HfZn22 crystallizes in the cubic Fd-3m space group. Hf(1) is bonded in a 16-coordinate geometry to four equivalent Zn(3) and twelve equivalent Zn(2) atoms. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Zn(4), four equivalent Zn(1), and six equivalent Zn(2) atoms to form distorted ZnZn12 cuboctahedra that share corners with two equivalent Zn(1)Zn12 cuboctahedra, corners with sixteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(4)Zn12 cuboctahedra, faces with two equivalent Zn(4)Zn12 cuboctahedra, faces with nine equivalent Zn(1)Zn12 cuboctahedra, and faces with fourteen equivalent Zn(2)HfZn11 cuboctahedra. In the second Zn site, Zn(3) is bonded in a 14-coordinate geometry to two equivalent Hf(1) and twelve equivalent Zn(2) atoms. In the third Zn site, Zn(4) is bonded to six equivalent Zn(1) and six equivalent Zn(2) atoms to form ZnZn12 cuboctahedra that share corners with six equivalent Zn(4)Zn12 cuboctahedra, edges with six equivalent Zn(1)Zn12 cuboctahedra, edges with eighteen equivalent Zn(2)HfZn11 cuboctahedra, faces with six equivalent Zn(2)HfZn11 cuboctahedra, and faces with six equivalent Zn(1)Zn12 cuboctahedra. In the fourth Zn site, Zn(2) is bonded to one Hf(1), one Zn(4), two equivalent Zn(3), three equivalent Zn(1), and five equivalent Zn(2) atoms to form ZnHfZn11 cuboctahedra that share corners with eight equivalent Zn(1)Zn12 cuboctahedra, corners with fifteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(2)HfZn11 cuboctahedra, edges with three equivalent Zn(4)Zn12 cuboctahedra,  a faceface with one Zn(4)Zn12 cuboctahedra, faces with seven equivalent Zn(1)Zn12 cuboctahedra, and faces with fifteen equivalent Zn(2)HfZn11 cuboctahedra.
HfZn22 crystallizes in the cubic Fd-3m space group. Hf(1) is bonded in a 16-coordinate geometry to four equivalent Zn(3) and twelve equivalent Zn(2) atoms. All Hf(1)-Zn(3) bond lengths are 3.01 Å. All Hf(1)-Zn(2) bond lengths are 2.97 Å. There are four inequivalent Zn sites. In the first Zn site, Zn(1) is bonded to two equivalent Zn(4), four equivalent Zn(1), and six equivalent Zn(2) atoms to form distorted ZnZn12 cuboctahedra that share corners with two equivalent Zn(1)Zn12 cuboctahedra, corners with sixteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(4)Zn12 cuboctahedra, faces with two equivalent Zn(4)Zn12 cuboctahedra, faces with nine equivalent Zn(1)Zn12 cuboctahedra, and faces with fourteen equivalent Zn(2)HfZn11 cuboctahedra. Both Zn(1)-Zn(4) bond lengths are 2.47 Å. All Zn(1)-Zn(1) bond lengths are 2.75 Å. There are two shorter (2.63 Å) and four longer (2.79 Å) Zn(1)-Zn(2) bond lengths. In the second Zn site, Zn(3) is bonded in a 14-coordinate geometry to two equivalent Hf(1) and twelve equivalent Zn(2) atoms. All Zn(3)-Zn(2) bond lengths are 2.92 Å. In the third Zn site, Zn(4) is bonded to six equivalent Zn(1) and six equivalent Zn(2) atoms to form ZnZn12 cuboctahedra that share corners with six equivalent Zn(4)Zn12 cuboctahedra, edges with six equivalent Zn(1)Zn12 cuboctahedra, edges with eighteen equivalent Zn(2)HfZn11 cuboctahedra, faces with six equivalent Zn(2)HfZn11 cuboctahedra, and faces with six equivalent Zn(1)Zn12 cuboctahedra. All Zn(4)-Zn(2) bond lengths are 2.80 Å. In the fourth Zn site, Zn(2) is bonded to one Hf(1), one Zn(4), two equivalent Zn(3), three equivalent Zn(1), and five equivalent Zn(2) atoms to form ZnHfZn11 cuboctahedra that share corners with eight equivalent Zn(1)Zn12 cuboctahedra, corners with fifteen equivalent Zn(2)HfZn11 cuboctahedra, edges with two equivalent Zn(2)HfZn11 cuboctahedra, edges with three equivalent Zn(4)Zn12 cuboctahedra,  a faceface with one Zn(4)Zn12 cuboctahedra, faces with seven equivalent Zn(1)Zn12 cuboctahedra, and faces with fifteen equivalent Zn(2)HfZn11 cuboctahedra. There are a spread of Zn(2)-Zn(2) bond distances ranging from 2.48-2.91 Å.