The crystal structure described by Al2O3 crystallizes in the triclinic P1 space group. There are twelve inequivalent Al sites. In the first Al site, Al(1) is bonded in a trigonal planar geometry to one O(16), one O(18), and one O(2) atom. In the second Al site, Al(2) is bonded in a trigonal planar geometry to one O(1), one O(2), and one O(3) atom. In the third Al site, Al(3) is bonded to one O(10), one O(5), one O(7), one O(8), and one O(9) atom to form AlO5 trigonal bipyramids that share  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Al(9)O4 trigonal pyramids,  an edgeedge with one Al(6)O4 tetrahedra, and edges with two equivalent Al(8)O5 trigonal bipyramids. In the fourth Al site, Al(4) is bonded in a trigonal planar geometry to one O(1), one O(3), and one O(4) atom. In the fifth Al site, Al(5) is bonded in a trigonal planar geometry to one O(4), one O(5), and one O(6) atom. In the sixth Al site, Al(6) is bonded to one O(5), one O(6), one O(7), and one O(8) atom to form a mixture of distorted corner and edge-sharing AlO4 tetrahedra. In the seventh Al site, Al(7) is bonded to one O(11), one O(13), one O(14), one O(15), and one O(17) atom to form a mixture of distorted corner and edge-sharing AlO5 trigonal bipyramids. In the eighth Al site, Al(8) is bonded to one O(10), one O(12), one O(7), one O(8), and one O(9) atom to form distorted AlO5 trigonal bipyramids that share corners with two equivalent Al(6)O4 tetrahedra,  a cornercorner with one Al(10)O4 trigonal pyramid,  a cornercorner with one Al(9)O4 trigonal pyramid, edges with two equivalent Al(3)O5 trigonal bipyramids, and  an edgeedge with one Al(9)O4 trigonal pyramid. In the ninth Al site, Al(9) is bonded to one O(10), one O(11), one O(12), and one O(9) atom to form distorted AlO4 trigonal pyramids that share  a cornercorner with one Al(7)O5 trigonal bipyramid,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(3)O5 trigonal bipyramids, corners with two equivalent Al(10)O4 trigonal pyramids, and  an edgeedge with one Al(8)O5 trigonal bipyramid. In the tenth Al site, Al(10) is bonded to one O(11), one O(12), one O(13), and one O(14) atom to form distorted AlO4 trigonal pyramids that share  a cornercorner with one Al(7)O5 trigonal bipyramid,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(9)O4 trigonal pyramids, and  an edgeedge with one Al(7)O5 trigonal bipyramid. In the eleventh Al site, Al(11) is bonded in a distorted see-saw-like geometry to one O(13), one O(14), one O(15), and one O(17) atom. In the twelfth Al site, Al(12) is bonded to one O(15), one O(16), one O(17), and one O(18) atom to form corner-sharing AlO4 tetrahedra. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Al(2) and one Al(4) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Al(1) and one Al(2) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Al(2) and one Al(4) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to one Al(4) and one Al(5) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(5), and one Al(6) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Al(5) and one Al(6) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(6), and one Al(8) atom. In the eighth O site, O(8) is bonded in a T-shaped geometry to one Al(3), one Al(6), and one Al(8) atom. In the ninth O site, O(9) is bonded in a T-shaped geometry to one Al(3), one Al(8), and one Al(9) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(8), and one Al(9) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(7), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(8), and one Al(9) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(11), and one Al(7) atom. In the fourteenth O site, O(14) is bonded in a T-shaped geometry to one Al(10), one Al(11), and one Al(7) atom. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Al(11), one Al(12), and one Al(7) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Al(1) and one Al(12) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Al(11), one Al(12), and one Al(7) atom. In the eighteenth O site, O(18) is bonded in a distorted bent 120 degrees geometry to one Al(1) and one Al(12) atom. is represented by the CIF file [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.223
