HfCoSi is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Hf(2), three equivalent Co(1), four equivalent Co(2), one Si(3), two equivalent Si(1), and two equivalent Si(2) atoms. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to three equivalent Hf(1), two equivalent Co(2), three equivalent Co(1), one Si(1), two equivalent Si(3), and four equivalent Si(2) atoms. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three equivalent Hf(1), three equivalent Hf(2), two equivalent Co(2), one Si(1), one Si(3), and two equivalent Si(2) atoms to form distorted CoHf6Co2Si4 cuboctahedra that share corners with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with two equivalent Si(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, corners with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, faces with two equivalent Co(1)Hf6Co2Si4 cuboctahedra, faces with three equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with three equivalent Si(1)Hf6Co6 cuboctahedra, faces with six equivalent Co(2)Hf6Co4Si2 cuboctahedra, and faces with six equivalent Si(2)Hf6Co2Si4 cuboctahedra. In the second Co site, Co(2) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), two equivalent Co(2), and two equivalent Si(1) atoms to form distorted CoHf6Co4Si2 cuboctahedra that share corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, corners with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with six equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with two equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with two equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with four equivalent Si(1)Hf6Co6 cuboctahedra, and faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra. There are three inequivalent Si sites. In the first Si site, Si(1) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), and four equivalent Co(2) atoms to form SiHf6Co6 cuboctahedra that share corners with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(1)Hf6Co6 cuboctahedra, corners with eight equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with two equivalent Si(1)Hf6Co6 cuboctahedra, edges with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, and faces with eight equivalent Co(2)Hf6Co4Si2 cuboctahedra. In the second Si site, Si(2) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), two equivalent Si(2), and two equivalent Si(3) atoms to form distorted SiHf6Co2Si4 cuboctahedra that share corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(1)Hf6Co6 cuboctahedra, corners with six equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with two equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with two equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with two equivalent Si(1)Hf6Co6 cuboctahedra, faces with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, and faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra. In the third Si site, Si(3) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), and four equivalent Si(2) atoms to form SiHf6Co2Si4 cuboctahedra that share corners with two equivalent Si(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with eight equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, edges with four equivalent Si(1)Hf6Co6 cuboctahedra, faces with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, and faces with eight equivalent Si(2)Hf6Co2Si4 cuboctahedra.
HfCoSi is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Hf(2), three equivalent Co(1), four equivalent Co(2), one Si(3), two equivalent Si(1), and two equivalent Si(2) atoms. The Hf(1)-Hf(1) bond length is 2.87 Å. There is one shorter (2.95 Å) and two longer (3.04 Å) Hf(1)-Hf(2) bond lengths. There are two shorter (2.94 Å) and one longer (3.02 Å) Hf(1)-Co(1) bond length. There are two shorter (2.79 Å) and two longer (2.94 Å) Hf(1)-Co(2) bond lengths. The Hf(1)-Si(3) bond length is 2.90 Å. Both Hf(1)-Si(1) bond lengths are 2.91 Å. Both Hf(1)-Si(2) bond lengths are 2.89 Å. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to three equivalent Hf(1), two equivalent Co(2), three equivalent Co(1), one Si(1), two equivalent Si(3), and four equivalent Si(2) atoms. Both Hf(2)-Co(2) bond lengths are 2.72 Å. There is one shorter (2.77 Å) and two longer (2.93 Å) Hf(2)-Co(1) bond lengths. The Hf(2)-Si(1) bond length is 2.83 Å. Both Hf(2)-Si(3) bond lengths are 3.00 Å. There are two shorter (2.94 Å) and two longer (2.99 Å) Hf(2)-Si(2) bond lengths. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three equivalent Hf(1), three equivalent Hf(2), two equivalent Co(2), one Si(1), one Si(3), and two equivalent Si(2) atoms to form distorted CoHf6Co2Si4 cuboctahedra that share corners with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with two equivalent Si(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, corners with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, faces with two equivalent Co(1)Hf6Co2Si4 cuboctahedra, faces with three equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with three equivalent Si(1)Hf6Co6 cuboctahedra, faces with six equivalent Co(2)Hf6Co4Si2 cuboctahedra, and faces with six equivalent Si(2)Hf6Co2Si4 cuboctahedra. Both Co(1)-Co(2) bond lengths are 2.65 Å. The Co(1)-Si(1) bond length is 2.45 Å. The Co(1)-Si(3) bond length is 2.37 Å. Both Co(1)-Si(2) bond lengths are 2.32 Å. In the second Co site, Co(2) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), two equivalent Co(2), and two equivalent Si(1) atoms to form distorted CoHf6Co4Si2 cuboctahedra that share corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, corners with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with six equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with two equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with two equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with four equivalent Si(1)Hf6Co6 cuboctahedra, and faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra. There is one shorter (2.51 Å) and one longer (2.54 Å) Co(2)-Co(2) bond length. There is one shorter (2.42 Å) and one longer (2.53 Å) Co(2)-Si(1) bond length. There are three inequivalent Si sites. In the first Si site, Si(1) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), and four equivalent Co(2) atoms to form SiHf6Co6 cuboctahedra that share corners with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(1)Hf6Co6 cuboctahedra, corners with eight equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with two equivalent Si(1)Hf6Co6 cuboctahedra, edges with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, faces with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, and faces with eight equivalent Co(2)Hf6Co4Si2 cuboctahedra. In the second Si site, Si(2) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), two equivalent Si(2), and two equivalent Si(3) atoms to form distorted SiHf6Co2Si4 cuboctahedra that share corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(1)Hf6Co6 cuboctahedra, corners with six equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with two equivalent Si(2)Hf6Co2Si4 cuboctahedra, edges with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with two equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with two equivalent Si(1)Hf6Co6 cuboctahedra, faces with four equivalent Si(2)Hf6Co2Si4 cuboctahedra, faces with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, and faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra. There is one shorter (2.44 Å) and one longer (2.60 Å) Si(2)-Si(2) bond length. There is one shorter (2.43 Å) and one longer (2.52 Å) Si(2)-Si(3) bond length. In the third Si site, Si(3) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), and four equivalent Si(2) atoms to form SiHf6Co2Si4 cuboctahedra that share corners with two equivalent Si(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(1)Hf6Co2Si4 cuboctahedra, corners with four equivalent Si(3)Hf6Co2Si4 cuboctahedra, corners with eight equivalent Co(2)Hf6Co4Si2 cuboctahedra, edges with two equivalent Si(3)Hf6Co2Si4 cuboctahedra, edges with four equivalent Si(1)Hf6Co6 cuboctahedra, faces with four equivalent Co(2)Hf6Co4Si2 cuboctahedra, faces with six equivalent Co(1)Hf6Co2Si4 cuboctahedra, and faces with eight equivalent Si(2)Hf6Co2Si4 cuboctahedra.