The crystal structure described by Li4Co3Sn5O16 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(3)O6 octahedra, corners with three equivalent Sn(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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(3)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Sn(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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(3)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Sn(2)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Sn(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(2)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 52°. In the second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Sn(2)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(4)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Sn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are four 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 Sn(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, edges with two equivalent Co(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 52°. In the second Sn site, Sn(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form SnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the third Sn site, Sn(3) 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 Sn(2)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(4)O6 octahedra, and edges with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the fourth Sn site, Sn(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Co(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(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Co(2), one Sn(2), and one Sn(3) atom. In the second O site, O(2) is bonded to one Li(4), one Sn(2), and two equivalent Sn(1) atoms to form distorted OLiSn3 trigonal pyramids that share corners with two equivalent O(4)LiCoSn2 tetrahedra and  a cornercorner with one O(10)LiCo2Sn trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Co(1), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiCoSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Co(2), and one Sn(3) atom to form distorted corner-sharing OLiCo2Sn tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Co(1), one Sn(1), and one Sn(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Sn(4), 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), two equivalent Co(2), and one Sn(2) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Co(2), one Sn(3), and one Sn(4) atom. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Co(2), and one Sn(3) atom to form distorted OLiCo2Sn trigonal pyramids that share corners with three equivalent O(5)LiCo2Sn tetrahedra,  a cornercorner with one O(2)LiSn3 trigonal pyramid, and  an edgeedge with one O(12)LiCo2Sn tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(1), one Sn(1), and one Sn(4) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Co(2), and one Sn(4) atom to form a mixture of distorted corner and edge-sharing OLiCo2Sn tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Co3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.146
_cell_length_b   6.146
_cell_length_c   9.888
_cell_angle_alpha   89.943
_cell_angle_beta   89.943
_cell_angle_gamma   60.014
_symmetry_Int_Tables_number   1
_cell_volume   323.528
_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  0.670  0.670  0.892  1.0
  Li  Li1  1  0.984  0.984  0.989  1.0
  Li  Li2  1  0.992  0.992  0.497  1.0
  Li  Li3  1  0.332  0.332  0.403  1.0
  Co  Co4  1  0.830  0.830  0.214  1.0
  Co  Co5  1  0.662  0.172  0.714  1.0
  Co  Co6  1  0.172  0.662  0.714  1.0
  Sn  Sn7  1  0.833  0.340  0.215  1.0
  Sn  Sn8  1  0.670  0.670  0.493  1.0
  Sn  Sn9  1  0.340  0.833  0.215  1.0
  Sn  Sn10  1  0.170  0.170  0.714  1.0
  Sn  Sn11  1  0.341  0.341  0.986  1.0
  O  O12  1  0.835  0.323  0.598  1.0
  O  O13  1  0.515  0.515  0.345  1.0
  O  O14  1  0.665  0.665  0.101  1.0
  O  O15  1  0.000  0.000  0.312  1.0
  O  O16  1  0.997  0.997  0.805  1.0
  O  O17  1  0.323  0.835  0.598  1.0
  O  O18  1  0.966  0.511  0.348  1.0
  O  O19  1  0.511  0.966  0.348  1.0
  O  O20  1  0.163  0.163  0.092  1.0
  O  O21  1  0.837  0.837  0.606  1.0
  O  O22  1  0.486  0.039  0.843  1.0
  O  O23  1  0.039  0.486  0.843  1.0
  O  O24  1  0.336  0.336  0.606  1.0
  O  O25  1  0.675  0.170  0.095  1.0
  O  O26  1  0.484  0.484  0.831  1.0
  O  O27  1  0.170  0.675  0.095  1.0
[/CIF]
.
The crystal structure described by Li4Co3Sn5O16 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(3)O6 octahedra, corners with three equivalent Sn(4)O6 octahedra, and corners with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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(3)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Sn(4)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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(3)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Sn(2)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Sn(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(2)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 52°. In the second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Sn(2)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(4)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Sn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are four 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 Sn(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, edges with two equivalent Co(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 52°. In the second Sn site, Sn(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form SnO6 octahedra that share corners with two equivalent Sn(3)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-54°. In the third Sn site, Sn(3) 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 Sn(2)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(4)O6 octahedra, and edges with four equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the fourth Sn site, Sn(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Co(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(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Co(2), one Sn(2), and one Sn(3) atom. In the second O site, O(2) is bonded to one Li(4), one Sn(2), and two equivalent Sn(1) atoms to form distorted OLiSn3 trigonal pyramids that share corners with two equivalent O(4)LiCoSn2 tetrahedra and  a cornercorner with one O(10)LiCo2Sn trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Co(1), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiCoSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Co(2), and one Sn(3) atom to form distorted corner-sharing OLiCo2Sn tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Co(1), one Sn(1), and one Sn(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Sn(4), 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), two equivalent Co(2), and one Sn(2) atom. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Co(2), one Sn(3), and one Sn(4) atom. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Co(2), and one Sn(3) atom to form distorted OLiCo2Sn trigonal pyramids that share corners with three equivalent O(5)LiCo2Sn tetrahedra,  a cornercorner with one O(2)LiSn3 trigonal pyramid, and  an edgeedge with one O(12)LiCo2Sn tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(1), one Sn(1), and one Sn(4) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Co(2), and one Sn(4) atom to form a mixture of distorted corner and edge-sharing OLiCo2Sn tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Co3Sn5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.146
_cell_length_b   6.146
_cell_length_c   9.888
_cell_angle_alpha   89.943
_cell_angle_beta   89.943
_cell_angle_gamma   60.014
_symmetry_Int_Tables_number   1
_cell_volume   323.528
_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  0.670  0.670  0.892  1.0
  Li  Li1  1  0.984  0.984  0.989  1.0
  Li  Li2  1  0.992  0.992  0.497  1.0
  Li  Li3  1  0.332  0.332  0.403  1.0
  Co  Co4  1  0.830  0.830  0.214  1.0
  Co  Co5  1  0.662  0.172  0.714  1.0
  Co  Co6  1  0.172  0.662  0.714  1.0
  Sn  Sn7  1  0.833  0.340  0.215  1.0
  Sn  Sn8  1  0.670  0.670  0.493  1.0
  Sn  Sn9  1  0.340  0.833  0.215  1.0
  Sn  Sn10  1  0.170  0.170  0.714  1.0
  Sn  Sn11  1  0.341  0.341  0.986  1.0
  O  O12  1  0.835  0.323  0.598  1.0
  O  O13  1  0.515  0.515  0.345  1.0
  O  O14  1  0.665  0.665  0.101  1.0
  O  O15  1  0.000  0.000  0.312  1.0
  O  O16  1  0.997  0.997  0.805  1.0
  O  O17  1  0.323  0.835  0.598  1.0
  O  O18  1  0.966  0.511  0.348  1.0
  O  O19  1  0.511  0.966  0.348  1.0
  O  O20  1  0.163  0.163  0.092  1.0
  O  O21  1  0.837  0.837  0.606  1.0
  O  O22  1  0.486  0.039  0.843  1.0
  O  O23  1  0.039  0.486  0.843  1.0
  O  O24  1  0.336  0.336  0.606  1.0
  O  O25  1  0.675  0.170  0.095  1.0
  O  O26  1  0.484  0.484  0.831  1.0
  O  O27  1  0.170  0.675  0.095  1.0
[/CIF]
.