The material structure described by Li3Co13O16 is Caswellsilverite-like structured and crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and edges with four equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(7)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(7)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(6)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and edges with two equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second Co site, Co(2) is bonded to one O(3), one O(8), two equivalent O(1), and two equivalent O(5) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with three equivalent Co(4)O6 octahedra, and edges with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third Co site, Co(3) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, corners with two equivalent Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with four equivalent Co(6)O6 octahedra, and edges with four equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth Co site, Co(4) is bonded to one O(1), one O(3), one O(4), one O(8), and two equivalent O(5) atoms to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fifth Co site, Co(5) is bonded to one O(1), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the sixth Co site, Co(6) is bonded to one O(4), one O(7), two equivalent O(2), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, edges with three equivalent Li(2)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-3°. In the seventh Co site, Co(7) is bonded to one O(2), one O(4), one O(7), one O(8), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(6)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Co(1), one Co(4), one Co(5), and two equivalent Co(2) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(1)LiCo5 octahedra,  an edgeedge with one O(4)LiCo5 octahedra,  an edgeedge with one O(7)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(3)Li2Co4 octahedra, and edges with four equivalent O(5)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Li(2), one Co(1), one Co(3), one Co(7), and two equivalent Co(6) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(3)Li2Co4 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(8)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with three equivalent O(7)LiCo5 octahedra, and edges with four equivalent O(6)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Co(1), one Co(2), one Co(4), and one Co(5) atom to form OLi2Co4 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(7)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(1)LiCo5 octahedra, and edges with three equivalent O(5)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to one Li(2), one Co(1), one Co(4), one Co(5), one Co(6), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(1)LiCo5 octahedra,  an edgeedge with one O(5)LiCo5 octahedra, edges with two equivalent O(3)Li2Co4 octahedra, edges with two equivalent O(2)LiCo5 octahedra, edges with two equivalent O(6)LiCo5 octahedra, edges with two equivalent O(7)LiCo5 octahedra, and edges with two equivalent O(8)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fifth O site, O(5) is bonded to one Li(1), one Co(5), two equivalent Co(2), and two equivalent Co(4) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(4)LiCo5 octahedra, edges with two equivalent O(5)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(3)Li2Co4 octahedra, and edges with four equivalent O(1)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the sixth O site, O(6) is bonded to one Li(2), one Co(3), two equivalent Co(6), and two equivalent Co(7) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(8)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(6)LiCo5 octahedra, edges with three equivalent O(7)LiCo5 octahedra, and edges with four equivalent O(2)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the seventh O site, O(7) is bonded to one Li(2), one Co(1), one Co(3), one Co(5), one Co(6), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  an edgeedge with one O(3)Li2Co4 octahedra,  an edgeedge with one O(1)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(2)LiCo5 octahedra, and edges with three equivalent O(6)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the eighth O site, O(8) is bonded to one Li(2), one Co(1), one Co(2), one Co(4), one Co(5), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(6)LiCo5 octahedra, edges with two equivalent O(3)Li2Co4 octahedra, edges with two equivalent O(1)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(5)LiCo5 octahedra, and edges with two equivalent O(7)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Co13O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.161
