Yb4ZrCo33 crystallizes in the trigonal P3m1 space group. There are four inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 20-coordinate geometry to one Zr(1), one Co(11), three equivalent Co(1), three equivalent Co(4), three equivalent Co(5), three equivalent Co(6), and six equivalent Co(8) atoms. In the second Yb site, Yb(2) is bonded in a 20-coordinate geometry to one Co(10), one Co(9), three equivalent Co(2), three equivalent Co(3), three equivalent Co(5), three equivalent Co(6), and six equivalent Co(7) atoms. In the third Yb site, Yb(3) is bonded in a 18-coordinate geometry to three equivalent Co(1), three equivalent Co(2), three equivalent Co(3), three equivalent Co(4), and six equivalent Co(7) atoms. In the fourth Yb site, Yb(4) is bonded in a 18-coordinate geometry to three equivalent Co(1), three equivalent Co(2), three equivalent Co(3), three equivalent Co(4), and six equivalent Co(8) atoms. Zr(1) is bonded in a 14-coordinate geometry to one Yb(1), one Co(11), three equivalent Co(1), three equivalent Co(5), and six equivalent Co(7) atoms. There are eleven inequivalent Co sites. In the first Co site, Co(1) is bonded to one Yb(1), one Yb(3), one Yb(4), one Zr(1), two equivalent Co(2), two equivalent Co(5), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3ZrCo8 cuboctahedra that share corners with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(6)Yb2Co10 cuboctahedra, corners with six equivalent Co(4)Yb3Co9 cuboctahedra,  an edgeedge with one Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(2)Yb3Co9 cuboctahedra, edges with two equivalent Co(6)Yb2Co10 cuboctahedra, edges with four equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(1)Yb3ZrCo8 cuboctahedra. In the second Co site, Co(9) is bonded in a 14-coordinate geometry to one Yb(2), one Co(10), three equivalent Co(2), three equivalent Co(5), and six equivalent Co(8) atoms. In the third Co site, Co(10) is bonded in a 14-coordinate geometry to one Yb(2), one Co(9), three equivalent Co(3), three equivalent Co(6), and six equivalent Co(8) atoms. In the fourth Co site, Co(2) is bonded to one Yb(2), one Yb(3), one Yb(4), one Co(9), two equivalent Co(1), two equivalent Co(5), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3Co9 cuboctahedra that share corners with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(6)Yb2Co10 cuboctahedra, corners with six equivalent Co(3)Yb3Co9 cuboctahedra,  an edgeedge with one Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(1)Yb3ZrCo8 cuboctahedra, edges with two equivalent Co(6)Yb2Co10 cuboctahedra, edges with four equivalent Co(4)Yb3Co9 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(2)Yb3Co9 cuboctahedra. In the fifth Co site, Co(11) is bonded in a distorted linear geometry to one Yb(1), one Zr(1), three equivalent Co(4), three equivalent Co(6), and six equivalent Co(7) atoms. In the sixth Co site, Co(3) is bonded to one Yb(2), one Yb(3), one Yb(4), one Co(10), two equivalent Co(4), two equivalent Co(6), two equivalent Co(7), and two equivalent Co(8) atoms to form CoYb3Co9 cuboctahedra that share corners with two equivalent Co(6)Yb2Co10 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with six equivalent Co(2)Yb3Co9 cuboctahedra,  an edgeedge with one Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(4)Yb3Co9 cuboctahedra, edges with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, edges with four equivalent Co(1)Yb3ZrCo8 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(3)Yb3Co9 cuboctahedra. In the seventh Co site, Co(4) is bonded to one Yb(1), one Yb(3), one Yb(4), one Co(11), two equivalent Co(3), two equivalent Co(6), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3Co9 cuboctahedra