The crystal structure described by Al2O3 crystallizes in the orthorhombic Pna2_1 space group. There are four inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(2), and two equivalent O(4) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, corners with four equivalent Al(3)O6 octahedra, and corners with two equivalent Al(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-67°. In the second Al site, Al(2) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form AlO6 octahedra that share corners with two equivalent Al(4)O6 octahedra, corners with three equivalent Al(1)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, edges with two equivalent Al(4)O6 octahedra, and edges with three equivalent Al(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 15-50°. In the third Al site, Al(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted AlO6 octahedra that share corners with four equivalent Al(4)O6 octahedra, corners with four equivalent Al(1)O4 tetrahedra,  an edgeedge with one Al(4)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. In the fourth Al site, Al(4) is bonded to one O(1), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form distorted AlO6 octahedra that share corners with two equivalent Al(2)O6 octahedra, corners with four equivalent Al(3)O6 octahedra,  a cornercorner with one Al(1)O4 tetrahedra,  an edgeedge with one Al(3)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Al(1), one Al(2), one Al(3), and one Al(4) atom to form OAl4 tetrahedra that share  a cornercorner with one O(3)Al5 square pyramid, corners with two equivalent O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, and  an edgeedge with one O(2)Al4 tetrahedra. In the second O site, O(2) is bonded to one Al(1), one Al(3), and two equivalent Al(2) atoms to form distorted OAl4 tetrahedra that share  a cornercorner with one O(3)Al5 square pyramid, corners with two equivalent O(1)Al4 tetrahedra, corners with two equivalent O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, and  an edgeedge with one O(1)Al4 tetrahedra. In the third O site, O(3) is bonded to one Al(3), two equivalent Al(2), and two equivalent Al(4) atoms to form OAl5 square pyramids that share  a cornercorner with one O(1)Al4 tetrahedra,  a cornercorner with one O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, edges with two equivalent O(1)Al4 tetrahedra, and edges with two equivalent O(2)Al4 tetrahedra. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Al(3) and two equivalent Al(1) atoms. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Al(3) and two equivalent Al(4) atoms. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Al(2), one Al(3), and one Al(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.833
_cell_length_b   8.303
_cell_length_c   8.924
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   358.102
_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  0.677  0.152  0.207  1.0
  Al  Al1  1  0.823  0.652  0.707  1.0
  Al  Al2  1  0.684  0.840  0.016  1.0
  Al  Al3  1  0.816  0.340  0.516  1.0
  Al  Al4  1  0.316  0.160  0.516  1.0
  Al  Al5  1  0.173  0.030  0.006  1.0
  Al  Al6  1  0.686  0.154  0.794  1.0
  Al  Al7  1  0.186  0.346  0.794  1.0
  Al  Al8  1  0.314  0.846  0.294  1.0
  Al  Al9  1  0.827  0.970  0.506  1.0
  Al  Al10  1  0.673  0.470  0.006  1.0
  Al  Al11  1  0.177  0.348  0.207  1.0
  Al  Al12  1  0.323  0.848  0.707  1.0
  Al  Al13  1  0.814  0.654  0.294  1.0
  Al  Al14  1  0.327  0.530  0.506  1.0
  Al  Al15  1  0.184  0.660  0.016  1.0
  O  O16  1  0.978  0.512  0.142  1.0
  O  O17  1  0.343  0.839  0.906  1.0
  O  O18  1  0.020  0.824  0.135  1.0
  O  O19  1  0.481  0.668  0.647  1.0
  O  O20  1  0.843  0.661  0.906  1.0
  O  O21  1  0.343  0.168  0.880  1.0
  O  O22  1  0.980  0.176  0.635  1.0
  O  O23  1  0.157  0.339  0.406  1.0
  O  O24  1  0.981  0.832  0.647  1.0
  O  O25  1  0.520  0.676  0.135  1.0
  O  O26  1  0.522  0.012  0.642  1.0
  O  O27  1  0.657  0.161  0.406  1.0
  O  O28  1  0.657  0.501  0.412  1.0
  O  O29  1  0.519  0.332  0.147  1.0
  O  O30  1  0.019  0.168  0.147  1.0
  O  O31  1  0.022  0.488  0.642  1.0
  O  O32  1  0.157  0.999  0.412  1.0
  O  O33  1  0.157  0.668  0.380  1.0
  O  O34  1  0.480  0.324  0.635  1.0
  O  O35  1  0.657  0.832  0.380  1.0
  O  O36  1  0.478  0.988  0.142  1.0
  O  O37  1  0.843  0.001  0.912  1.0
  O  O38  1  0.343  0.499  0.912  1.0
  O  O39  1  0.843  0.332  0.880  1.0
[/CIF]
.
