LuNi2Ga is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 12-coordinate geometry to three equivalent Ni(4) and nine equivalent Ga(1) atoms. In the second Lu site, Lu(2) is bonded in a 12-coordinate geometry to three equivalent Ni(3) and nine equivalent Ni(5) atoms. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent Ni(1), three equivalent Ni(2), six equivalent Ni(5), and six equivalent Ga(1) atoms. There are five inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the second Ni site, Ni(2) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. In the third Ni site, Ni(3) is bonded to six equivalent Lu(2) and six equivalent Ni(5) atoms to form NiLu6Ni6 cuboctahedra that share corners with twelve equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with six equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with eighteen equivalent Ni(5)Lu5Ni7 cuboctahedra. In the fourth Ni site, Ni(4) is bonded to six equivalent Lu(1) and six equivalent Ga(1) atoms to form NiLu6Ga6 cuboctahedra that share corners with twelve equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with six equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with eighteen equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. In the fifth Ni site, Ni(5) is bonded to two equivalent Lu(3), three equivalent Lu(2), one Ni(1), one Ni(2), one Ni(3), and four equivalent Ni(5) atoms to form NiLu5Ni7 cuboctahedra that share corners with two equivalent Ni(3)Lu6Ni6 cuboctahedra, corners with six equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, corners with nine equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ga(1)Lu5Ga4Ni3 cuboctahedra, faces with three equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with ten equivalent Ni(5)Lu5Ni7 cuboctahedra. Ga(1) is bonded to two equivalent Lu(3), three equivalent Lu(1), one Ni(1), one Ni(2), one Ni(4), and four equivalent Ga(1) atoms to form distorted GaLu5Ga4Ni3 cuboctahedra that share corners with two equivalent Ni(4)Lu6Ga6 cuboctahedra, corners with six equivalent Ni(5)Lu5Ni7 cuboctahedra, corners with nine equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ni(5)Lu5Ni7 cuboctahedra, faces with three equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with ten equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra.
LuNi2Ga is Frank-Kasper $\mu$ Phase-derived structured and crystallizes in the trigonal P-3m1 space group. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 12-coordinate geometry to three equivalent Ni(4) and nine equivalent Ga(1) atoms. All Lu(1)-Ni(4) bond lengths are 2.99 Å. There are six shorter (2.98 Å) and three longer (3.02 Å) Lu(1)-Ga(1) bond lengths. In the second Lu site, Lu(2) is bonded in a 12-coordinate geometry to three equivalent Ni(3) and nine equivalent Ni(5) atoms. All Lu(2)-Ni(3) bond lengths are 3.01 Å. There are six shorter (2.89 Å) and three longer (3.01 Å) Lu(2)-Ni(5) bond lengths. In the third Lu site, Lu(3) is bonded in a 6-coordinate geometry to three equivalent Ni(1), three equivalent Ni(2), six equivalent Ni(5), and six equivalent Ga(1) atoms. All Lu(3)-Ni(1) bond lengths are 2.94 Å. All Lu(3)-Ni(2) bond lengths are 2.94 Å. All Lu(3)-Ni(5) bond lengths are 3.18 Å. All Lu(3)-Ga(1) bond lengths are 3.27 Å. There are five inequivalent Ni sites. In the first Ni site, Ni(1) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. All Ni(1)-Ni(5) bond lengths are 2.44 Å. All Ni(1)-Ga(1) bond lengths are 2.47 Å. In the second Ni site, Ni(2) is bonded in a 9-coordinate geometry to three equivalent Lu(3), three equivalent Ni(5), and three equivalent Ga(1) atoms. All Ni(2)-Ni(5) bond lengths are 2.47 Å. All Ni(2)-Ga(1) bond lengths are 2.46 Å. In the third Ni site, Ni(3) is bonded to six equivalent Lu(2) and six equivalent Ni(5) atoms to form NiLu6Ni6 cuboctahedra that share corners with twelve equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with six equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with eighteen equivalent Ni(5)Lu5Ni7 cuboctahedra. All Ni(3)-Ni(5) bond lengths are 2.48 Å. In the fourth Ni site, Ni(4) is bonded to six equivalent Lu(1) and six equivalent Ga(1) atoms to form NiLu6Ga6 cuboctahedra that share corners with twelve equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with six equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with eighteen equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. All Ni(4)-Ga(1) bond lengths are 2.57 Å. In the fifth Ni site, Ni(5) is bonded to two equivalent Lu(3), three equivalent Lu(2), one Ni(1), one Ni(2), one Ni(3), and four equivalent Ni(5) atoms to form NiLu5Ni7 cuboctahedra that share corners with two equivalent Ni(3)Lu6Ni6 cuboctahedra, corners with six equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, corners with nine equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ga(1)Lu5Ga4Ni3 cuboctahedra, faces with three equivalent Ni(3)Lu6Ni6 cuboctahedra, and faces with ten equivalent Ni(5)Lu5Ni7 cuboctahedra. There are two shorter (2.53 Å) and two longer (2.56 Å) Ni(5)-Ni(5) bond lengths. Ga(1) is bonded to two equivalent Lu(3), three equivalent Lu(1), one Ni(1), one Ni(2), one Ni(4), and four equivalent Ga(1) atoms to form distorted GaLu5Ga4Ni3 cuboctahedra that share corners with two equivalent Ni(4)Lu6Ga6 cuboctahedra, corners with six equivalent Ni(5)Lu5Ni7 cuboctahedra, corners with nine equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra, edges with four equivalent Ni(5)Lu5Ni7 cuboctahedra, edges with four equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra,  a faceface with one Ni(5)Lu5Ni7 cuboctahedra, faces with three equivalent Ni(4)Lu6Ga6 cuboctahedra, and faces with ten equivalent Ga(1)Lu5Ga4Ni3 cuboctahedra. There are two shorter (2.54 Å) and two longer (2.56 Å) Ga(1)-Ga(1) bond lengths.