that share corners with two equivalent Co(6)Yb2Co10 cuboctahedra, corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with six equivalent Co(1)Yb3ZrCo8 cuboctahedra,  an edgeedge with one Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(3)Yb3Co9 cuboctahedra, edges with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, edges with four equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(4)Yb3Co9 cuboctahedra. In the eighth Co site, Co(5) is bonded to one Yb(1), one Yb(2), one Zr(1), one Co(9), two equivalent Co(1), two equivalent Co(2), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb2ZrCo9 cuboctahedra that share corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(4)Yb3Co9 cuboctahedra, corners with four equivalent Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(2)Yb3Co9 cuboctahedra,  an edgeedge with one Co(1)Yb3ZrCo8 cuboctahedra, edges with two equivalent Co(3)Yb3Co9 cuboctahedra, edges with two equivalent Co(4)Yb3Co9 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(5)Yb2ZrCo9 cuboctahedra. In the ninth Co site, Co(6) is bonded to one Yb(1), one Yb(2), one Co(10), one Co(11), two equivalent Co(3), two equivalent Co(4), two equivalent Co(7), and two equivalent Co(8) atoms to form CoYb2Co10 cuboctahedra that share corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with three equivalent Co(2)Yb3Co9 cuboctahedra, corners with three equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with four equivalent Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(3)Yb3Co9 cuboctahedra,  an edgeedge with one Co(4)Yb3Co9 cuboctahedra, edges with two equivalent Co(2)Yb3Co9 cuboctahedra, edges with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(6)Yb2Co10 cuboctahedra. In the tenth Co site, Co(7) is bonded in a 12-coordinate geometry to one Yb(2), one Yb(3), one Zr(1), one Co(1), one Co(11), one Co(2), one Co(3), one Co(4), one Co(5), one Co(6), and two equivalent Co(7) atoms. In the eleventh Co site, Co(8) is bonded in a 12-coordinate geometry to one Yb(1), one Yb(4), one Co(1), one Co(10), one Co(2), one Co(3), one Co(4), one Co(5), one Co(6), one Co(9), and two equivalent Co(8) atoms.
Yb4ZrCo33 crystallizes in the trigonal P3m1 space group. There are four inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 20-coordinate geometry to one Zr(1), one Co(11), three equivalent Co(1), three equivalent Co(4), three equivalent Co(5), three equivalent Co(6), and six equivalent Co(8) atoms. The Yb(1)-Zr(1) bond length is 3.05 Å. The Yb(1)-Co(11) bond length is 2.67 Å. All Yb(1)-Co(1) bond lengths are 3.14 Å. All Yb(1)-Co(4) bond lengths are 3.00 Å. All Yb(1)-Co(5) bond lengths are 3.27 Å. All Yb(1)-Co(6) bond lengths are 3.10 Å. All Yb(1)-Co(8) bond lengths are 2.99 Å. In the second Yb site, Yb(2) is bonded in a 20-coordinate geometry to one Co(10), one Co(9), three equivalent Co(2), three equivalent Co(3), three equivalent Co(5), three equivalent Co(6), and six equivalent Co(7) atoms. The Yb(2)-Co(10) bond length is 2.90 Å. The Yb(2)-Co(9) bond length is 2.95 Å. All Yb(2)-Co(2) bond lengths are 3.06 Å. All Yb(2)-Co(3) bond lengths are 3.06 Å. All Yb(2)-Co(5) bond lengths are 3.09 Å. All Yb(2)-Co(6) bond lengths are 3.14 Å. All Yb(2)-Co(7) bond lengths are 2.95 Å. In the third Yb site, Yb(3) is bonded in a 18-coordinate geometry to three equivalent Co(1), three equivalent Co(2), three equivalent Co(3), three equivalent Co(4), and six equivalent Co(7) atoms. All Yb(3)-Co(1) bond lengths are 3.24 Å. All Yb(3)-Co(2) bond lengths are 3.06 Å. All Yb(3)-Co(3) bond lengths are 3.07 Å. All Yb(3)-Co(4) bond lengths are 3.23 Å. All Yb(3)-Co(7) bond lengths are 2.88 Å. In the fourth Yb site, Yb(4) is bonded