Th6Cd7 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the orthorhombic Pbam space group. There are three inequivalent Th sites. In the first Th site, Th(1) is bonded in a 15-coordinate geometry to one Th(1), two equivalent Th(2), four equivalent Th(3), one Cd(1), three equivalent Cd(2), and four equivalent Cd(3) atoms. In the second Th site, Th(2) is bonded in a 16-coordinate geometry to one Th(2), two equivalent Th(1), three equivalent Th(3), two equivalent Cd(1), two equivalent Cd(2), and six equivalent Cd(3) atoms. In the third Th site, Th(3) is bonded in a 7-coordinate geometry to one Th(3), three equivalent Th(2), four equivalent Th(1), two equivalent Cd(2), and four equivalent Cd(3) atoms. There are three inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to two equivalent Th(1), four equivalent Th(2), two equivalent Cd(2), and four equivalent Cd(3) atoms to form CdTh6Cd6 cuboctahedra that share corners with four equivalent Cd(3)Th7Cd5 cuboctahedra, corners with six equivalent Cd(2)Th7Cd5 cuboctahedra, edges with two equivalent Cd(1)Th6Cd6 cuboctahedra, faces with four equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with twelve equivalent Cd(3)Th7Cd5 cuboctahedra. In the second Cd site, Cd(2) is bonded to two equivalent Th(2), two equivalent Th(3), three equivalent Th(1), one Cd(1), and four equivalent Cd(3) atoms to form CdTh7Cd5 cuboctahedra that share corners with three equivalent Cd(1)Th6Cd6 cuboctahedra, corners with three equivalent Cd(2)Th7Cd5 cuboctahedra, corners with six equivalent Cd(3)Th7Cd5 cuboctahedra, edges with three equivalent Cd(2)Th7Cd5 cuboctahedra, faces with two equivalent Cd(1)Th6Cd6 cuboctahedra, faces with two equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with ten equivalent Cd(3)Th7Cd5 cuboctahedra. In the third Cd site, Cd(3) is bonded to two equivalent Th(1), two equivalent Th(3), three equivalent Th(2), one Cd(1), two equivalent Cd(2), and two equivalent Cd(3) atoms to form CdTh7Cd5 cuboctahedra that share  a cornercorner with one Cd(1)Th6Cd6 cuboctahedra, corners with three equivalent Cd(2)Th7Cd5 cuboctahedra, corners with nine equivalent Cd(3)Th7Cd5 cuboctahedra, edges with five equivalent Cd(3)Th7Cd5 cuboctahedra, faces with three equivalent Cd(1)Th6Cd6 cuboctahedra, faces with five equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with five equivalent Cd(3)Th7Cd5 cuboctahedra.
Th6Cd7 is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the orthorhombic Pbam space group. There are three inequivalent Th sites. In the first Th site, Th(1) is bonded in a 15-coordinate geometry to one Th(1), two equivalent Th(2), four equivalent Th(3), one Cd(1), three equivalent Cd(2), and four equivalent Cd(3) atoms. The Th(1)-Th(1) bond length is 3.24 Å. Both Th(1)-Th(2) bond lengths are 3.51 Å. There are two shorter (3.75 Å) and two longer (3.78 Å) Th(1)-Th(3) bond lengths. The Th(1)-Cd(1) bond length is 3.44 Å. There are a spread of Th(1)-Cd(2) bond distances ranging from 3.38-3.51 Å. All Th(1)-Cd(3) bond lengths are 3.57 Å. In the second Th site, Th(2) is bonded in a 16-coordinate geometry to one Th(2), two equivalent Th(1), three equivalent Th(3), two equivalent Cd(1), two equivalent Cd(2), and six equivalent Cd(3) atoms. The Th(2)-Th(2) bond length is 3.92 Å. There are a spread of Th(2)-Th(3) bond distances ranging from 3.52-3.82 Å. Both Th(2)-Cd(1) bond lengths are 3.59 Å. Both Th(2)-Cd(2) bond lengths are 3.61 Å. There are a spread of Th(2)-Cd(3) bond distances ranging from 3.44-3.66 Å. In the third Th site, Th(3) is bonded in a 7-coordinate geometry to one Th(3), three equivalent Th(2), four equivalent Th(1), two equivalent Cd(2), and four equivalent Cd(3) atoms. The Th(3)-Th(3) bond length is 3.12 Å. Both Th(3)-Cd(2) bond lengths are 3.38 Å. There are two shorter (3.33 Å) and two longer (3.37 Å) Th(3)-Cd(3) bond lengths. There are three inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to two equivalent Th(1), four equivalent Th(2), two equivalent Cd(2), and four equivalent Cd(3) atoms to form CdTh6Cd6 cuboctahedra that share corners with four equivalent Cd(3)Th7Cd5 cuboctahedra, corners with six equivalent Cd(2)Th7Cd5 cuboctahedra, edges with two equivalent Cd(1)Th6Cd6 cuboctahedra, faces with four equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with twelve equivalent Cd(3)Th7Cd5 cuboctahedra. Both Cd(1)-Cd(2) bond lengths are 3.04 Å. All Cd(1)-Cd(3) bond lengths are 3.00 Å. In the second Cd site, Cd(2) is bonded to two equivalent Th(2), two equivalent Th(3), three equivalent Th(1), one Cd(1), and four equivalent Cd(3) atoms to form CdTh7Cd5 cuboctahedra that share corners with three equivalent Cd(1)Th6Cd6 cuboctahedra, corners with three equivalent Cd(2)Th7Cd5 cuboctahedra, corners with six equivalent Cd(3)Th7Cd5 cuboctahedra, edges with three equivalent Cd(2)Th7Cd5 cuboctahedra, faces with two equivalent Cd(1)Th6Cd6 cuboctahedra, faces with two equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with ten equivalent Cd(3)Th7Cd5 cuboctahedra. There are two shorter (3.02 Å) and two longer (3.03 Å) Cd(2)-Cd(3) bond lengths. In the third Cd site, Cd(3) is bonded to two equivalent Th(1), two equivalent Th(3), three equivalent Th(2), one Cd(1), two equivalent Cd(2), and two equivalent Cd(3) atoms to form CdTh7Cd5 cuboctahedra that share  a cornercorner with one Cd(1)Th6Cd6 cuboctahedra, corners with three equivalent Cd(2)Th7Cd5 cuboctahedra, corners with nine equivalent Cd(3)Th7Cd5 cuboctahedra, edges with five equivalent Cd(3)Th7Cd5 cuboctahedra, faces with three equivalent Cd(1)Th6Cd6 cuboctahedra, faces with five equivalent Cd(2)Th7Cd5 cuboctahedra, and faces with five equivalent Cd(3)Th7Cd5 cuboctahedra. There is one shorter (2.95 Å) and one longer (3.08 Å) Cd(3)-Cd(3) bond length.