Lu5Co19P12 crystallizes in the hexagonal P-62m space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 15-coordinate geometry to three equivalent Co(1), six equivalent Co(3), and six equivalent P(2) atoms. In the second Lu site, Lu(2) is bonded in a 16-coordinate geometry to two equivalent Co(3), two equivalent Co(4), two equivalent Co(5), four equivalent Co(1), two equivalent P(1), and four equivalent P(3) atoms. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to one Lu(1), two equivalent Lu(2), one P(1), one P(3), and two equivalent P(2) atoms to form distorted CoLu3P4 tetrahedra that share corners with two equivalent Co(4)Lu2P4 tetrahedra, corners with two equivalent Co(3)Lu3P4 tetrahedra, corners with five equivalent Co(1)Lu3P4 tetrahedra, edges with two equivalent Co(1)Lu3P4 tetrahedra, edges with four equivalent Co(3)Lu3P4 tetrahedra,  a faceface with one Co(1)Lu3P4 tetrahedra, faces with two equivalent Co(4)Lu2P4 tetrahedra, and faces with two equivalent Co(3)Lu3P4 tetrahedra. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one P(1) and four equivalent P(2) atoms. In the third Co site, Co(3) is bonded to one Lu(2), two equivalent Lu(1), two equivalent P(1), and two equivalent P(2) atoms to form distorted CoLu3P4 tetrahedra that share corners with two equivalent Co(4)Lu2P4 tetrahedra, corners with two equivalent Co(1)Lu3P4 tetrahedra, corners with six equivalent Co(3)Lu3P4 tetrahedra,  an edgeedge with one Co(4)Lu2P4 tetrahedra, edges with two equivalent Co(3)Lu3P4 tetrahedra, edges with four equivalent Co(1)Lu3P4 tetrahedra, faces with two equivalent Co(1)Lu3P4 tetrahedra, and faces with three equivalent Co(3)Lu3P4 tetrahedra. In the fourth Co site, Co(4) is bonded to two equivalent Lu(2), two equivalent P(2), and two equivalent P(3) atoms to form distorted CoLu2P4 tetrahedra that share corners with four equivalent Co(4)Lu2P4 tetrahedra, corners with four equivalent Co(1)Lu3P4 tetrahedra, corners with four equivalent Co(3)Lu3P4 tetrahedra, edges with two equivalent Co(3)Lu3P4 tetrahedra, and faces with four equivalent Co(1)Lu3P4 tetrahedra. In the fifth Co site, Co(5) is bonded in a distorted trigonal planar geometry to six equivalent Lu(2) and three equivalent P(3) atoms. There are three inequivalent P sites. In the first P site, P(3) is bonded in a 9-coordinate geometry to four equivalent Lu(2), one Co(5), two equivalent Co(1), and two equivalent Co(4) atoms. In the second P site, P(1) is bonded in a 9-coordinate geometry to two equivalent Lu(2), one Co(2), two equivalent Co(1), and four equivalent Co(3) atoms. In the third P site, P(2) is bonded in a 9-coordinate geometry to two equivalent Lu(1), one Co(4), two equivalent Co(1), two equivalent Co(2), and two equivalent Co(3) atoms.
Lu5Co19P12 crystallizes in the hexagonal P-62m space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 15-coordinate geometry to three equivalent Co(1), six equivalent Co(3), and six equivalent P(2) atoms. All Lu(1)-Co(1) bond lengths are 2.96 Å. All Lu(1)-Co(3) bond lengths are 2.94 Å. All Lu(1)-P(2) bond lengths are 2.76 Å. In the second Lu site, Lu(2) is bonded in a 16-coordinate geometry to two equivalent Co(3), two equivalent Co(4), two equivalent Co(5), four equivalent Co(1), two equivalent P(1), and four equivalent P(3) atoms. Both Lu(2)-Co(3) bond lengths are 3.04 Å. Both Lu(2)-Co(4) bond lengths are 2.96 Å. Both Lu(2)-Co(5) bond lengths are 2.86 Å. All Lu(2)-Co(1) bond lengths are 2.93 Å. Both Lu(2)-P(1) bond lengths are 2.79 Å. All Lu(2)-P(3) bond lengths are 2.82 Å. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to one Lu(1), two equivalent Lu(2), one P(1), one P(3), and two equivalent P(2) atoms to form distorted CoLu3P4 tetrahedra that share corners with two equivalent Co(4)Lu2P4 tetrahedra, corners with two equivalent Co(3)Lu3P4 tetrahedra, corners with five equivalent Co(1)Lu3P4 tetrahedra, edges with two equivalent Co(1)Lu3P4 tetrahedra, edges with four equivalent Co(3)Lu3P4 tetrahedra,  a faceface with one Co(1)Lu3P4 tetrahedra, faces with two equivalent Co(4)Lu2P4 tetrahedra, and faces with two equivalent Co(3)Lu3P4 tetrahedra. The Co(1)-P(1) bond length is 2.29 Å. The Co(1)-P(3) bond length is 2.23 Å. Both Co(1)-P(2) bond lengths are 2.23 Å. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one P(1) and four equivalent P(2) atoms. The Co(2)-P(1) bond length is 2.21 Å. All Co(2)-P(2) bond lengths are 2.56 Å. In the third Co site, Co(3) is bonded to one Lu(2), two equivalent Lu(1), two equivalent P(1), and two equivalent P(2) atoms to form distorted CoLu3P4 tetrahedra that share corners with two equivalent Co(4)Lu2P4 tetrahedra, corners with two equivalent Co(1)Lu3P4 tetrahedra, corners with six equivalent Co(3)Lu3P4 tetrahedra,  an edgeedge with one Co(4)Lu2P4 tetrahedra, edges with two equivalent Co(3)Lu3P4 tetrahedra, edges with four equivalent Co(1)Lu3P4 tetrahedra, faces with two equivalent Co(1)Lu3P4 tetrahedra, and faces with three equivalent Co(3)Lu3P4 tetrahedra. Both Co(3)-P(1) bond lengths are 2.32 Å. There is one shorter (2.18 Å) and one longer (2.24 Å) Co(3)-P(2) bond length. In the fourth Co site, Co(4) is bonded to two equivalent Lu(2), two equivalent P(2), and two equivalent P(3) atoms to form distorted CoLu2P4 tetrahedra that share corners with four equivalent Co(4)Lu2P4 tetrahedra, corners with four equivalent Co(1)Lu3P4 tetrahedra, corners with four equivalent Co(3)Lu3P4 tetrahedra, edges with two equivalent Co(3)Lu3P4 tetrahedra, and faces with four equivalent Co(1)Lu3P4 tetrahedra. Both Co(4)-P(2) bond lengths are 2.17 Å. Both Co(4)-P(3) bond lengths are 2.20 Å. In the fifth Co site, Co(5) is bonded in a distorted trigonal planar geometry to six equivalent Lu(2) and three equivalent P(3) atoms. All Co(5)-P(3) bond lengths are 2.11 Å. There are three inequivalent P sites. In the first P site, P(3) is bonded in a 9-coordinate geometry to four equivalent Lu(2), one Co(5), two equivalent Co(1), and two equivalent Co(4) atoms. In the second P site, P(1) is bonded in a 9-coordinate geometry to two equivalent Lu(2), one Co(2), two equivalent Co(1), and four equivalent Co(3) atoms. In the third P site, P(2) is bonded in a 9-coordinate geometry to two equivalent Lu(1), one Co(4), two equivalent Co(1), two equivalent Co(2), and two equivalent Co(3) atoms.