in a 18-coordinate geometry to three equivalent Co(1), three equivalent Co(2), three equivalent Co(3), three equivalent Co(4), and six equivalent Co(8) atoms. All Yb(4)-Co(1) bond lengths are 2.97 Å. All Yb(4)-Co(2) bond lengths are 3.26 Å. All Yb(4)-Co(3) bond lengths are 3.23 Å. All Yb(4)-Co(4) bond lengths are 3.04 Å. All Yb(4)-Co(8) bond lengths are 2.93 Å. Zr(1) is bonded in a 14-coordinate geometry to one Yb(1), one Co(11), three equivalent Co(1), three equivalent Co(5), and six equivalent Co(7) atoms. The Zr(1)-Co(11) bond length is 2.44 Å. All Zr(1)-Co(1) bond lengths are 2.71 Å. All Zr(1)-Co(5) bond lengths are 2.65 Å. All Zr(1)-Co(7) bond lengths are 2.75 Å. There are eleven inequivalent Co sites. In the first Co site, Co(1) is bonded to one Yb(1), one Yb(3), one Yb(4), one Zr(1), two equivalent Co(2), two equivalent Co(5), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3ZrCo8 cuboctahedra that share corners with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(6)Yb2Co10 cuboctahedra, corners with six equivalent Co(4)Yb3Co9 cuboctahedra,  an edgeedge with one Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(2)Yb3Co9 cuboctahedra, edges with two equivalent Co(6)Yb2Co10 cuboctahedra, edges with four equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(1)Yb3ZrCo8 cuboctahedra. Both Co(1)-Co(2) bond lengths are 2.39 Å. Both Co(1)-Co(5) bond lengths are 2.49 Å. Both Co(1)-Co(7) bond lengths are 2.58 Å. Both Co(1)-Co(8) bond lengths are 2.52 Å. In the second Co site, Co(9) is bonded in a 14-coordinate geometry to one Yb(2), one Co(10), three equivalent Co(2), three equivalent Co(5), and six equivalent Co(8) atoms. The Co(9)-Co(10) bond length is 2.31 Å. All Co(9)-Co(2) bond lengths are 2.62 Å. All Co(9)-Co(5) bond lengths are 2.48 Å. All Co(9)-Co(8) bond lengths are 2.68 Å. In the third Co site, Co(10) is bonded in a 14-coordinate geometry to one Yb(2), one Co(9), three equivalent Co(3), three equivalent Co(6), and six equivalent Co(8) atoms. All Co(10)-Co(3) bond lengths are 2.59 Å. All Co(10)-Co(6) bond lengths are 2.55 Å. All Co(10)-Co(8) bond lengths are 2.69 Å. In the fourth Co site, Co(2) is bonded to one Yb(2), one Yb(3), one Yb(4), one Co(9), two equivalent Co(1), two equivalent Co(5), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3Co9 cuboctahedra that share corners with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(6)Yb2Co10 cuboctahedra, corners with six equivalent Co(3)Yb3Co9 cuboctahedra,  an edgeedge with one Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(1)Yb3ZrCo8 cuboctahedra, edges with two equivalent Co(6)Yb2Co10 cuboctahedra, edges with four equivalent Co(4)Yb3Co9 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(2)Yb3Co9 cuboctahedra. Both Co(2)-Co(5) bond lengths are 2.37 Å. Both Co(2)-Co(7) bond lengths are 2.52 Å. Both Co(2)-Co(8) bond lengths are 2.51 Å. In the fifth Co site, Co(11) is bonded in a distorted linear geometry to one Yb(1), one Zr(1), three equivalent Co(4), three equivalent Co(6), and six equivalent Co(7) atoms. All Co(11)-Co(4) bond lengths are 2.56 Å. All Co(11)-Co(6) bond lengths are 2.51 Å. All Co(11)-Co(7) bond lengths are 2.82 Å. In the sixth Co site, Co(3) is bonded to one Yb(2), one Yb(3), one Yb(4), one Co(10), two equivalent Co(4), two equivalent Co(6), two equivalent Co(7), and two equivalent Co(8) atoms to form CoYb3Co9 cuboctahedra that share corners with two equivalent Co(6)Yb2Co10 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with six equivalent Co(2)Yb3Co9 cuboctahedra,  an edgeedge with one Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(4)Yb3Co9 cuboctahedra, edges with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, edges