The material described by Li3(CoO2)4 crystallizes in the monoclinic C2 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(4), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with three equivalent Co(6)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-12°. In the second Li site, Li(2) is bonded to one O(3), one O(7), two equivalent O(2), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with three equivalent Co(6)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-13°. In the third Li site, Li(3) 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 LiO6 octahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(5)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. There are six inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-7°. In the third Co site, Co(3) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(7) atoms to form CoO6 octahedra that share edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. In the fourth Co site, Co(4) is bonded to two equivalent O(4), two equivalent O(6), and two equivalent O(8) atoms to form CoO6 octahedra that share edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. In the fifth Co site, Co(5) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the sixth Co site, Co(6) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. There are eight inequivalent O sites. In the first O site, O(3) is bonded to one Li(2), one Li(3), one Co(3), one Co(5), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid, corners with two equivalent O(8)Li2Co3 square pyramids, corners with four equivalent O(7)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, and edges with two equivalent O(5)Li2Co3 square pyramids. In the second O site, O(4) is bonded to one Li(1), one Li(3), one Co(1), one Co(2), and one Co(4) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid, corners with two equivalent O(7)Li2Co3 square pyramids, corners with four equivalent O(8)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, and edges with two equivalent O(6)Li2Co3 square pyramids. In the third O site, O(5) is bonded to two equivalent Li(2), one Co(2), one Co(3), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(6)Li2Co3 square pyramids, corners with three equivalent O(5)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra, edges with two equivalent O(3)Li2Co3 square pyramids, and edges with two equivalent O(7)Li2Co3 square pyramids. In the fourth O site, O(6) is bonded to two equivalent Li(1), one Co(2), one Co(4), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(5)Li2Co3 square pyramids, corners with three equivalent O(6)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra, edges with two equivalent O(4)Li2Co3 square pyramids, and edges with two equivalent O(8)Li2Co3 square pyramids. In the fifth O site, O(7) is bonded to one Li(2), one Li(3), one Co(2), one Co(3), and one Co(5) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(4)Li2Co3 square pyramids, corners with four equivalent O(3)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, and edges with two equivalent O(5)Li2Co3 square pyramids. In the sixth O site, O(8) is bonded to one Li(1), one Li(3), one Co(1), one Co(4), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid, corners with two equivalent O(3)Li2Co3 square pyramids, corners with four equivalent O(4)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, and edges with two equivalent O(6)Li2Co3 square pyramids. In the seventh O site, O(1) is bonded to one Li(3), two equivalent Li(1), one Co(1), one Co(2), and one Co(6) atom to form OLi3Co3 octahedra that share corners with three equivalent O(1)Li3Co3 octahedra, corners with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(5)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, edges with three equivalent O(4)Li2Co3 square pyramids, edges with three equivalent O(6)Li2Co3 square pyramids, and edges with three equivalent O(8)Li2Co3 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(2) is bonded to one Li(3), two equivalent Li(2), one Co(2), one Co(5), and one Co(6) atom to form OLi3Co3 octahedra that share corners with three equivalent O(1)Li3Co3 octahedra, corners with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(6)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, edges with three equivalent O(3)Li2Co3 square pyramids, edges with three equivalent O(5)Li2Co3 square pyramids, and edges with three equivalent O(7)Li2Co3 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3(CoO2)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.791
