrahedra that share corners with four equivalent O(10)LiCrSn2 tetrahedra, corners with two equivalent O(1)LiSn3 trigonal pyramids, and corners with three equivalent O(2)LiCrSn2 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Cr(2), and one Sn(2) atom to form distorted corner-sharing OLiCr2Sn 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 distorted rectangular see-saw-like geometry to one Li(3), two equivalent Cr(2), and one Sn(1) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), two equivalent Cr(2), and one Sn(2) atom. In the eighth O site, O(8) is bonded to one Li(1), two equivalent Cr(2), and one Sn(3) atom to form distorted OLiCr2Sn tetrahedra that share corners with two equivalent O(4)LiCr2Sn tetrahedra and  a cornercorner with one O(2)LiCrSn2 trigonal pyramid. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Sn(1), and one Sn(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Cr(1), one Sn(1), and one Sn(4) atom to form distorted OLiCrSn2 tetrahedra that share  a cornercorner with one O(10)LiCrSn2 tetrahedra, corners with two equivalent O(3)LiCrSn2 tetrahedra,  a cornercorner with one O(1)LiSn3 trigonal pyramid,  an edgeedge with one O(10)LiCrSn2 tetrahedra,  an edgeedge with one O(2)LiCrSn2 trigonal pyramid, and  an edgeedge with one O(1)LiSn3 trigonal pyramid. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(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 Cr(1), one Sn(3), and one Sn(4) atom. is represented by the CIF file [CIF]
data_Li4Cr3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.175
_cell_length_b   6.175
_cell_length_c   9.939
_cell_angle_alpha   90.249
_cell_angle_beta   90.249
_cell_angle_gamma   60.336
_symmetry_Int_Tables_number   1
_cell_volume   329.251
_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
  Cr  Cr0  1  0.832  0.831  0.785  1.0
  Cr  Cr1  1  0.660  0.171  0.287  1.0
  Cr  Cr2  1  0.171  0.660  0.287  1.0
  Li  Li3  1  0.669  0.669  0.110  1.0
  Li  Li4  1  0.990  0.990  0.011  1.0
  Li  Li5  1  0.992  0.992  0.502  1.0
  Li  Li6  1  0.333  0.333  0.596  1.0
  O  O7  1  0.516  0.516  0.655  1.0
  O  O8  1  0.671  0.671  0.896  1.0
  O  O9  1  0.996  0.996  0.686  1.0
  O  O10  1  0.996  0.996  0.194  1.0
  O  O11  1  0.161  0.161  0.906  1.0
  O  O12  1  0.838  0.838  0.397  1.0
  O  O13  1  0.338  0.338  0.393  1.0
  O  O14  1  0.484  0.484  0.170  1.0
  O  O15  1  0.836  0.320  0.404  1.0
  O  O16  1  0.320  0.836  0.404  1.0
  O  O17  1  0.965  0.517  0.656  1.0
  O  O18  1  0.517  0.965  0.656  1.0
  O  O19  1  0.488  0.037  0.162  1.0
  O  O20  1  0.037  0.488  0.162  1.0
  O  O21  1  0.679  0.161  0.901  1.0
  O  O22  1  0.161  0.679  0.901  1.0
  Sn  Sn23  1  0.671  0.671  0.504  1.0
  Sn  Sn24  1  0.169  0.169  0.286  1.0
  Sn  Sn25  1  0.341  0.341  0.014  1.0
  Sn  Sn26  1  0.832  0.339  0.784  1.0
  Sn  Sn27  1  0.339  0.832  0.784  1.0
[/CIF]
.
