K3Lu(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to two equivalent O(2), two equivalent O(3), two equivalent O(4), and three equivalent O(1) atoms. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. In the third K site, K(3) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form KO12 cuboctahedra that share edges with six equivalent P(1)O4 tetrahedra and faces with two equivalent Lu(2)O6 octahedra. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra. In the second Lu site, Lu(2) is bonded to six equivalent O(3) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and faces with two equivalent K(3)O12 cuboctahedra. 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  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O6 octahedra, and  an edgeedge with one K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 5-31°. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted single-bond geometry to one K(2), one K(3), two equivalent K(1), and one P(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to three equivalent K(1), one Lu(1), and one P(1) atom. In the third O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(1), one Lu(1), and one P(1) atom. In the fourth O site, O(3) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(2), and one P(1) atom.
K3Lu(PO4)2 crystallizes in the trigonal P-3 space group. There are three inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to two equivalent O(2), two equivalent O(3), two equivalent O(4), and three equivalent O(1) atoms. There is one shorter (2.77 Å) and one longer (2.81 Å) K(1)-O(2) bond length. There is one shorter (2.78 Å) and one longer (2.89 Å) K(1)-O(3) bond length. There is one shorter (2.60 Å) and one longer (2.98 Å) K(1)-O(4) bond length. There are a spread of K(1)-O(1) bond distances ranging from 2.90-3.09 Å. In the second K site, K(2) is bonded in a 6-coordinate geometry to three equivalent O(2) and three equivalent O(4) atoms. All K(2)-O(2) bond lengths are 2.85 Å. All K(2)-O(4) bond lengths are 2.74 Å. In the third K site, K(3) is bonded to six equivalent O(3) and six equivalent O(4) atoms to form KO12 cuboctahedra that share edges with six equivalent P(1)O4 tetrahedra and faces with two equivalent Lu(2)O6 octahedra. All K(3)-O(3) bond lengths are 3.07 Å. All K(3)-O(4) bond lengths are 3.30 Å. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra. All Lu(1)-O(1) bond lengths are 2.15 Å. All Lu(1)-O(2) bond lengths are 2.19 Å. In the second Lu site, Lu(2) is bonded to six equivalent O(3) atoms to form LuO6 octahedra that share corners with six equivalent P(1)O4 tetrahedra and faces with two equivalent K(3)O12 cuboctahedra. All Lu(2)-O(3) bond lengths are 2.15 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  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O6 octahedra, and  an edgeedge with one K(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 5-31°. The P(1)-O(1) bond length is 1.55 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 1.51 Å. There are four inequivalent O sites. In the first O site, O(4) is bonded in a distorted single-bond geometry to one K(2), one K(3), two equivalent K(1), and one P(1) atom. In the second O site, O(1) is bonded in a distorted linear geometry to three equivalent K(1), one Lu(1), and one P(1) atom. In the third O site, O(2) is bonded in a 5-coordinate geometry to one K(2), two equivalent K(1), one Lu(1), and one P(1) atom. In the fourth O site, O(3) is bonded in a 2-coordinate geometry to one K(3), two equivalent K(1), one Lu(2), and one P(1) atom.