_cell_length_b   5.166
_cell_length_c   11.583
_cell_angle_alpha   85.861
_cell_angle_beta   81.521
_cell_angle_gamma   80.714
_symmetry_Int_Tables_number   1
_cell_volume   301.077
_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  0.500  0.000  0.000  1.0
  Li  Li1  1  0.311  0.750  0.688  1.0
  Li  Li2  1  0.689  0.250  0.312  1.0
  Co  Co3  1  0.253  0.004  0.249  1.0
  Co  Co4  1  0.066  0.754  0.937  1.0
  Co  Co5  1  0.000  0.000  0.500  1.0
  Co  Co6  1  0.381  0.496  0.124  1.0
  Co  Co7  1  0.809  0.752  0.188  1.0
  Co  Co8  1  0.565  0.749  0.437  1.0
  Co  Co9  1  0.747  0.996  0.751  1.0
  Co  Co10  1  0.619  0.504  0.876  1.0
  Co  Co11  1  0.126  0.496  0.374  1.0
  Co  Co12  1  0.934  0.246  0.063  1.0
  Co  Co13  1  0.874  0.504  0.626  1.0
  Co  Co14  1  0.435  0.251  0.563  1.0
  Co  Co15  1  0.191  0.248  0.812  1.0
  O  O16  1  0.848  0.131  0.905  1.0
  O  O17  1  0.340  0.122  0.407  1.0
  O  O18  1  0.594  0.125  0.156  1.0
  O  O19  1  0.406  0.875  0.844  1.0
  O  O20  1  0.466  0.634  0.280  1.0
  O  O21  1  0.726  0.619  0.031  1.0
  O  O22  1  0.220  0.623  0.527  1.0
  O  O23  1  0.087  0.134  0.657  1.0
  O  O24  1  0.274  0.381  0.969  1.0
  O  O25  1  0.660  0.878  0.593  1.0
  O  O26  1  0.152  0.869  0.095  1.0
  O  O27  1  0.913  0.866  0.343  1.0
  O  O28  1  0.964  0.621  0.784  1.0
  O  O29  1  0.780  0.377  0.473  1.0
  O  O30  1  0.036  0.379  0.216  1.0
  O  O31  1  0.534  0.366  0.720  1.0
[/CIF]
.
The material structure described by Li3Co13O16 is Caswellsilverite-like structured and crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with four equivalent Co(2)O6 octahedra, and edges with four equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(7)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(7)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(6)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and edges with two equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second Co site, Co(2) is bonded to one O(3), one O(8), two equivalent O(1), and two equivalent O(5) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with three equivalent Co(4)O6 octahedra, and edges with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third Co site, Co(3) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra, corners with two equivalent Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with four equivalent Co(6)O6 octahedra, and edges with four equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth Co site, Co(4) is bonded to one O(1), one O(3), one O(4), one O(8), and two equivalent O(5) atoms to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fifth Co site, Co(5) is bonded to one O(1), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and edges with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the sixth Co site, Co(6) is bonded to one O(4), one O(7), two equivalent O(2), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(7)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, edges with three equivalent Li(2)O6 octahedra, and edges with three equivalent Co(7)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-3°. In the seventh Co site, Co(7) is bonded to one O(2), one O(4), one O(7), one O(8), and two equivalent O(6) atoms to form CoO6 octahedra that share  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(5)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Co(6)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with three equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-3°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Co(1), one Co(4), one Co(5), and two equivalent Co(2) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(1)LiCo5 octahedra,  an edgeedge with one O(4)LiCo5 octahedra,  an edgeedge with one O(7)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(3)Li2Co4 octahedra, and edges with four equivalent O(5)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the second O site, O(2) is bonded to one Li(2), one Co(1), one Co(3), one Co(7), and two equivalent Co(6) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(3)Li2Co4 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(8)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with three equivalent O(7)LiCo5 