The structure described by Al2O3 crystallizes in the triclinic P1 space group. There are sixteen inequivalent Al sites. In the first Al site, Al(1) is bonded in a 4-coordinate geometry to one O(10), one O(13), one O(22), and one O(6) atom. In the second Al site, Al(2) is bonded to one O(1), one O(10), one O(2), one O(20), one O(4), and one O(9) atom to form distorted AlO6 octahedra that share  a cornercorner with one Al(15)O4 tetrahedra,  a cornercorner with one Al(4)O4 tetrahedra, and  an edgeedge with one Al(3)O6 octahedra. In the third Al site, Al(3) is bonded to one O(11), one O(14), one O(18), one O(20), one O(8), and one O(9) atom to form distorted AlO6 octahedra that share  a cornercorner with one Al(12)O4 tetrahedra and  an edgeedge with one Al(2)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(1), one O(13), one O(3), and one O(6) atom to form distorted AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra and corners with two equivalent Al(15)O4 tetrahedra. The corner-sharing octahedral tilt angles are 72°. In the fifth Al site, Al(5) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(8), and one O(9) atom. In the sixth Al site, Al(6) is bonded in a 6-coordinate geometry to one O(1), one O(13), one O(18), one O(2), one O(4), and one O(9) atom. In the seventh Al site, Al(7) is bonded in a 5-coordinate geometry to one O(14), one O(18), one O(20), one O(7), and one O(8) atom. In the eighth Al site, Al(8) is bonded to one O(12), one O(19), one O(21), one O(23), and one O(24) atom to form distorted corner-sharing AlO5 trigonal bipyramids. In the ninth Al site, Al(9) is bonded in a 6-coordinate geometry to one O(11), one O(16), one O(17), one O(24), one O(5), and one O(7) atom. In the tenth Al site, Al(10) is bonded in a 5-coordinate geometry to one O(14), one O(18), one O(20), one O(5), and one O(8) atom. In the eleventh Al site, Al(11) is bonded in a 6-coordinate geometry to one O(16), one O(17), one O(23), one O(24), one O(5), and one O(7) atom. In the twelfth Al site, Al(12) is bonded to one O(11), one O(16), one O(17), and one O(7) atom to form distorted corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles are 89°. In the thirteenth Al site, Al(13) is bonded to one O(15), one O(21), one O(22), and one O(23) atom to form distorted corner-sharing AlO4 tetrahedra. In the fourteenth Al site, Al(14) is bonded in a 5-coordinate geometry to one O(12), one O(15), one O(16), one O(19), and one O(21) atom. In the fifteenth Al site, Al(15) is bonded to one O(10), one O(12), one O(3), and one O(6) atom to form distorted AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(4)O4 tetrahedra, and  a cornercorner with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 69°. In the sixteenth Al site, Al(16) is bonded in a 4-coordinate geometry to one O(15), one O(19), one O(22), and one O(3) atom. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Al(2), one Al(4), one Al(5), and one Al(6) atom. In the second O site, O(2) is bonded in a T-shaped geometry to one Al(2), one Al(5), and one Al(6) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Al(15), one Al(16), and one Al(4) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Al(2), one Al(5), and one Al(6) atom. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Al(10), one Al(11), and one Al(9) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Al(1), one Al(15), and one Al(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Al(11), one Al(12), one Al(7), and one Al(9) atom. In the eighth O site, O(8) is bonded to one Al(10), one Al(3), one Al(5), and one Al(7) atom to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Al(2), one Al(3), one Al(5), and one Al(6) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Al(1), one Al(15), and one Al(2) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Al(12), one Al(3), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Al(14), one Al(15), and one Al(8) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Al(1), one Al(4), and one Al(6) atom. In the fourteenth O site, O(14) is bonded in a distorted T-shaped geometry to one Al(10), one Al(3), and one Al(7) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Al(13), one Al(14), and one Al(16) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Al(11), one Al(12), one Al(14), and one Al(9) 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(9) atom. In the eighteenth O site, O(18) is bonded to one Al(10), one Al(3), one Al(6), and one Al(7) atom to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the nineteenth O site, O(19) is bonded in a 3-coordinate geometry to one Al(14), one Al(16), and one Al(8) atom. In the twentieth O site, O(20) is bonded in a distorted see-saw-like geometry to one Al(10), one Al(2), one Al(3), and one Al(7) atom. In the twenty-first O site, O(21) is bonded in a 3-coordinate geometry to one Al(13), one Al(14), and one Al(8) atom. In the twenty-second O site, O(22) is bonded in a distorted trigonal planar geometry to one Al(1), one Al(13), and one Al(16) atom. In the twenty-third O site, O(23) is bonded in a 3-coordinate geometry to one Al(11), one Al(13), and one Al(8) atom. In the twenty-fourth O site, O(24) is bonded in a distorted T-shaped geometry to one Al(11), one Al(8), and one Al(9) atom. is represented by the CIF file [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.592
_cell_length_b   5.882
_cell_length_c   14.192
_cell_angle_alpha   101.803
_cell_angle_beta   86.745
_cell_angle_gamma   115.412
_symmetry_Int_Tables_number   1
_cell_volume   412.467
_cell_formula_units_Z   8
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  0.919  0.122  0.093  1.0
  Al  Al1  1  0.967  0.754  0.267  1.0
  Al  Al2  1  0.632  0.480  0.427  1.0
  Al  Al3  1  0.410  0.139  0.121  1.0
  Al  Al4  1  0.750  0.230  0.284  1.0
  Al  Al5  1  0.269  0.321  0.262  1.0
  Al  Al6  1  0.383  0.927  0.442  1.0
  Al  Al7  1  0.129  0.770  0.818  1.0
  Al  Al8  1  0.296  0.152  0.620  1.0
  Al  Al9  1  0.109  0.406  0.449  1.0
  Al  Al10  1  0.221  0.644  0.655  1.0
  Al  Al11  1  0.682  0.692  0.608  1.0
  Al  Al12  1  0.050  0.212  0.849  1.0
  Al  Al13  1  0.615  0.640  0.842  1.0
  Al  Al14  1  0.000  0.649  0.052  1.0
  Al  Al15  1  0.519  0.040  0.939  1.0
  O  O16  1  0.391  0.048  0.251  1.0
  O  O17  1  0.078  0.504  0.263  1.0
  O  O18  1  0.352  0.901  0.052  1.0
  O  O19  1  0.919  0.049  0.254  1.0
  O  O20  1  0.125  0.363  0.581  1.0
  O  O21  1  0.757  0.320  0.104  1.0
  O  O22  1  0.476  0.864  0.566  1.0
  O  O23  1  0.748  0.200  0.415  1.0
  O  O24  1  0.626  0.504  0.280  1.0
  O  O25  1  0.928  0.819  0.126  1.0
  O  O26  1  0.601  0.401  0.560  1.0
  O  O27  1  0.903  0.632  0.931  1.0
  O  O28  1  0.251  0.346  0.115  1.0
  O  O29  1  0.443  0.673  0.413  1.0
  O  O30  1  0.391  0.273  0.891  1.0
  O  O31  1  0.511  0.572  0.720  1.0
  O  O32  1  0.025  0.840  0.593  1.0
  O  O33  1  0.282  0.207  0.409  1.0
  O  O34  1  0.415  0.754  0.895  1.0
  O  O35  1  0.003  0.687  0.408  1.0
  O  O36  1  0.912  0.943  0.793  1.0
  O  O37  1  0.866  0.134  0.960  1.0
  O  O38  1  0.023  0.478  0.770  1.0
  O  O39  1  0.355  0.970  0.726  1.0
[/CIF]
.