The crystal structure described by Al2O3 crystallizes in the orthorhombic Pna2_1 space group. There are four inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(2), and two equivalent O(4) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, corners with four equivalent Al(3)O6 octahedra, and corners with two equivalent Al(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-67°. In the second Al site, Al(2) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form AlO6 octahedra that share corners with two equivalent Al(4)O6 octahedra, corners with three equivalent Al(1)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, edges with two equivalent Al(4)O6 octahedra, and edges with three equivalent Al(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 15-50°. In the third Al site, Al(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form distorted AlO6 octahedra that share corners with four equivalent Al(4)O6 octahedra, corners with four equivalent Al(1)O4 tetrahedra,  an edgeedge with one Al(4)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. In the fourth Al site, Al(4) is bonded to one O(1), one O(6), two equivalent O(3), and two equivalent O(5) atoms to form distorted AlO6 octahedra that share corners with two equivalent Al(2)O6 octahedra, corners with four equivalent Al(3)O6 octahedra,  a cornercorner with one Al(1)O4 tetrahedra,  an edgeedge with one Al(3)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-57°. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Al(1), one Al(2), one Al(3), and one Al(4) atom to form OAl4 tetrahedra that share  a cornercorner with one O(3)Al5 square pyramid, corners with two equivalent O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, and  an edgeedge with one O(2)Al4 tetrahedra. In the second O site, O(2) is bonded to one Al(1), one Al(3), and two equivalent Al(2) atoms to form distorted OAl4 tetrahedra that share  a cornercorner with one O(3)Al5 square pyramid, corners with two equivalent O(1)Al4 tetrahedra, corners with two equivalent O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, and  an edgeedge with one O(1)Al4 tetrahedra. In the third O site, O(3) is bonded to one Al(3), two equivalent Al(2), and two equivalent Al(4) atoms to form OAl5 square pyramids that share  a cornercorner with one O(1)Al4 tetrahedra,  a cornercorner with one O(2)Al4 tetrahedra, edges with two equivalent O(3)Al5 square pyramids, edges with two equivalent O(1)Al4 tetrahedra, and edges with two equivalent O(2)Al4 tetrahedra. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Al(3) and two equivalent Al(1) atoms. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Al(3) and two equivalent Al(4) atoms. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Al(2), one Al(3), and one Al(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Al2O3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.833
_cell_length_b   8.303
_cell_length_c   8.924
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   358.102
_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  0.677  0.152  0.207  1.0
  Al  Al1  1  0.823  0.652  0.707  1.0
  Al  Al2  1  0.684  0.840  0.016  1.0
  Al  Al3  1  0.816  0.340  0.516  1.0
  Al  Al4  1  0.316  0.160  0.516  1.0
  Al  Al5  1  0.173  0.030  0.006  1.0
  Al  Al6  1  0.686  0.154  0.794  1.0
  Al  Al7  1  0.186  0.346  0.794  1.0
  Al  Al8  1  0.314  0.846  0.294  1.0
  Al  Al9  1  0.827  0.970  0.506  1.0
  Al  Al10  1  0.673  0.470  0.006  1.0
  Al  Al11  1  0.177  0.348  0.207  1.0
  Al  Al12  1  0.323  0.848  0.707  1.0
  Al  Al13  1  0.814  0.654  0.294  1.0
  Al  Al14  1  0.327  0.530  0.506  1.0
  Al  Al15  1  0.184  0.660  0.016  1.0
  O  O16  1  0.978  0.512  0.142  1.0
  O  O17  1  0.343  0.839  0.906  1.0
  O  O18  1  0.020  0.824  0.135  1.0
  O  O19  1  0.481  0.668  0.647  1.0
  O  O20  1  0.843  0.661  0.906  1.0
  O  O21  1  0.343  0.168  0.880  1.0
  O  O22  1  0.980  0.176  0.635  1.0
  O  O23  1  0.157  0.339  0.406  1.0
  O  O24  1  0.981  0.832  0.647  1.0
  O  O25  1  0.520  0.676  0.135  1.0
  O  O26  1  0.522  0.012  0.642  1.0
  O  O27  1  0.657  0.161  0.406  1.0
  O  O28  1  0.657  0.501  0.412  1.0
  O  O29  1  0.519  0.332  0.147  1.0
  O  O30  1  0.019  0.168  0.147  1.0
  O  O31  1  0.022  0.488  0.642  1.0
  O  O32  1  0.157  0.999  0.412  1.0
  O  O33  1  0.157  0.668  0.380  1.0
  O  O34  1  0.480  0.324  0.635  1.0
  O  O35  1  0.657  0.832  0.380  1.0
  O  O36  1  0.478  0.988  0.142  1.0
  O  O37  1  0.843  0.001  0.912  1.0
  O  O38  1  0.343  0.499  0.912  1.0
  O  O39  1  0.843  0.332  0.880  1.0
[/CIF]
.