_cell_length_b   5.345
_cell_length_c   20.008
_cell_angle_alpha   91.319
_cell_angle_beta   96.444
_cell_angle_gamma   115.742
_symmetry_Int_Tables_number   1
_cell_volume   498.398
_cell_formula_units_Z   6
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
  Al  Al0  1  0.750  0.922  0.976  1.0
  Al  Al1  1  0.963  0.025  0.141  1.0
  Al  Al2  1  0.512  0.259  0.524  1.0
  Al  Al3  1  0.550  0.160  0.223  1.0
  Al  Al4  1  0.404  0.303  0.368  1.0
  Al  Al5  1  0.938  0.256  0.457  1.0
  Al  Al6  1  0.153  0.869  0.788  1.0
  Al  Al7  1  0.508  0.762  0.559  1.0
  Al  Al8  1  0.026  0.859  0.622  1.0
  Al  Al9  1  0.586  0.902  0.722  1.0
  Al  Al10  1  0.184  0.378  0.821  1.0
  Al  Al11  1  0.714  0.403  0.891  1.0
  O  O12  1  0.246  0.963  0.170  1.0
  O  O13  1  0.804  0.917  0.061  1.0
  O  O14  1  0.860  0.190  0.199  1.0
  O  O15  1  0.537  0.326  0.295  1.0
  O  O16  1  0.653  0.369  0.439  1.0
  O  O17  1  0.060  0.192  0.384  1.0
  O  O18  1  0.263  0.436  0.514  1.0
  O  O19  1  0.707  0.024  0.509  1.0
  O  O20  1  0.748  0.552  0.578  1.0
  O  O21  1  0.277  0.954  0.563  1.0
  O  O22  1  0.257  0.950  0.700  1.0
  O  O23  1  0.721  0.918  0.644  1.0
  O  O24  1  0.913  0.053  0.778  1.0
  O  O25  1  0.376  0.650  0.772  1.0
  O  O26  1  0.389  0.179  0.840  1.0
  O  O27  1  0.866  0.228  0.940  1.0
  O  O28  1  0.981  0.573  0.837  1.0
  O  O29  1  0.587  0.622  0.925  1.0
[/CIF]
.
The crystal structure described by Al2O3 crystallizes in the triclinic P1 space group. There are twelve inequivalent Al sites. In the first Al site, Al(1) is bonded in a trigonal planar geometry to one O(16), one O(18), and one O(2) atom. In the second Al site, Al(2) is bonded in a trigonal planar geometry to one O(1), one O(2), and one O(3) atom. In the third Al site, Al(3) is bonded to one O(10), one O(5), one O(7), one O(8), and one O(9) atom to form AlO5 trigonal bipyramids that share  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Al(9)O4 trigonal pyramids,  an edgeedge with one Al(6)O4 tetrahedra, and edges with two equivalent Al(8)O5 trigonal bipyramids. In the fourth Al site, Al(4) is bonded in a trigonal planar geometry to one O(1), one O(3), and one O(4) atom. In the fifth Al site, Al(5) is bonded in a trigonal planar geometry to one O(4), one O(5), and one O(6) atom. In the sixth Al site, Al(6) is bonded to one O(5), one O(6), one O(7), and one O(8) atom to form a mixture of distorted corner and edge-sharing AlO4 tetrahedra. In the seventh Al site, Al(7) is bonded to one O(11), one O(13), one O(14), one O(15), and one O(17) atom to form a mixture of distorted corner and edge-sharing AlO5 trigonal bipyramids. In the eighth Al site, Al(8) is bonded to one O(10), one O(12), one O(7), one O(8), and one O(9) atom to form distorted AlO5 trigonal bipyramids that share corners with two equivalent Al(6)O4 tetrahedra,  a cornercorner with one Al(10)O4 trigonal pyramid,  a cornercorner with one Al(9)O4 trigonal pyramid, edges with two equivalent Al(3)O5 trigonal bipyramids, and  an edgeedge with one Al(9)O4 trigonal pyramid. In the ninth Al site, Al(9) is bonded to one O(10), one O(11), one O(12), and one O(9) atom to form distorted AlO4 trigonal pyramids that share  a cornercorner with one Al(7)O5 trigonal bipyramid,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(3)O5 trigonal bipyramids, corners with two equivalent Al(10)O4 trigonal pyramids, and  an edgeedge