Li3AlB2O6 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(2), one O(4), and two equivalent O(3) atoms to form LiO4 trigonal pyramids that share  a cornercorner with one Al(1)O4 tetrahedra, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Al(1)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. In the third Li site, Li(3) is bonded in a distorted trigonal non-coplanar geometry to one O(1), one O(4), and one O(6) atom. Al(1) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form AlO4 tetrahedra that share  a cornercorner with one Li(1)O4 trigonal pyramid and  an edgeedge with one Li(2)O4 trigonal pyramid. There are two inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(2), one O(3), and one O(6) atom. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(5) atom. There are six inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Li(3), one Al(1), and one B(2) atom. In the second O site, O(2) is bonded in a distorted trigonal pyramidal geometry to one Li(1), one Li(2), one Al(1), and one B(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Li(1), and one B(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(3), and one B(2) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Li(2), one Al(1), and one B(2) atom. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Li(3), one Al(1), and one B(1) atom.
Li3AlB2O6 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(2), one O(4), and two equivalent O(3) atoms to form LiO4 trigonal pyramids that share  a cornercorner with one Al(1)O4 tetrahedra, corners with two equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Li(1)O4 trigonal pyramid, and  an edgeedge with one Li(2)O4 trigonal pyramid. The Li(1)-O(2) bond length is 2.03 Å. The Li(1)-O(4) bond length is 1.98 Å. There is one shorter (1.95 Å) and one longer (2.06 Å) Li(1)-O(3) bond length. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(4), and one O(5) atom to form distorted LiO4 trigonal pyramids that share corners with two equivalent Li(1)O4 trigonal pyramids,  an edgeedge with one Al(1)O4 tetrahedra, and  an edgeedge with one Li(1)O4 trigonal pyramid. The Li(2)-O(2) bond length is 2.23 Å. The Li(2)-O(3) bond length is 1.90 Å. The Li(2)-O(4) bond length is 1.92 Å. The Li(2)-O(5) bond length is 1.98 Å. In the third Li site, Li(3) is bonded in a distorted trigonal non-coplanar geometry to one O(1), one O(4), and one O(6) atom. The Li(3)-O(1) bond length is 1.93 Å. The Li(3)-O(4) bond length is 1.92 Å. The Li(3)-O(6) bond length is 1.95 Å. Al(1) is bonded to one O(1), one O(2), one O(5), and one O(6) atom to form AlO4 tetrahedra that share  a cornercorner with one Li(1)O4 trigonal pyramid and  an edgeedge with one Li(2)O4 trigonal pyramid. The Al(1)-O(1) bond length is 1.77 Å. The Al(1)-O(2) bond length is 1.78 Å. The Al(1)-O(5) bond length is 1.80 Å. The Al(1)-O(6) bond length is 1.77 Å. There are two inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(2), one O(3), and one O(6) atom. The B(1)-O(2) bond length is 1.41 Å. The B(1)-O(3) bond length is 1.35 Å. The B(1)-O(6) bond length is 1.41 Å. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(5) atom. The B(2)-O(1) bond length is 1.40 Å. The B(2)-O(4) bond length is 1.36 Å. The B(2)-O(5) bond length is 1.41 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Li(3), one Al(1), and one B(2) atom. In the second O site, O(2) is bonded in a distorted trigonal pyramidal geometry to one Li(1), one Li(2), one Al(1), and one B(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Li(1), and one B(1) atom. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Li(2), one Li(3), and one B(2) atom. In the fifth O site, O(5) is bonded in a 3-coordinate geometry to one Li(2), one Al(1), and one B(2) atom. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Li(3), one Al(1), and one B(1) atom.