The structure described by Li4CoO4 crystallizes in the monoclinic Pm space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Co(2)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(2), one O(3), one O(4), and one O(5) atom. In the third Li site, Li(3) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form LiO4 tetrahedra that share corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Li(1)O4 trigonal pyramids, edges with two equivalent Li(5)O4 tetrahedra, and edges with two equivalent Li(4)O4 trigonal pyramids. In the fourth Li site, Li(4) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form distorted LiO4 trigonal pyramids that share corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, edges with two equivalent Li(3)O4 tetrahedra, and edges with two equivalent Li(1)O4 trigonal pyramids. In the fifth Li site, Li(5) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(4)O4 trigonal pyramids,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Co(1)O4 tetrahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(4), one O(6), and two equivalent O(2) atoms to form CoO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, corners with four equivalent Li(1)O4 trigonal pyramids, and edges with two equivalent Li(5)O4 tetrahedra. In the second Co site, Co(2) is bonded to one O(1), one O(3), and two equivalent O(5) atoms to form CoO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, and edges with two equivalent Li(1)O4 trigonal pyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to two equivalent Li(5) and one Co(2) atom. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(5), and one Co(1) atom to form OLi3Co trigonal pyramids that share  a cornercorner with one O(4)Li6Co pentagonal bipyramid, corners with two equivalent O(3)Li4Co trigonal bipyramids,  a cornercorner with one O(2)Li3Co trigonal pyramid,  an edgeedge with one O(4)Li6Co pentagonal bipyramid, and  an edgeedge with one O(6)Li4Co trigonal bipyramid. In the third O site, O(3) is bonded to two equivalent Li(1), two equivalent Li(2), and one Co(2) atom to form distorted OLi4Co trigonal bipyramids that share corners with four equivalent O(2)Li3Co trigonal pyramids and edges with two equivalent O(4)Li6Co pentagonal bipyramids. In the fourth O site, O(4) is bonded to one Li(3), one Li(4), two equivalent Li(1), two equivalent Li(2), and one Co(1) atom to form distorted OLi6Co pentagonal bipyramids that share  a cornercorner with one O(6)Li4Co trigonal bipyramid, corners with two equivalent O(2)Li3Co trigonal pyramids,  an edgeedge with one O(6)Li4Co trigonal bipyramid, edges with two equivalent O(3)Li4Co trigonal bipyramids, and edges with two equivalent O(2)Li3Co trigonal pyramids. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Li(1), one Li(2), one Li(3), one Li(4), one Li(5), and one Co(2) atom. In the sixth O site, O(6) is bonded to one Li(3), one Li(4), two equivalent Li(5), and one Co(1) atom to form distorted OLi4Co trigonal bipyramids that share  a cornercorner with one O(4)Li6Co pentagonal bipyramid,  an edgeedge with one O(4)Li6Co pentagonal bipyramid, and edges with two equivalent O(2)Li3Co trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4CoO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.407
_cell_length_b   4.858
_cell_length_c   6.412
_cell_angle_alpha   89.253
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   199.541
_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  0.757  0.756  0.572  1.0
  Li  Li1  1  0.243  0.756  0.572  1.0
  Li  Li2  1  0.306  0.244  0.478  1.0
  Li  Li3  1  0.694  0.244  0.478  1.0
  Li  Li4  1  0.000  0.309  0.265  1.0
  Li  Li5  1  0.000  0.790  0.195  1.0
  Li  Li6  1  0.292  0.271  0.006  1.0
  Li  Li7  1  0.708  0.271  0.006  1.0
  Co  Co8  1  0.000  0.236  0.747  1.0
  Co  Co9  1  0.500  0.742  0.239  1.0
  O  O10  1  0.500  0.985  0.037  1.0
  O  O11  1  0.235  0.428  0.731  1.0
  O  O12  1  0.765  0.428  0.731  1.0
  O  O13  1  0.500  0.945  0.479  1.0
  O  O14  1  0.000  0.025  0.503  1.0
  O  O15  1  0.742  0.533  0.260  1.0
  O  O16  1  0.258  0.533  0.260  1.0
  O  O17  1  0.000  0.101  0.011  1.0
[/CIF]
.