The structure described by Li4Cr3Sn5O16 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 Cr(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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. In the second Li site, Li(2) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(5), and two equivalent O(12) atoms. In the third Li site, Li(3) is bonded to one O(3), one O(6), and two equivalent O(9) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(4)O6 octahedra, corners with three equivalent Sn(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(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 58-61°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), two equivalent O(10), and two equivalent O(12) atoms to form CrO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, and edges with four equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the second Cr site, Cr(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 CrO6 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,  an edgeedge with one Sn(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-53°. 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 Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. 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,  an edgeedge with one Sn(3)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. 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 Cr(1)O6 octahedra, corners with four equivalent Sn(4)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Sn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-54°. 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 a mixture of distorted corner and edge-sharing OLiSn3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Cr(1), and two equivalent Sn(4) atoms to form distorted OLiCrSn2 trigonal pyramids that share  a cornercorner with one O(8)LiCr2Sn tetrahedra, corners with three equivalent O(3)LiCrSn2 tetrahedra, edges with two equivalent O(10)LiCrSn2 tetrahedra, and  an edgeedge with one O(1)LiSn3 trigonal pyramid. In the third O site, O(3) is bonded to one Li(3), one Cr(1), and two equivalent Sn(4) atoms to form distorted OLiCrSn2 tetrahedra that share corners with four equivalent O(10)LiCrSn2 tetrahedra, corners with two equivalent O(1)LiSn3 trigonal pyramids, and corners with three equivalent O(2)LiCrSn2 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Cr(2), and one Sn(2) atom to form distorted corner-sharing OLiCr2Sn 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 distorted rectangular see-saw-like geometry to one Li(3), two equivalent Cr(2), and one Sn(1) atom. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), two equivalent Cr(2), and one Sn(2) atom. In the eighth O site, O(8) is bonded to one Li(1), two equivalent Cr(2), and one Sn(3) atom to form distorted OLiCr2Sn tetrahedra that share corners with two equivalent O(4)LiCr2Sn tetrahedra and  a cornercorner with one O(2)LiCrSn2 trigonal pyramid. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Sn(1), and one Sn(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Cr(1), one Sn(1), and one Sn(4) atom to form distorted OLiCrSn2 tetrahedra that share  a cornercorner with one O(10)LiCrSn2 tetrahedra, corners with two equivalent O(3)LiCrSn2 tetrahedra,  a cornercorner with one O(1)LiSn3 trigonal pyramid,  an edgeedge with one O(10)LiCrSn2 tetrahedra,  an edgeedge with one O(2)LiCrSn2 trigonal pyramid, and  an edgeedge with one O(1)LiSn3 trigonal pyramid. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(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 Cr(1), one Sn(3), and one Sn(4) atom. is represented by the CIF file [CIF]
data_Li4Cr3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.175
_cell_length_b   6.175
_cell_length_c   9.939
_cell_angle_alpha   90.249
_cell_angle_beta   90.249
_cell_angle_gamma   60.336
_symmetry_Int_Tables_number   1
_cell_volume   329.251
_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
  Cr  Cr0  1  0.832  0.831  0.785  1.0
  Cr  Cr1  1  0.660  0.171  0.287  1.0
  Cr  Cr2  1  0.171  0.660  0.287  1.0
  Li  Li3  1  0.669  0.669  0.110  1.0
  Li  Li4  1  0.990  0.990  0.011  1.0
  Li  Li5  1  0.992  0.992  0.502  1.0
  Li  Li6  1  0.333  0.333  0.596  1.0
  O  O7  1  0.516  0.516  0.655  1.0
  O  O8  1  0.671  0.671  0.896  1.0
  O  O9  1  0.996  0.996  0.686  1.0
  O  O10  1  0.996  0.996  0.194  1.0
  O  O11  1  0.161  0.161  0.906  1.0
  O  O12  1  0.838  0.838  0.397  1.0
  O  O13  1  0.338  0.338  0.393  1.0
  O  O14  1  0.484  0.484  0.170  1.0
  O  O15  1  0.836  0.320  0.404  1.0
  O  O16  1  0.320  0.836  0.404  1.0
  O  O17  1  0.965  0.517  0.656  1.0
  O  O18  1  0.517  0.965  0.656  1.0
  O  O19  1  0.488  0.037  0.162  1.0
  O  O20  1  0.037  0.488  0.162  1.0
  O  O21  1  0.679  0.161  0.901  1.0
  O  O22  1  0.161  0.679  0.901  1.0
  Sn  Sn23  1  0.671  0.671  0.504  1.0
  Sn  Sn24  1  0.169  0.169  0.286  1.0
  Sn  Sn25  1  0.341  0.341  0.014  1.0
  Sn  Sn26  1  0.832  0.339  0.784  1.0
  Sn  Sn27  1  0.339  0.832  0.784  1.0
[/CIF]
.