with one Al(8)O5 trigonal bipyramid. In the tenth Al site, Al(10) is bonded to one O(11), one O(12), one O(13), and one O(14) atom to form distorted AlO4 trigonal pyramids that share  a cornercorner with one Al(7)O5 trigonal bipyramid,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(9)O4 trigonal pyramids, and  an edgeedge with one Al(7)O5 trigonal bipyramid. In the eleventh Al site, Al(11) is bonded in a distorted see-saw-like geometry to one O(13), one O(14), one O(15), and one O(17) atom. In the twelfth Al site, Al(12) is bonded to one O(15), one O(16), one O(17), and one O(18) atom to form corner-sharing AlO4 tetrahedra. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Al(2) and one Al(4) atom. In the second O site, O(2) is bonded in a bent 150 degrees geometry to one Al(1) and one Al(2) atom. In the third O site, O(3) is bonded in a bent 150 degrees geometry to one Al(2) and one Al(4) atom. In the fourth O site, O(4) is bonded in a bent 150 degrees geometry to one Al(4) and one Al(5) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(5), and one Al(6) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Al(5) and one Al(6) atom. In the seventh O site, O(7) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(6), and one Al(8) atom. In the eighth O site, O(8) is bonded in a T-shaped geometry to one Al(3), one Al(6), and one Al(8) atom. In the ninth O site, O(9) is bonded in a T-shaped geometry to one Al(3), one Al(8), and one Al(9) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(8), and one Al(9) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(7), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(8), and one Al(9) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(11), and one Al(7) atom. In the fourteenth O site, O(14) is bonded in a T-shaped geometry to one Al(10), one Al(11), and one Al(7) atom. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Al(11), one Al(12), and one Al(7) atom. In the sixteenth O site, O(16) is bonded in a bent 150 degrees geometry to one Al(1) and one Al(12) atom. In the seventeenth O site, O(17) is bonded in a distorted trigonal non-coplanar geometry to one Al(11), one Al(12), and one Al(7) atom. In the eighteenth O site, O(18) is bonded in a distorted bent 120 degrees geometry to one Al(1) and one Al(12) atom. is represented by the CIF file [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.223
_cell_length_b   5.345
_cell_length_c   20.008
_cell_angle_alpha   91.319
_cell_angle_beta   96.444
_cell_angle_gamma   115.742
_symmetry_Int_Tables_number   1
_cell_volume   498.398
_cell_formula_units_Z   6
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
  Al  Al0  1  0.750  0.922  0.976  1.0
  Al  Al1  1  0.963  0.025  0.141  1.0
  Al  Al2  1  0.512  0.259  0.524  1.0
  Al  Al3  1  0.550  0.160  0.223  1.0
  Al  Al4  1  0.404  0.303  0.368  1.0
  Al  Al5  1  0.938  0.256  0.457  1.0
  Al  Al6  1  0.153  0.869  0.788  1.0
  Al  Al7  1  0.508  0.762  0.559  1.0
  Al  Al8  1  0.026  0.859  0.622  1.0
  Al  Al9  1  0.586  0.902  0.722  1.0
  Al  Al10  1  0.184  0.378  0.821  1.0
  Al  Al11  1  0.714  0.403  0.891  1.0
  O  O12  1  0.246  0.963  0.170  1.0
  O  O13  1  0.804  0.917  0.061  1.0
  O  O14  1  0.860  0.190  0.199  1.0
  O  O15  1  0.537  0.326  0.295  1.0
  O  O16  1  0.653  0.369  0.439  1.0
  O  O17  1  0.060  0.192  0.384  1.0
  O  O18  1  0.263  0.436  0.514  1.0
  O  O19  1  0.707  0.024  0.509  1.0
  O  O20  1  0.748  0.552  0.578  1.0
  O  O21  1  0.277  0.954  0.563  1.0
  O  O22  1  0.257  0.950  0.700  1.0
  O  O23  1  0.721  0.918  0.644  1.0
  O  O24  1  0.913  0.053  0.778  1.0
  O  O25  1  0.376  0.650  0.772  1.0
  O  O26  1  0.389  0.179  0.840  1.0
  O  O27  1  0.866  0.228  0.940  1.0
  O  O28  1  0.981  0.573  0.837  1.0
  O  O29  1  0.587  0.622  0.925  1.0
[/CIF]
.