Al2O3 crystallizes in the triclinic P1 space group. There are ten inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(13), one O(3), and one O(4) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(10)O6 octahedra,  a cornercorner with one Al(6)O6 octahedra,  a cornercorner with one Al(9)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, corners with two equivalent Al(2)O5 square pyramids, and  an edgeedge with one Al(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 15-70°. In the second Al site, Al(2) is bonded to one O(1), one O(10), one O(14), one O(15), and one O(3) atom to form distorted AlO5 square pyramids that share corners with two equivalent Al(10)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(9)O6 octahedra,  a cornercorner with one Al(4)O5 square pyramid, corners with two equivalent Al(1)O4 tetrahedra, and  an edgeedge with one Al(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. 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(8) atom to form AlO6 octahedra that share  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Al(8)O4 tetrahedra, corners with three equivalent Al(1)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra,  an edgeedge with one Al(2)O5 square pyramid, and edges with two equivalent Al(4)O5 square pyramids. In the fourth Al site, Al(4) is bonded to one O(2), one O(3), one O(4), one O(5), and one O(9) atom to form AlO5 square pyramids that share  a cornercorner with one Al(2)O5 square pyramid,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Al(8)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(3)O6 octahedra, and  an edgeedge with one Al(1)O4 tetrahedra. In the fifth Al site, Al(5) is bonded to one O(12), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(3)O6 octahedra, corners with two equivalent Al(10)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(9)O6 octahedra, corners with three equivalent Al(7)O6 octahedra, and  a cornercorner with one Al(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 54-61°. In the sixth Al site, Al(6) is bonded to one O(11), one O(13), one O(14), one O(15), one O(6), and one O(7) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(10)O6 octahedra, and edges with two equivalent Al(9)O6 octahedra. In the seventh Al site, Al(7) is bonded to one O(12), one O(2), one O(6), one O(7), one O(8), and one O(9) atom to form AlO6 octahedra that share corners with three equivalent Al(5)O4 tetrahedra, corners with three equivalent Al(8)O4 tetrahedra,  an edgeedge with one Al(10)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra,  an edgeedge with one Al(6)O6 octahedra,  an edgeedge with one Al(9)O6 octahedra, and  an edgeedge with one Al(4)O5 square pyramid. In the eighth Al site, Al(8) is bonded to one O(11), one O(2), one O(8), and one O(9) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(10)O6 octahedra,  a cornercorner with one Al(6)O6 octahedra,  a cornercorner with one Al(9)O6 octahedra, corners with two equivalent Al(3)O6 octahedra, corners with three equivalent Al(7)O6 octahedra, and corners with two equivalent Al(4)O5 square pyramids. The corner-sharing octahedral tilt angles range from 51-59°. In the ninth Al site, Al(9) is bonded to one O(10), one O(11), one O(12), one O(13), one O(15), and one O(7) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(10)O6 octahedra, and edges with two equivalent Al(6)O6 octahedra. In the tenth Al site, Al(10) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), and one O(6) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(6)O6 octahedra, and edges with two equivalent Al(9)O6 octahedra. There are fifteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Al(1), one Al(2), and one Al(3) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(4), one Al(7), and one Al(8) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Al(1), one Al(2), one Al(3), and one Al(4) atom. In the fourth O site, O(4) is bonded in a T-shaped geometry to one Al(1), one Al(3), and one Al(4) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(4), and one Al(5) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Al(10), one Al(5), one Al(6), and one Al(7) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Al(5), one Al(6), one Al(7), and one Al(9) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Al(3), one Al(7), and one Al(8) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Al(4), one Al(7), and one Al(8) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(2), and one Al(9) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Al(10), one Al(6), one Al(8), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Al(10), one Al(5), one Al(7), and one Al(9) atom. In the thirteenth O site, O(13) is bonded in a tetrahedral geometry to one Al(1), one Al(10), one Al(6), and one Al(9) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(2), and one Al(6) atom. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Al(2), one Al(6), and one Al(9) atom.
Al2O3 crystallizes in the triclinic P1 space group. There are ten inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(13), one O(3), and one O(4) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(10)O6 octahedra,  a cornercorner with one Al(6)O6 octahedra,  a cornercorner with one Al(9)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, corners with two equivalent Al(2)O5 square pyramids, and  an edgeedge with one Al(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 15-70°. The Al(1)-O(1) bond length is 1.73 Å. The Al(1)-O(13) bond length is 1.81 Å. The Al(1)-O(3) bond length is 1.81 Å. The Al(1)-O(4) bond length is 1.78 Å. In the second Al site, Al(2) is bonded to one O(1), one O(10), one O(14), one O(15), and one O(3) atom to form distorted AlO5 square pyramids that share corners with two equivalent Al(10)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(9)O6 octahedra,  a cornercorner with one Al(4)O5 square pyramid, corners with two equivalent Al(1)O4 tetrahedra, and  an edgeedge with one Al(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. The Al(2)-O(1) bond length is 1.88 Å. The Al(2)-O(10) bond length is 1.84 Å. The Al(2)-O(14) bond length is 1.83 Å. The Al(2)-O(15) bond length is 1.79 Å. The Al(2)-O(3) bond length is 2.08 Å. 