The structure described by Al2O3 crystallizes in the triclinic P1 space group. There are sixteen inequivalent Al sites. In the first Al site, Al(1) is bonded in a 4-coordinate geometry to one O(10), one O(13), one O(22), and one O(6) atom. In the second Al site, Al(2) is bonded to one O(1), one O(10), one O(2), one O(20), one O(4), and one O(9) atom to form distorted AlO6 octahedra that share  a cornercorner with one Al(15)O4 tetrahedra,  a cornercorner with one Al(4)O4 tetrahedra, and  an edgeedge with one Al(3)O6 octahedra. In the third Al site, Al(3) is bonded to one O(11), one O(14), one O(18), one O(20), one O(8), and one O(9) atom to form distorted AlO6 octahedra that share  a cornercorner with one Al(12)O4 tetrahedra and  an edgeedge with one Al(2)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(1), one O(13), one O(3), and one O(6) atom to form distorted AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra and corners with two equivalent Al(15)O4 tetrahedra. The corner-sharing octahedral tilt angles are 72°. In the fifth Al site, Al(5) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), one O(8), and one O(9) atom. In the sixth Al site, Al(6) is bonded in a 6-coordinate geometry to one O(1), one O(13), one O(18), one O(2), one O(4), and one O(9) atom. In the seventh Al site, Al(7) is bonded in a 5-coordinate geometry to one O(14), one O(18), one O(20), one O(7), and one O(8) atom. In the eighth Al site, Al(8) is bonded to one O(12), one O(19), one O(21), one O(23), and one O(24) atom to form distorted corner-sharing AlO5 trigonal bipyramids. In the ninth Al site, Al(9) is bonded in a 6-coordinate geometry to one O(11), one O(16), one O(17), one O(24), one O(5), and one O(7) atom. In the tenth Al site, Al(10) is bonded in a 5-coordinate geometry to one O(14), one O(18), one O(20), one O(5), and one O(8) atom. In the eleventh Al site, Al(11) is bonded in a 6-coordinate geometry to one O(16), one O(17), one O(23), one O(24), one O(5), and one O(7) atom. In the twelfth Al site, Al(12) is bonded to one O(11), one O(16), one O(17), and one O(7) atom to form distorted corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles are 89°. In the thirteenth Al site, Al(13) is bonded to one O(15), one O(21), one O(22), and one O(23) atom to form distorted corner-sharing AlO4 tetrahedra. In the fourteenth Al site, Al(14) is bonded in a 5-coordinate geometry to one O(12), one O(15), one O(16), one O(19), and one O(21) atom. In the fifteenth Al site, Al(15) is bonded to one O(10), one O(12), one O(3), and one O(6) atom to form distorted AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(4)O4 tetrahedra, and  a cornercorner with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 69°. In the sixteenth Al site, Al(16) is bonded in a 4-coordinate geometry to one O(15), one O(19), one O(22), and one O(3) atom. There are twenty-four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Al(2), one Al(4), one Al(5), and one Al(6) atom. In the second O site, O(2) is bonded in a T-shaped geometry to one Al(2), one Al(5), and one Al(6) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Al(15), one Al(16), and one Al(4) atom. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Al(2), one Al(5), and one Al(6) atom. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Al(10), one Al(11), and one Al(9) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Al(1), one Al(15), and one Al(4) atom. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to one Al(11), one Al(12), one Al(7), and one Al(9) atom. In the eighth O site, O(8) is bonded to one Al(10), one Al(3), one Al(5), and one Al(7) atom to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Al(2), one Al(3), one Al(5), and one Al(6) atom. In the tenth O site, O(10) is bonded in a 3-coordinate geometry to one Al(1), one Al(15), and one Al(2) atom. In the eleventh O site, O(11) is bonded in a 3-coordinate geometry to one Al(12), one Al(3), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Al(14), one Al(15), and one Al(8) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Al(1), one Al(4), and one Al(6) atom. In the fourteenth O site, O(14) is bonded in a distorted T-shaped geometry to one Al(10), one Al(3), and one Al(7) atom. In the fifteenth O site, O(15) is bonded in a 3-coordinate geometry to one Al(13), one Al(14), and one Al(16) atom. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Al(11), one Al(12), one Al(14), and one Al(9) 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(9) atom. In the eighteenth O site, O(18) is bonded to one Al(10), one Al(3), one Al(6), and one Al(7) atom to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the nineteenth O site, O(19) is bonded in a 3-coordinate geometry to one Al(14), one Al(16), and one Al(8) atom. In the twentieth O site, O(20) is bonded in a distorted see-saw-like geometry to one Al(10), one Al(2), one Al(3), and one Al(7) atom. In the twenty-first O site, O(21) is bonded in a 3-coordinate geometry to one Al(13), one Al(14), and one Al(8) atom. In the twenty-second O site, O(22) is bonded in a distorted trigonal planar geometry to one Al(1), one Al(13), and one Al(16) atom. In the twenty-third O site, O(23) is bonded in a 3-coordinate geometry to one Al(11), one Al(13), and one Al(8) atom. In the twenty-fourth O site, O(24) is bonded in a distorted T-shaped geometry to one Al(11), one Al(8), and one Al(9) atom. is represented by the CIF file [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.592
_cell_length_b   5.882
_cell_length_c   14.192
_cell_angle_alpha   101.803
_cell_angle_beta   86.745
_cell_angle_gamma   115.412
_symmetry_Int_Tables_number   1
_cell_volume   412.467
_cell_formula_units_Z   8
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  0.919  0.122  0.093  1.0
  Al  Al1  1  0.967  0.754  0.267  1.0
  Al  Al2  1  0.632  0.480  0.427  1.0
  Al  Al3  1  0.410  0.139  0.121  1.0
  Al  Al4  1  0.750  0.230  0.284  1.0
  Al  Al5  1  0.269  0.321  0.262  1.0
  Al  Al6  1  0.383  0.927  0.442  1.0
  Al  Al7  1  0.129  0.770  0.818  1.0
  Al  Al8  1  0.296  0.152  0.620  1.0
  Al  Al9  1  0.109  0.406  0.449  1.0
  Al  Al10  1  0.221  0.644  0.655  1.0
  Al  Al11  1  0.682  0.692  0.608  1.0
  Al  Al12  1  0.050  0.212  0.849  1.0
  Al  Al13  1  0.615  0.640  0.842  1.0
  Al  Al14  1  0.000  0.649  0.052  1.0
  Al  Al15  1  0.519  0.040  0.939  1.0
  O  O16  1  0.391  0.048  0.251  1.0
  O  O17  1  0.078  0.504  0.263  1.0
  O  O18  1  0.352  0.901  0.052  1.0
  O  O19  1  0.919  0.049  0.254  1.0
  O  O20  1  0.125  0.363  0.581  1.0
  O  O21  1  0.757  0.320  0.104  1.0
  O  O22  1  0.476  0.864  0.566  1.0
  O  O23  1  0.748  0.200  0.415  1.0
  O  O24  1  0.626  0.504  0.280  1.0
  O  O25  1  0.928  0.819  0.126  1.0
  O  O26  1  0.601  0.401  0.560  1.0
  O  O27  1  0.903  0.632  0.931  1.0
  O  O28  1  0.251  0.346  0.115  1.0
  O  O29  1  0.443  0.673  0.413  1.0
  O  O30  1  0.391  0.273  0.891  1.0
  O  O31  1  0.511  0.572  0.720  1.0
  O  O32  1  0.025  0.840  0.593  1.0
  O  O33  1  0.282  0.207  0.409  1.0
  O  O34  1  0.415  0.754  0.895  1.0
  O  O35  1  0.003  0.687  0.408  1.0
  O  O36  1  0.912  0.943  0.793  1.0
  O  O37  1  0.866  0.134  0.960  1.0
  O  O38  1  0.023  0.478  0.770  1.0
  O  O39  1  0.355  0.970  0.726  1.0
[/CIF]
.