_cell_length_b   5.904
_cell_length_c   9.969
_cell_angle_alpha   106.429
_cell_angle_beta   89.999
_cell_angle_gamma   119.368
_symmetry_Int_Tables_number   1
_cell_volume   280.973
_cell_formula_units_Z   2
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  0.252  0.999  0.743  1.0
  Li  Li1  1  0.748  0.001  0.258  1.0
  Li  Li2  1  0.500  0.003  0.000  1.0
  Li  Li3  1  0.996  0.997  0.500  1.0
  Li  Li4  1  0.753  0.001  0.757  1.0
  Li  Li5  1  0.247  0.999  0.242  1.0
  Co  Co6  1  0.756  0.500  0.750  1.0
  Co  Co7  1  0.999  0.499  0.500  1.0
  Co  Co8  1  0.000  0.501  0.000  1.0
  Co  Co9  1  0.755  0.500  0.250  1.0
  Co  Co10  1  0.245  0.500  0.750  1.0
  Co  Co11  1  0.248  0.500  0.250  1.0
  Co  Co12  1  0.501  0.504  0.000  1.0
  Co  Co13  1  0.497  0.496  0.500  1.0
  O  O14  1  0.654  0.276  0.884  1.0
  O  O15  1  0.120  0.273  0.383  1.0
  O  O16  1  0.348  0.727  0.117  1.0
  O  O17  1  0.878  0.724  0.616  1.0
  O  O18  1  0.404  0.287  0.131  1.0
  O  O19  1  0.902  0.288  0.627  1.0
  O  O20  1  0.870  0.712  0.123  1.0
  O  O21  1  0.339  0.709  0.622  1.0
  O  O22  1  0.888  0.291  0.127  1.0
  O  O23  1  0.386  0.289  0.632  1.0
  O  O24  1  0.114  0.712  0.873  1.0
  O  O25  1  0.617  0.713  0.369  1.0
  O  O26  1  0.130  0.291  0.878  1.0
  O  O27  1  0.659  0.288  0.377  1.0
  O  O28  1  0.597  0.711  0.868  1.0
  O  O29  1  0.098  0.709  0.373  1.0
[/CIF]
.
The material described by Li3(CoO2)4 crystallizes in the monoclinic C2 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(4), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form LiO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with three equivalent Co(6)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-12°. In the second Li site, Li(2) is bonded to one O(3), one O(7), two equivalent O(2), and two equivalent O(5) atoms to form LiO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with three equivalent Co(6)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-13°. In the third Li site, Li(3) 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 LiO6 octahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(5)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. There are six inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-11°. In the second Co site, Co(2) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-7°. In the third Co site, Co(3) is bonded to two equivalent O(3), two equivalent O(5), and two equivalent O(7) atoms to form CoO6 octahedra that share edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(5)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. In the fourth Co site, Co(4) is bonded to two equivalent O(4), two equivalent O(6), and two equivalent O(8) atoms to form CoO6 octahedra that share edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. In the fifth Co site, Co(5) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(6)O6 octahedra, and edges with four equivalent Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the sixth Co site, Co(6) is bonded to one O(1), one O(2), one O(3), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-13°. There are eight inequivalent O sites. In the first O site, O(3) is bonded to one Li(2), one Li(3), one Co(3), one Co(5), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid, corners with two equivalent O(8)Li2Co3 square pyramids, corners with four equivalent O(7)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, and edges with two equivalent O(5)Li2Co3 square pyramids. In the second O site, O(4) is bonded to one Li(1), one Li(3), one Co(1), one Co(2), and one Co(4) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid, corners with two equivalent O(7)Li2Co3 square pyramids, corners with four equivalent O(8)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, and edges with two equivalent O(6)Li2Co3 square pyramids. In the third O site, O(5) is bonded to two equivalent Li(2), one Co(2), one Co(3), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(6)Li2Co3 square pyramids, corners with three equivalent O(5)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra, edges