The structure described by Li4V2Cr3Sn3O16 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(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent V(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent V(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-65°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent V(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 53-61°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) 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 V(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-63°. There are two inequivalent V sites. In the first V site, V(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted VO6 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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. In the second V site, V(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form VO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Sn(1)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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent V(2)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 V(1)O6 octahedra, edges with four equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 49°. In the second Cr site, Cr(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form CrO6 octahedra that share corners with two equivalent V(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 V(2)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 49-50°. There are two inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form SnO6 octahedra that share corners with two equivalent V(2)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 V(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. In the second Sn site, Sn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent V(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 V(2)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 56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), one Cr(2), and one Sn(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one V(1), and two equivalent Sn(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Cr(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Cr(1), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiCrSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Cr(2), and one Sn(2) atom to form corner-sharing OLiCr2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one V(1), one Cr(1), and one Sn(1) atom to form distorted OLiVCrSn tetrahedra that share  a cornercorner with one O(6)LiVCrSn tetrahedra, corners with two equivalent O(4)LiCrSn2 tetrahedra, and  an edgeedge with one O(6)LiVCrSn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), and two equivalent Sn(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one V(2), one Cr(2), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Cr(2), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), one Cr(1), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one V(2), and two equivalent Cr(2) atoms to form distorted corner-sharing OLiVCr2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4V2Cr3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.100
_cell_length_b   6.100
_cell_length_c   9.639
_cell_angle_alpha   89.493
_cell_angle_beta   89.493
_cell_angle_gamma   60.359
_symmetry_Int_Tables_number   1
_cell_volume   311.685
_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  0.329  0.329  0.113  1.0
  Li  Li1  1  0.013  0.013  0.009  1.0
  Li  Li2  1  0.007  0.007  0.499  1.0
  Li  Li3  1  0.665  0.665  0.601  1.0
  V  V4  1  0.323  0.323  0.503  1.0
  V  V5  1  0.661  0.661  0.015  1.0
  Cr  Cr6  1  0.170  0.170  0.785  1.0
  Cr  Cr7  1  0.823  0.344  0.285  1.0
  Cr  Cr8  1  0.344  0.823  0.285  1.0
  Sn  Sn9  1  0.662  0.169  0.786  1.0
  Sn  Sn10  1  0.169  0.662  0.786  1.0
  Sn  Sn11  1  0.830  0.830  0.286  1.0
  O  O12  1  0.666  0.171  0.406  1.0
  O  O13  1  0.479  0.479  0.651  1.0
  O  O14  1  0.328  0.328  0.901  1.0
  O  O15  1  0.005  0.005  0.684  1.0
  O  O16  1  0.005  0.005  0.195  1.0
  O  O17  1  0.171  0.666  0.406  1.0
  O  O18  1  0.473  0.044  0.655  1.0
  O  O19  1  0.044  0.473  0.655  1.0
  O  O20  1  0.837  0.837  0.905  1.0
  O  O21  1  0.177  0.177  0.403  1.0
  O  O22  1  0.960  0.513  0.158  1.0
  O  O23  1  0.513  0.960  0.158  1.0
  O  O24  1  0.661  0.661  0.397  1.0
  O  O25  1  0.838  0.328  0.900  1.0
  O  O26  1  0.520  0.520  0.164  1.0
  O  O27  1  0.328  0.838  0.900  1.0
[/CIF]
.
The structure described by Li4V2Cr3Sn3O16 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(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent V(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent V(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-65°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent V(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 53-61°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) 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 V(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-63°. There are two inequivalent V sites. In the first V site, V(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted VO6 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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-56°. In the second V site, V(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form VO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Sn(1)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 Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent V(2)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 V(1)O6 octahedra, edges with four equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 49°. In the second Cr site, Cr(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form CrO6 octahedra that share corners with two equivalent V(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 V(2)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 49-50°. There are two inequivalent Sn sites. In the first Sn site, Sn(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form SnO6 octahedra that share corners with two equivalent V(2)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 V(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. In the second Sn site, Sn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent V(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 V(2)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 56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), one Cr(2), and one Sn(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one V(1), and two equivalent Sn(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Cr(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Cr(1), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiCrSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Cr(2), and one Sn(2) atom to form corner-sharing OLiCr2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one V(1), one Cr(1), and one Sn(1) atom to form distorted OLiVCrSn tetrahedra that share  a cornercorner with one O(6)LiVCrSn tetrahedra, corners with two equivalent O(4)LiCrSn2 tetrahedra, and  an edgeedge with one O(6)LiVCrSn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), and two equivalent Sn(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one V(2), one Cr(2), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Cr(2), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one V(2), one Cr(1), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one V(2), and two equivalent Cr(2) atoms to form distorted corner-sharing OLiVCr2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4V2Cr3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.100
_cell_length_b   6.100
_cell_length_c   9.639
_cell_angle_alpha   89.493
_cell_angle_beta   89.493
_cell_angle_gamma   60.359
_symmetry_Int_Tables_number   1
_cell_volume   311.685
_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  0.329  0.329  0.113  1.0
  Li  Li1  1  0.013  0.013  0.009  1.0
  Li  Li2  1  0.007  0.007  0.499  1.0
  Li  Li3  1  0.665  0.665  0.601  1.0
  V  V4  1  0.323  0.323  0.503  1.0
  V  V5  1  0.661  0.661  0.015  1.0
  Cr  Cr6  1  0.170  0.170  0.785  1.0
  Cr  Cr7  1  0.823  0.344  0.285  1.0
  Cr  Cr8  1  0.344  0.823  0.285  1.0
  Sn  Sn9  1  0.662  0.169  0.786  1.0
  Sn  Sn10  1  0.169  0.662  0.786  1.0
  Sn  Sn11  1  0.830  0.830  0.286  1.0
  O  O12  1  0.666  0.171  0.406  1.0
  O  O13  1  0.479  0.479  0.651  1.0
  O  O14  1  0.328  0.328  0.901  1.0
  O  O15  1  0.005  0.005  0.684  1.0
  O  O16  1  0.005  0.005  0.195  1.0
  O  O17  1  0.171  0.666  0.406  1.0
  O  O18  1  0.473  0.044  0.655  1.0
  O  O19  1  0.044  0.473  0.655  1.0
  O  O20  1  0.837  0.837  0.905  1.0
  O  O21  1  0.177  0.177  0.403  1.0
  O  O22  1  0.960  0.513  0.158  1.0
  O  O23  1  0.513  0.960  0.158  1.0
  O  O24  1  0.661  0.661  0.397  1.0
  O  O25  1  0.838  0.328  0.900  1.0
  O  O26  1  0.520  0.520  0.164  1.0
  O  O27  1  0.328  0.838  0.900  1.0
[/CIF]
.