LuYGa6 crystallizes in the hexagonal P6_3/mmc space group. Lu(1) is bonded to six equivalent Ga(1) and six equivalent Ga(2) atoms to form LuGa12 cuboctahedra that share corners with six equivalent Lu(1)Ga12 cuboctahedra, corners with twelve equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, edges with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with two equivalent Lu(1)Ga12 cuboctahedra, faces with six equivalent Y(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. Y(1) is bonded to six equivalent Ga(1) and six equivalent Ga(2) atoms to form YGa12 cuboctahedra that share corners with twelve equivalent Y(1)Ga12 cuboctahedra, edges with twelve equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with six equivalent Lu(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. There are two inequivalent Ga sites. In the first Ga site, Ga(2) is bonded to two equivalent Lu(1), two equivalent Y(1), four equivalent Ga(1), and four equivalent Ga(2) atoms to form distorted GaY2Lu2Ga8 cuboctahedra that share corners with four equivalent Lu(1)Ga12 cuboctahedra, corners with fourteen equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, edges with two equivalent Lu(1)Ga12 cuboctahedra, edges with four equivalent Y(1)Ga12 cuboctahedra, edges with four equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with two equivalent Lu(1)Ga12 cuboctahedra, faces with two equivalent Y(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. In the second Ga site, Ga(1) is bonded in a 10-coordinate geometry to two equivalent Lu(1), two equivalent Y(1), two equivalent Ga(1), and four equivalent Ga(2) atoms.
LuYGa6 crystallizes in the hexagonal P6_3/mmc space group. Lu(1) is bonded to six equivalent Ga(1) and six equivalent Ga(2) atoms to form LuGa12 cuboctahedra that share corners with six equivalent Lu(1)Ga12 cuboctahedra, corners with twelve equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, edges with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with two equivalent Lu(1)Ga12 cuboctahedra, faces with six equivalent Y(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. All Lu(1)-Ga(1) bond lengths are 3.08 Å. All Lu(1)-Ga(2) bond lengths are 3.05 Å. Y(1) is bonded to six equivalent Ga(1) and six equivalent Ga(2) atoms to form YGa12 cuboctahedra that share corners with twelve equivalent Y(1)Ga12 cuboctahedra, edges with twelve equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with six equivalent Lu(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. All Y(1)-Ga(1) bond lengths are 3.06 Å. All Y(1)-Ga(2) bond lengths are 2.97 Å. There are two inequivalent Ga sites. In the first Ga site, Ga(2) is bonded to two equivalent Lu(1), two equivalent Y(1), four equivalent Ga(1), and four equivalent Ga(2) atoms to form distorted GaY2Lu2Ga8 cuboctahedra that share corners with four equivalent Lu(1)Ga12 cuboctahedra, corners with fourteen equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, edges with two equivalent Lu(1)Ga12 cuboctahedra, edges with four equivalent Y(1)Ga12 cuboctahedra, edges with four equivalent Ga(2)Y2Lu2Ga8 cuboctahedra, faces with two equivalent Lu(1)Ga12 cuboctahedra, faces with two equivalent Y(1)Ga12 cuboctahedra, and faces with six equivalent Ga(2)Y2Lu2Ga8 cuboctahedra. All Ga(2)-Ga(1) bond lengths are 2.92 Å. All Ga(2)-Ga(2) bond lengths are 3.05 Å. In the second Ga site, Ga(1) is bonded in a 10-coordinate geometry to two equivalent Lu(1), two equivalent Y(1), two equivalent Ga(1), and four equivalent Ga(2) atoms. Both Ga(1)-Ga(1) bond lengths are 2.74 Å.