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(8) atom to form AlO6 octahedra that share  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Al(8)O4 tetrahedra, corners with three equivalent Al(1)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra,  an edgeedge with one Al(2)O5 square pyramid, and edges with two equivalent Al(4)O5 square pyramids. The Al(3)-O(1) bond length is 1.86 Å. The Al(3)-O(2) bond length is 1.96 Å. The Al(3)-O(3) bond length is 2.05 Å. The Al(3)-O(4) bond length is 1.87 Å. The Al(3)-O(5) bond length is 1.90 Å. The Al(3)-O(8) bond length is 1.89 Å. In the fourth Al site, Al(4) is bonded to one O(2), one O(3), one O(4), one O(5), and one O(9) atom to form AlO5 square pyramids that share  a cornercorner with one Al(2)O5 square pyramid,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Al(8)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(3)O6 octahedra, and  an edgeedge with one Al(1)O4 tetrahedra. The Al(4)-O(2) bond length is 1.85 Å. The Al(4)-O(3) bond length is 1.95 Å. The Al(4)-O(4) bond length is 1.83 Å. The Al(4)-O(5) bond length is 1.81 Å. The Al(4)-O(9) bond length is 1.81 Å. In the fifth Al site, Al(5) is bonded to one O(12), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(3)O6 octahedra, corners with two equivalent Al(10)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(9)O6 octahedra, corners with three equivalent Al(7)O6 octahedra, and  a cornercorner with one Al(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 54-61°. The Al(5)-O(12) bond length is 1.80 Å. The Al(5)-O(5) bond length is 1.77 Å. The Al(5)-O(6) bond length is 1.81 Å. The Al(5)-O(7) bond length is 1.82 Å. In the sixth Al site, Al(6) is bonded to one O(11), one O(13), one O(14), one O(15), one O(6), and one O(7) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(10)O6 octahedra, and edges with two equivalent Al(9)O6 octahedra. The Al(6)-O(11) bond length is 1.97 Å. The Al(6)-O(13) bond length is 1.91 Å. The Al(6)-O(14) bond length is 1.80 Å. The Al(6)-O(15) bond length is 1.80 Å. The Al(6)-O(6) bond length is 1.97 Å. The Al(6)-O(7) bond length is 1.95 Å. In the seventh Al site, Al(7) is bonded to one O(12), one O(2), one O(6), one O(7), one O(8), and one O(9) atom to form AlO6 octahedra that share corners with three equivalent Al(5)O4 tetrahedra, corners with three equivalent Al(8)O4 tetrahedra,  an edgeedge with one Al(10)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra,  an edgeedge with one Al(6)O6 octahedra,  an edgeedge with one Al(9)O6 octahedra, and  an edgeedge with one Al(4)O5 square pyramid. The Al(7)-O(12) bond length is 1.85 Å. The Al(7)-O(2) bond length is 2.02 Å. The Al(7)-O(6) bond length is 1.92 Å. The Al(7)-O(7) bond length is 1.95 Å. The Al(7)-O(8) bond length is 1.81 Å. The Al(7)-O(9) bond length is 1.82 Å. In the eighth Al site, Al(8) is bonded to one O(11), one O(2), one O(8), and one O(9) atom to form AlO4 tetrahedra that share  a cornercorner with one Al(10)O6 octahedra,  a cornercorner with one Al(6)O6 octahedra,  a cornercorner with one Al(9)O6 octahedra, corners with two equivalent Al(3)O6 octahedra, corners with three equivalent Al(7)O6 octahedra, and corners with two equivalent Al(4)O5 square pyramids. The corner-sharing octahedral tilt angles range from 51-59°. The Al(8)-O(11) bond length is 1.82 Å. The Al(8)-O(2) bond length is 1.80 Å. The Al(8)-O(8) bond length is 1.75 Å. The Al(8)-O(9) bond length is 1.74 Å. In the ninth Al site, Al(9) is bonded to one O(10), one O(11), one O(12), one O(13), one O(15), and one O(7) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(10)O6 octahedra, and edges with two equivalent Al(6)O6 octahedra. The Al(9)-O(10) bond length is 1.83 Å. The Al(9)-O(11) bond length is 1.95 Å. The Al(9)-O(12) bond length is 2.02 Å. The Al(9)-O(13) bond length is 1.89 Å. The Al(9)-O(15) bond length is 1.80 Å. The Al(9)-O(7) bond length is 1.96 Å. In the tenth Al site, Al(10) is bonded to one O(10), one O(11), one O(12), one O(13), one O(14), and one O(6) atom to form AlO6 octahedra that share corners with two equivalent Al(2)O5 square pyramids,  a cornercorner with one Al(1)O4 tetrahedra,  a cornercorner with one Al(8)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Al(7)O6 octahedra, edges with two equivalent Al(6)O6 octahedra, and edges with two equivalent Al(9)O6 octahedra. The Al(10)-O(10) bond length is 1.84 Å. The Al(10)-O(11) bond length is 1.92 Å. The Al(10)-O(12) bond length is 1.97 Å. The Al(10)-O(13) bond length is 1.87 Å. The Al(10)-O(14) bond length is 1.81 Å. The Al(10)-O(6) bond length is 1.98 Å. There are fifteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Al(1), one Al(2), and one Al(3) atom. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(4), one Al(7), and one Al(8) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Al(1), one Al(2), one Al(3), and one Al(4) atom. In the fourth O site, O(4) is bonded in a T-shaped geometry to one Al(1), one Al(3), and one Al(4) atom. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Al(3), one Al(4), and one Al(5) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Al(10), one Al(5), one Al(6), and one Al(7) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Al(5), one Al(6), one Al(7), and one Al(9) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Al(3), one Al(7), and one Al(8) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Al(4), one Al(7), and one Al(8) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(2), and one Al(9) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Al(10), one Al(6), one Al(8), and one Al(9) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Al(10), one Al(5), one Al(7), and one Al(9) atom. In the thirteenth O site, O(13) is bonded in a tetrahedral geometry to one Al(1), one Al(10), one Al(6), and one Al(9) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Al(10), one Al(2), and one Al(6) atom. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Al(2), one Al(6), and one Al(9) atom.