with four equivalent Co(1)Yb3ZrCo8 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(3)Yb3Co9 cuboctahedra. Both Co(3)-Co(4) bond lengths are 2.42 Å. Both Co(3)-Co(6) bond lengths are 2.40 Å. Both Co(3)-Co(7) bond lengths are 2.52 Å. Both Co(3)-Co(8) bond lengths are 2.49 Å. In the seventh Co site, Co(4) is bonded to one Yb(1), one Yb(3), one Yb(4), one Co(11), two equivalent Co(3), two equivalent Co(6), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb3Co9 cuboctahedra that share corners with two equivalent Co(6)Yb2Co10 cuboctahedra, corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(5)Yb2ZrCo9 cuboctahedra, corners with six equivalent Co(1)Yb3ZrCo8 cuboctahedra,  an edgeedge with one Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(3)Yb3Co9 cuboctahedra, edges with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, edges with four equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(4)Yb3Co9 cuboctahedra. Both Co(4)-Co(6) bond lengths are 2.41 Å. Both Co(4)-Co(7) bond lengths are 2.50 Å. Both Co(4)-Co(8) bond lengths are 2.57 Å. In the eighth Co site, Co(5) is bonded to one Yb(1), one Yb(2), one Zr(1), one Co(9), two equivalent Co(1), two equivalent Co(2), two equivalent Co(7), and two equivalent Co(8) atoms to form distorted CoYb2ZrCo9 cuboctahedra that share corners with two equivalent Co(2)Yb3Co9 cuboctahedra, corners with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with three equivalent Co(3)Yb3Co9 cuboctahedra, corners with three equivalent Co(4)Yb3Co9 cuboctahedra, corners with four equivalent Co(6)Yb2Co10 cuboctahedra,  an edgeedge with one Co(2)Yb3Co9 cuboctahedra,  an edgeedge with one Co(1)Yb3ZrCo8 cuboctahedra, edges with two equivalent Co(3)Yb3Co9 cuboctahedra, edges with two equivalent Co(4)Yb3Co9 cuboctahedra, faces with two equivalent Co(6)Yb2Co10 cuboctahedra, faces with two equivalent Co(2)Yb3Co9 cuboctahedra, faces with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, and faces with four equivalent Co(5)Yb2ZrCo9 cuboctahedra. Both Co(5)-Co(7) bond lengths are 2.45 Å. Both Co(5)-Co(8) bond lengths are 2.39 Å. In the ninth Co site, Co(6) is bonded to one Yb(1), one Yb(2), one Co(10), one Co(11), two equivalent Co(3), two equivalent Co(4), two equivalent Co(7), and two equivalent Co(8) atoms to form CoYb2Co10 cuboctahedra that share corners with two equivalent Co(3)Yb3Co9 cuboctahedra, corners with two equivalent Co(4)Yb3Co9 cuboctahedra, corners with three equivalent Co(2)Yb3Co9 cuboctahedra, corners with three equivalent Co(1)Yb3ZrCo8 cuboctahedra, corners with four equivalent Co(5)Yb2ZrCo9 cuboctahedra,  an edgeedge with one Co(3)Yb3Co9 cuboctahedra,  an edgeedge with one Co(4)Yb3Co9 cuboctahedra, edges with two equivalent Co(2)Yb3Co9 cuboctahedra, edges with two equivalent Co(1)Yb3ZrCo8 cuboctahedra, faces with two equivalent Co(5)Yb2ZrCo9 cuboctahedra, faces with two equivalent Co(3)Yb3Co9 cuboctahedra, faces with two equivalent Co(4)Yb3Co9 cuboctahedra, and faces with four equivalent Co(6)Yb2Co10 cuboctahedra. Both Co(6)-Co(7) bond lengths are 2.41 Å. Both Co(6)-Co(8) bond lengths are 2.42 Å. In the tenth Co site, Co(7) is bonded in a 12-coordinate geometry to one Yb(2), one Yb(3), one Zr(1), one Co(1), one Co(11), one Co(2), one Co(3), one Co(4), one Co(5), one Co(6), and two equivalent Co(7) atoms. There is one shorter (2.43 Å) and one longer (2.58 Å) Co(7)-Co(7) bond length. In the eleventh Co site, Co(8) is bonded in a 12-coordinate geometry to one Yb(1), one Yb(4), one Co(1), one Co(10), one Co(2), one Co(3), one Co(4), one Co(5), one Co(6), one Co(9), and two equivalent Co(8) atoms. There is one shorter (2.37 Å) and one longer (2.48 Å) Co(8)-Co(8) bond length.