with two equivalent O(3)Li2Co3 square pyramids, and edges with two equivalent O(7)Li2Co3 square pyramids. In the fourth O site, O(6) is bonded to two equivalent Li(1), one Co(2), one Co(4), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(3)Li2Co3 square pyramid,  a cornercorner with one O(4)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(5)Li2Co3 square pyramids, corners with three equivalent O(6)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra, edges with two equivalent O(4)Li2Co3 square pyramids, and edges with two equivalent O(8)Li2Co3 square pyramids. In the fifth O site, O(7) is bonded to one Li(2), one Li(3), one Co(2), one Co(3), and one Co(5) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid,  a cornercorner with one O(8)Li2Co3 square pyramid, corners with two equivalent O(4)Li2Co3 square pyramids, corners with four equivalent O(3)Li2Co3 square pyramids,  an edgeedge with one O(1)Li3Co3 octahedra, edges with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, and edges with two equivalent O(5)Li2Co3 square pyramids. In the sixth O site, O(8) is bonded to one Li(1), one Li(3), one Co(1), one Co(4), and one Co(6) atom to form OLi2Co3 square pyramids that share  a cornercorner with one O(5)Li2Co3 square pyramid,  a cornercorner with one O(6)Li2Co3 square pyramid,  a cornercorner with one O(7)Li2Co3 square pyramid, corners with two equivalent O(3)Li2Co3 square pyramids, corners with four equivalent O(4)Li2Co3 square pyramids,  an edgeedge with one O(2)Li3Co3 octahedra, edges with three equivalent O(1)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, and edges with two equivalent O(6)Li2Co3 square pyramids. In the seventh O site, O(1) is bonded to one Li(3), two equivalent Li(1), one Co(1), one Co(2), and one Co(6) atom to form OLi3Co3 octahedra that share corners with three equivalent O(1)Li3Co3 octahedra, corners with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(3)Li2Co3 square pyramid,  an edgeedge with one O(5)Li2Co3 square pyramid,  an edgeedge with one O(7)Li2Co3 square pyramid, edges with three equivalent O(4)Li2Co3 square pyramids, edges with three equivalent O(6)Li2Co3 square pyramids, and edges with three equivalent O(8)Li2Co3 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(2) is bonded to one Li(3), two equivalent Li(2), one Co(2), one Co(5), and one Co(6) atom to form OLi3Co3 octahedra that share corners with three equivalent O(1)Li3Co3 octahedra, corners with three equivalent O(2)Li3Co3 octahedra,  an edgeedge with one O(4)Li2Co3 square pyramid,  an edgeedge with one O(6)Li2Co3 square pyramid,  an edgeedge with one O(8)Li2Co3 square pyramid, edges with three equivalent O(3)Li2Co3 square pyramids, edges with three equivalent O(5)Li2Co3 square pyramids, and edges with three equivalent O(7)Li2Co3 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3(CoO2)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.791
_cell_length_b   5.904
_cell_length_c   9.969
_cell_angle_alpha   106.429
_cell_angle_beta   89.999
_cell_angle_gamma   119.368
_symmetry_Int_Tables_number   1
_cell_volume   280.973
_cell_formula_units_Z   2
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  0.252  0.999  0.743  1.0
  Li  Li1  1  0.748  0.001  0.258  1.0
  Li  Li2  1  0.500  0.003  0.000  1.0
  Li  Li3  1  0.996  0.997  0.500  1.0
  Li  Li4  1  0.753  0.001  0.757  1.0
  Li  Li5  1  0.247  0.999  0.242  1.0
  Co  Co6  1  0.756  0.500  0.750  1.0
  Co  Co7  1  0.999  0.499  0.500  1.0
  Co  Co8  1  0.000  0.501  0.000  1.0
  Co  Co9  1  0.755  0.500  0.250  1.0
  Co  Co10  1  0.245  0.500  0.750  1.0
  Co  Co11  1  0.248  0.500  0.250  1.0
  Co  Co12  1  0.501  0.504  0.000  1.0
  Co  Co13  1  0.497  0.496  0.500  1.0
  O  O14  1  0.654  0.276  0.884  1.0
  O  O15  1  0.120  0.273  0.383  1.0
  O  O16  1  0.348  0.727  0.117  1.0
  O  O17  1  0.878  0.724  0.616  1.0
  O  O18  1  0.404  0.287  0.131  1.0
  O  O19  1  0.902  0.288  0.627  1.0
  O  O20  1  0.870  0.712  0.123  1.0
  O  O21  1  0.339  0.709  0.622  1.0
  O  O22  1  0.888  0.291  0.127  1.0
  O  O23  1  0.386  0.289  0.632  1.0
  O  O24  1  0.114  0.712  0.873  1.0
  O  O25  1  0.617  0.713  0.369  1.0
  O  O26  1  0.130  0.291  0.878  1.0
  O  O27  1  0.659  0.288  0.377  1.0
  O  O28  1  0.597  0.711  0.868  1.0
  O  O29  1  0.098  0.709  0.373  1.0
[/CIF]
.