The structure described by Li4CoO4 crystallizes in the monoclinic Pm space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Co(2)O4 tetrahedra, and  an edgeedge with one Li(4)O4 trigonal pyramid. In the second Li site, Li(2) is bonded in a 4-coordinate geometry to one O(2), one O(3), one O(4), and one O(5) atom. In the third Li site, Li(3) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form LiO4 tetrahedra that share corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Li(1)O4 trigonal pyramids, edges with two equivalent Li(5)O4 tetrahedra, and edges with two equivalent Li(4)O4 trigonal pyramids. In the fourth Li site, Li(4) is bonded to one O(4), one O(6), and two equivalent O(5) atoms to form distorted LiO4 trigonal pyramids that share corners with two equivalent Co(1)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, edges with two equivalent Li(3)O4 tetrahedra, and edges with two equivalent Li(1)O4 trigonal pyramids. In the fifth Li site, Li(5) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form distorted LiO4 tetrahedra that share corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with two equivalent Li(1)O4 trigonal pyramids, corners with two equivalent Li(4)O4 trigonal pyramids,  an edgeedge with one Li(3)O4 tetrahedra, and  an edgeedge with one Co(1)O4 tetrahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(4), one O(6), and two equivalent O(2) atoms to form CoO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, corners with four equivalent Li(1)O4 trigonal pyramids, and edges with two equivalent Li(5)O4 tetrahedra. In the second Co site, Co(2) is bonded to one O(1), one O(3), and two equivalent O(5) atoms to form CoO4 tetrahedra that share corners with two equivalent Li(3)O4 tetrahedra, corners with four equivalent Li(5)O4 tetrahedra, corners with two equivalent Li(4)O4 trigonal pyramids, and edges with two equivalent Li(1)O4 trigonal pyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to two equivalent Li(5) and one Co(2) atom. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(5), and one Co(1) atom to form OLi3Co trigonal pyramids that share  a cornercorner with one O(4)Li6Co pentagonal bipyramid, corners with two equivalent O(3)Li4Co trigonal bipyramids,  a cornercorner with one O(2)Li3Co trigonal pyramid,  an edgeedge with one O(4)Li6Co pentagonal bipyramid, and  an edgeedge with one O(6)Li4Co trigonal bipyramid. In the third O site, O(3) is bonded to two equivalent Li(1), two equivalent Li(2), and one Co(2) atom to form distorted OLi4Co trigonal bipyramids that share corners with four equivalent O(2)Li3Co trigonal pyramids and edges with two equivalent O(4)Li6Co pentagonal bipyramids. In the fourth O site, O(4) is bonded to one Li(3), one Li(4), two equivalent Li(1), two equivalent Li(2), and one Co(1) atom to form distorted OLi6Co pentagonal bipyramids that share  a cornercorner with one O(6)Li4Co trigonal bipyramid, corners with two equivalent O(2)Li3Co trigonal pyramids,  an edgeedge with one O(6)Li4Co trigonal bipyramid, edges with two equivalent O(3)Li4Co trigonal bipyramids, and edges with two equivalent O(2)Li3Co trigonal pyramids. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Li(1), one Li(2), one Li(3), one Li(4), one Li(5), and one Co(2) atom. In the sixth O site, O(6) is bonded to one Li(3), one Li(4), two equivalent Li(5), and one Co(1) atom to form distorted OLi4Co trigonal bipyramids that share  a cornercorner with one O(4)Li6Co pentagonal bipyramid,  an edgeedge with one O(4)Li6Co pentagonal bipyramid, and edges with two equivalent O(2)Li3Co trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4CoO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.407
_cell_length_b   4.858
_cell_length_c   6.412
_cell_angle_alpha   89.253
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   199.541
_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  0.757  0.756  0.572  1.0
  Li  Li1  1  0.243  0.756  0.572  1.0
  Li  Li2  1  0.306  0.244  0.478  1.0
  Li  Li3  1  0.694  0.244  0.478  1.0
  Li  Li4  1  0.000  0.309  0.265  1.0
  Li  Li5  1  0.000  0.790  0.195  1.0
  Li  Li6  1  0.292  0.271  0.006  1.0
  Li  Li7  1  0.708  0.271  0.006  1.0
  Co  Co8  1  0.000  0.236  0.747  1.0
  Co  Co9  1  0.500  0.742  0.239  1.0
  O  O10  1  0.500  0.985  0.037  1.0
  O  O11  1  0.235  0.428  0.731  1.0
  O  O12  1  0.765  0.428  0.731  1.0
  O  O13  1  0.500  0.945  0.479  1.0
  O  O14  1  0.000  0.025  0.503  1.0
  O  O15  1  0.742  0.533  0.260  1.0
  O  O16  1  0.258  0.533  0.260  1.0
  O  O17  1  0.000  0.101  0.011  1.0
[/CIF]
.