octahedra, and edges with four equivalent O(6)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Co(1), one Co(2), one Co(4), and one Co(5) atom to form OLi2Co4 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(7)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(1)LiCo5 octahedra, and edges with three equivalent O(5)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fourth O site, O(4) is bonded to one Li(2), one Co(1), one Co(4), one Co(5), one Co(6), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(1)LiCo5 octahedra,  an edgeedge with one O(5)LiCo5 octahedra, edges with two equivalent O(3)Li2Co4 octahedra, edges with two equivalent O(2)LiCo5 octahedra, edges with two equivalent O(6)LiCo5 octahedra, edges with two equivalent O(7)LiCo5 octahedra, and edges with two equivalent O(8)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the fifth O site, O(5) is bonded to one Li(1), one Co(5), two equivalent Co(2), and two equivalent Co(4) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(4)LiCo5 octahedra, edges with two equivalent O(5)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(3)Li2Co4 octahedra, and edges with four equivalent O(1)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the sixth O site, O(6) is bonded to one Li(2), one Co(3), two equivalent Co(6), and two equivalent Co(7) atoms to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  a cornercorner with one O(8)LiCo5 octahedra,  an edgeedge with one O(8)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(6)LiCo5 octahedra, edges with three equivalent O(7)LiCo5 octahedra, and edges with four equivalent O(2)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the seventh O site, O(7) is bonded to one Li(2), one Co(1), one Co(3), one Co(5), one Co(6), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  a cornercorner with one O(7)LiCo5 octahedra,  an edgeedge with one O(3)Li2Co4 octahedra,  an edgeedge with one O(1)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(8)LiCo5 octahedra, edges with three equivalent O(2)LiCo5 octahedra, and edges with three equivalent O(6)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the eighth O site, O(8) is bonded to one Li(2), one Co(1), one Co(2), one Co(4), one Co(5), and one Co(7) atom to form OLiCo5 octahedra that share  a cornercorner with one O(3)Li2Co4 octahedra,  a cornercorner with one O(1)LiCo5 octahedra,  a cornercorner with one O(2)LiCo5 octahedra,  a cornercorner with one O(4)LiCo5 octahedra,  a cornercorner with one O(5)LiCo5 octahedra,  a cornercorner with one O(6)LiCo5 octahedra,  an edgeedge with one O(2)LiCo5 octahedra,  an edgeedge with one O(6)LiCo5 octahedra, edges with two equivalent O(3)Li2Co4 octahedra, edges with two equivalent O(1)LiCo5 octahedra, edges with two equivalent O(4)LiCo5 octahedra, edges with two equivalent O(5)LiCo5 octahedra, and edges with two equivalent O(7)LiCo5 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Co13O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.161
_cell_length_b   5.166
_cell_length_c   11.583
_cell_angle_alpha   85.861
_cell_angle_beta   81.521
_cell_angle_gamma   80.714
_symmetry_Int_Tables_number   1
_cell_volume   301.077
_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  0.500  0.000  0.000  1.0
  Li  Li1  1  0.311  0.750  0.688  1.0
  Li  Li2  1  0.689  0.250  0.312  1.0
  Co  Co3  1  0.253  0.004  0.249  1.0
  Co  Co4  1  0.066  0.754  0.937  1.0
  Co  Co5  1  0.000  0.000  0.500  1.0
  Co  Co6  1  0.381  0.496  0.124  1.0
  Co  Co7  1  0.809  0.752  0.188  1.0
  Co  Co8  1  0.565  0.749  0.437  1.0
  Co  Co9  1  0.747  0.996  0.751  1.0
  Co  Co10  1  0.619  0.504  0.876  1.0
  Co  Co11  1  0.126  0.496  0.374  1.0
  Co  Co12  1  0.934  0.246  0.063  1.0
  Co  Co13  1  0.874  0.504  0.626  1.0
  Co  Co14  1  0.435  0.251  0.563  1.0
  Co  Co15  1  0.191  0.248  0.812  1.0
  O  O16  1  0.848  0.131  0.905  1.0
  O  O17  1  0.340  0.122  0.407  1.0
  O  O18  1  0.594  0.125  0.156  1.0
  O  O19  1  0.406  0.875  0.844  1.0
  O  O20  1  0.466  0.634  0.280  1.0
  O  O21  1  0.726  0.619  0.031  1.0
  O  O22  1  0.220  0.623  0.527  1.0
  O  O23  1  0.087  0.134  0.657  1.0
  O  O24  1  0.274  0.381  0.969  1.0
  O  O25  1  0.660  0.878  0.593  1.0
  O  O26  1  0.152  0.869  0.095  1.0
  O  O27  1  0.913  0.866  0.343  1.0
  O  O28  1  0.964  0.621  0.784  1.0
  O  O29  1  0.780  0.377  0.473  1.0
  O  O30  1  0.036  0.379  0.216  1.0
  O  O31  1  0.534  0.366  0.720  1.0
[/CIF]
.