The structure described by Li3FeAl2O6 crystallizes in the triclinic P-1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(5), one O(6), and two equivalent O(2) atoms to form LiO5 trigonal bipyramids that share corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Al(2)O5 trigonal bipyramids. In the second Li site, Li(2) is bonded to one O(1), one O(3), one O(5), and two equivalent O(4) atoms to form LiO5 trigonal bipyramids that share corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Al(1)O5 trigonal bipyramids. In the third Li site, Li(3) is bonded to one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(6) atom to form FeO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(3)O5 trigonal bipyramids. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(4), one O(5), and two equivalent O(3) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. In the second Al site, Al(2) is bonded to one O(1), one O(2), one O(5), and two equivalent O(6) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Fe(1), one Al(1), and one Al(2) atom to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(5)Li3Al2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(3), two equivalent Li(1), one Fe(1), and one Al(2) atom to form OLi3AlFe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(6)Li2Al2Fe trigonal bipyramids. In the third O site, O(3) is bonded to one Li(2), one Li(3), one Fe(1), and two equivalent Al(1) atoms to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid, and edges with two equivalent O(4)Li3AlFe trigonal bipyramids. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Li(2), one Fe(1), and one Al(1) atom to form OLi3AlFe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(3)Li2Al2Fe trigonal bipyramids. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), one Li(3), one Al(1), and one Al(2) atom to form OLi3Al2 trigonal bipyramids that share corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(1)Li2Al2Fe trigonal bipyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Fe(1), and two equivalent Al(2) atoms to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid, and edges with two equivalent O(2)Li3AlFe trigonal bipyramids. is represented by the CIF file [CIF]
data_Li3Al2FeO6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.348
_cell_length_b   5.858
_cell_length_c   7.820
_cell_angle_alpha   90.781
_cell_angle_beta   98.559
_cell_angle_gamma   90.233
_symmetry_Int_Tables_number   1
_cell_volume   242.220
_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  0.176  0.843  0.094  1.0
  Li  Li1  1  0.347  0.664  0.420  1.0
  Li  Li2  1  0.502  0.835  0.744  1.0
  Li  Li3  1  0.498  0.165  0.256  1.0
  Li  Li4  1  0.653  0.336  0.580  1.0
  Li  Li5  1  0.824  0.157  0.906  1.0
  Al  Al6  1  0.175  0.168  0.589  1.0
  Al  Al7  1  0.658  0.672  0.078  1.0
  Al  Al8  1  0.342  0.328  0.922  1.0
  Al  Al9  1  0.825  0.832  0.411  1.0
  Fe  Fe10  1  0.995  0.669  0.753  1.0
  Fe  Fe11  1  0.005  0.331  0.247  1.0
  O  O12  1  0.977  0.665  0.254  1.0
  O  O13  1  0.173  0.188  0.075  1.0
  O  O14  1  0.145  0.854  0.581  1.0
  O  O15  1  0.308  0.322  0.426  1.0
  O  O16  1  0.532  0.828  0.245  1.0
  O  O17  1  0.341  0.642  0.921  1.0
  O  O18  1  0.659  0.358  0.079  1.0
  O  O19  1  0.468  0.172  0.755  1.0
  O  O20  1  0.692  0.678  0.574  1.0
  O  O21  1  0.855  0.146  0.419  1.0
  O  O22  1  0.827  0.812  0.925  1.0
  O  O23  1  0.023  0.335  0.746  1.0
[/CIF]
.
