Li3Bi(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(3), and two equivalent O(2) atoms to form LiO4 tetrahedra that share  a cornercorner with one Bi(1)O12 cuboctahedra,  a cornercorner with one Bi(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and corners with four equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 66°. In the second Li site, Li(2) is bonded in a distorted trigonal non-coplanar geometry to three equivalent O(1) and three equivalent O(2) atoms. In the third Li site, Li(3) is bonded in a 6-coordinate geometry to six equivalent O(3) atoms. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form distorted BiO12 cuboctahedra that share corners with six equivalent Bi(2)O6 octahedra, corners with six equivalent Li(1)O4 tetrahedra, and edges with six equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 41°. In the second Bi site, Bi(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted BiO6 octahedra that share corners with three equivalent Bi(1)O12 cuboctahedra, corners with three equivalent Li(1)O4 tetrahedra, and corners with six equivalent P(1)O4 tetrahedra. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share corners with two equivalent Bi(2)O6 octahedra, corners with four equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Bi(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 55-60°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Li(1), one Li(2), one Bi(2), and one P(1) atom. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), and one P(1) atom to form corner-sharing OLi3P tetrahedra. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Li(1), one Li(3), one Bi(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one Bi(1), one Bi(2), and one P(1) atom.
Li3Bi(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(3), and two equivalent O(2) atoms to form LiO4 tetrahedra that share  a cornercorner with one Bi(1)O12 cuboctahedra,  a cornercorner with one Bi(2)O6 octahedra, corners with two equivalent Li(1)O4 tetrahedra, and corners with four equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 66°. The Li(1)-O(1) bond length is 1.98 Å. The Li(1)-O(3) bond length is 1.91 Å. There is one shorter (2.07 Å) and one longer (2.09 Å) Li(1)-O(2) bond length. In the second Li site, Li(2) is bonded in a distorted trigonal non-coplanar geometry to three equivalent O(1) and three equivalent O(2) atoms. All Li(2)-O(1) bond lengths are 2.57 Å. All Li(2)-O(2) bond lengths are 1.95 Å. In the third Li site, Li(3) is bonded in a 6-coordinate geometry to six equivalent O(3) atoms. All Li(3)-O(3) bond lengths are 2.32 Å. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form distorted BiO12 cuboctahedra that share corners with six equivalent Bi(2)O6 octahedra, corners with six equivalent Li(1)O4 tetrahedra, and edges with six equivalent P(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 41°. All Bi(1)-O(3) bond lengths are 2.62 Å. All Bi(1)-O(4) bond lengths are 2.84 Å. In the second Bi site, Bi(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form distorted BiO6 octahedra that share corners with three equivalent Bi(1)O12 cuboctahedra, corners with three equivalent Li(1)O4 tetrahedra, and corners with six equivalent P(1)O4 tetrahedra. All Bi(2)-O(1) bond lengths are 2.34 Å. All Bi(2)-O(4) bond lengths are 2.43 Å. P(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form PO4 tetrahedra that share corners with two equivalent Bi(2)O6 octahedra, corners with four equivalent Li(1)O4 tetrahedra, and  an edgeedge with one Bi(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 55-60°. The P(1)-O(1) bond length is 1.58 Å. The P(1)-O(2) bond length is 1.54 Å. The P(1)-O(3) bond length is 1.55 Å. The P(1)-O(4) bond length is 1.55 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to one Li(1), one Li(2), one Bi(2), and one P(1) atom. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(1), and one P(1) atom to form corner-sharing OLi3P tetrahedra. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Li(1), one Li(3), one Bi(1), and one P(1) atom. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one Bi(1), one Bi(2), and one P(1) atom.