The structure described by Li3FeAl2O6 crystallizes in the triclinic P-1 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(5), one O(6), and two equivalent O(2) atoms to form LiO5 trigonal bipyramids that share corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Al(2)O5 trigonal bipyramids. In the second Li site, Li(2) is bonded to one O(1), one O(3), one O(5), and two equivalent O(4) atoms to form LiO5 trigonal bipyramids that share corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Al(1)O5 trigonal bipyramids. In the third Li site, Li(3) is bonded to one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Fe(1)O5 trigonal bipyramids. Fe(1) is bonded to one O(1), one O(2), one O(3), one O(4), and one O(6) atom to form FeO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Al(1)O5 trigonal bipyramids, corners with two equivalent Al(2)O5 trigonal bipyramids,  an edgeedge with one Li(1)O5 trigonal bipyramid,  an edgeedge with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(3)O5 trigonal bipyramids. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(4), one O(5), and two equivalent O(3) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(2)O5 trigonal bipyramids. In the second Al site, Al(2) is bonded to one O(1), one O(2), one O(5), and two equivalent O(6) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Li(1)O5 trigonal bipyramids, corners with two equivalent Li(2)O5 trigonal bipyramids, corners with two equivalent Li(3)O5 trigonal bipyramids, corners with two equivalent Fe(1)O5 trigonal bipyramids,  an edgeedge with one Li(3)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O5 trigonal bipyramid,  an edgeedge with one Al(1)O5 trigonal bipyramid,  an edgeedge with one Al(2)O5 trigonal bipyramid, and edges with two equivalent Li(1)O5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Fe(1), one Al(1), and one Al(2) atom to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(5)Li3Al2 trigonal bipyramids. In the second O site, O(2) is bonded to one Li(3), two equivalent Li(1), one Fe(1), and one Al(2) atom to form OLi3AlFe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(6)Li2Al2Fe trigonal bipyramids. In the third O site, O(3) is bonded to one Li(2), one Li(3), one Fe(1), and two equivalent Al(1) atoms to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid, and edges with two equivalent O(4)Li3AlFe trigonal bipyramids. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Li(2), one Fe(1), and one Al(1) atom to form OLi3AlFe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(3)Li2Al2Fe trigonal bipyramids. In the fifth O site, O(5) is bonded to one Li(1), one Li(2), one Li(3), one Al(1), and one Al(2) atom to form OLi3Al2 trigonal bipyramids that share corners with two equivalent O(3)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(6)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(2)Li3AlFe trigonal bipyramid,  an edgeedge with one O(4)Li3AlFe trigonal bipyramid, and edges with two equivalent O(1)Li2Al2Fe trigonal bipyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Fe(1), and two equivalent Al(2) atoms to form OLi2Al2Fe trigonal bipyramids that share corners with two equivalent O(1)Li2Al2Fe trigonal bipyramids, corners with two equivalent O(5)Li3Al2 trigonal bipyramids, corners with two equivalent O(2)Li3AlFe trigonal bipyramids, corners with two equivalent O(4)Li3AlFe trigonal bipyramids,  an edgeedge with one O(1)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(3)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(6)Li2Al2Fe trigonal bipyramid,  an edgeedge with one O(5)Li3Al2 trigonal bipyramid, and edges with two equivalent O(2)Li3AlFe trigonal bipyramids. is represented by the CIF file [CIF]
data_Li3Al2FeO6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.348
_cell_length_b   5.858
_cell_length_c   7.820
_cell_angle_alpha   90.781
_cell_angle_beta   98.559
_cell_angle_gamma   90.233
_symmetry_Int_Tables_number   1
_cell_volume   242.220
_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  0.176  0.843  0.094  1.0
  Li  Li1  1  0.347  0.664  0.420  1.0
  Li  Li2  1  0.502  0.835  0.744  1.0
  Li  Li3  1  0.498  0.165  0.256  1.0
  Li  Li4  1  0.653  0.336  0.580  1.0
  Li  Li5  1  0.824  0.157  0.906  1.0
  Al  Al6  1  0.175  0.168  0.589  1.0
  Al  Al7  1  0.658  0.672  0.078  1.0
  Al  Al8  1  0.342  0.328  0.922  1.0
  Al  Al9  1  0.825  0.832  0.411  1.0
  Fe  Fe10  1  0.995  0.669  0.753  1.0
  Fe  Fe11  1  0.005  0.331  0.247  1.0
  O  O12  1  0.977  0.665  0.254  1.0
  O  O13  1  0.173  0.188  0.075  1.0
  O  O14  1  0.145  0.854  0.581  1.0
  O  O15  1  0.308  0.322  0.426  1.0
  O  O16  1  0.532  0.828  0.245  1.0
  O  O17  1  0.341  0.642  0.921  1.0
  O  O18  1  0.659  0.358  0.079  1.0
  O  O19  1  0.468  0.172  0.755  1.0
  O  O20  1  0.692  0.678  0.574  1.0
  O  O21  1  0.855  0.146  0.419  1.0
  O  O22  1  0.827  0.812  0.925  1.0
  O  O23  1  0.023  0.335  0.746  1.0
[/CIF]
.