Gd4Co3Ga16 crystallizes in the tetragonal P4/mmm space group. Gd(1) is bonded to two equivalent Ga(1); two equivalent Ga(2); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form GdGa12 cuboctahedra that share corners with eight equivalent Gd(1)Ga12 cuboctahedra, edges with two equivalent Ga(2)Gd4Ga8 cuboctahedra, faces with two equivalent Ga(2)Gd4Ga8 cuboctahedra, faces with five equivalent Gd(1)Ga12 cuboctahedra, and faces with two equivalent Co(1)Ga6 octahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent Ga(1) and four equivalent Ga(3) atoms to form CoGa6 octahedra that share corners with eight equivalent Ga(2)Gd4Ga8 cuboctahedra and faces with eight equivalent Gd(1)Ga12 cuboctahedra. In the second Co site, Co(2) is bonded in a body-centered cubic geometry to eight Ga(4,4,4,4,4,4) atoms. There are nine inequivalent Ga sites. In the first Ga site, Ga(1) is bonded in a 9-coordinate geometry to four equivalent Gd(1); one Co(1); and four Ga(4,4,4,4) atoms. In the second Ga site, Ga(2) is bonded to four equivalent Gd(1); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form distorted GaGd4Ga8 cuboctahedra that share corners with four equivalent Ga(2)Gd4Ga8 cuboctahedra, corners with four equivalent Co(1)Ga6 octahedra, edges with four equivalent Gd(1)Ga12 cuboctahedra,  a faceface with one Ga(2)Gd4Ga8 cuboctahedra, and faces with four equivalent Gd(1)Ga12 cuboctahedra. The corner-sharing octahedral tilt angles are 49°. In the third Ga site, Ga(3) is bonded in a 9-coordinate geometry to four equivalent Gd(1), one Co(1), two equivalent Ga(2), and two equivalent Ga(3) atoms. In the fourth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the fifth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the sixth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the seventh Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the eighth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. In the ninth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms.
Gd4Co3Ga16 crystallizes in the tetragonal P4/mmm space group. Gd(1) is bonded to two equivalent Ga(1); two equivalent Ga(2); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form GdGa12 cuboctahedra that share corners with eight equivalent Gd(1)Ga12 cuboctahedra, edges with two equivalent Ga(2)Gd4Ga8 cuboctahedra, faces with two equivalent Ga(2)Gd4Ga8 cuboctahedra, faces with five equivalent Gd(1)Ga12 cuboctahedra, and faces with two equivalent Co(1)Ga6 octahedra. Both Gd(1)-Ga(1) bond lengths are 3.01 Å. Both Gd(1)-Ga(2) bond lengths are 3.00 Å. All Gd(1)-Ga(3) bond lengths are 3.04 Å. All Gd(1)-Ga(4,4,4,4) bond lengths are 2.99 Å. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent Ga(1) and four equivalent Ga(3) atoms to form CoGa6 octahedra that share corners with eight equivalent Ga(2)Gd4Ga8 cuboctahedra and faces with eight equivalent Gd(1)Ga12 cuboctahedra. Both Co(1)-Ga(1) bond lengths are 2.42 Å. All Co(1)-Ga(3) bond lengths are 2.38 Å. In the second Co site, Co(2) is bonded in a body-centered cubic geometry to eight Ga(4,4,4,4,4,4) atoms. All Co(2)-Ga(4,4,4,4,4,4) bond lengths are 2.47 Å. There are nine inequivalent Ga sites. In the first Ga site, Ga(1) is bonded in a 9-coordinate geometry to four equivalent Gd(1); one Co(1); and four Ga(4,4,4,4) atoms. All Ga(1)-Ga(4,4,4,4) bond lengths are 2.80 Å. In the second Ga site, Ga(2) is bonded to four equivalent Gd(1); four equivalent Ga(3); and four Ga(4,4,4,4) atoms to form distorted GaGd4Ga8 cuboctahedra that share corners with four equivalent Ga(2)Gd4Ga8 cuboctahedra, corners with four equivalent Co(1)Ga6 octahedra, edges with four equivalent Gd(1)Ga12 cuboctahedra,  a faceface with one Ga(2)Gd4Ga8 cuboctahedra, and faces with four equivalent Gd(1)Ga12 cuboctahedra. The corner-sharing octahedral tilt angles are 49°. All Ga(2)-Ga(3) bond lengths are 2.83 Å. All Ga(2)-Ga(4,4,4,4) bond lengths are 3.00 Å. In the third Ga site, Ga(3) is bonded in a 9-coordinate geometry to four equivalent Gd(1), one Co(1), two equivalent Ga(2), and two equivalent Ga(3) atoms. Both Ga(3)-Ga(3) bond lengths are 2.63 Å. In the fourth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. The Ga(4)-Ga(1) bond length is 2.80 Å. There are a spread of Ga(4)-Ga(4,4,4) bond distances ranging from 2.52-3.01 Å. In the fifth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. The Ga(4)-Ga(1) bond length is 2.80 Å. There are a spread of Ga(4)-Ga(4,4,4) bond distances ranging from 2.52-3.01 Å. In the sixth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. There are a spread of Ga(4)-Ga(4,4,4) bond distances ranging from 2.52-3.01 Å. In the seventh Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. There are a spread of Ga(4)-Ga(4,4,4) bond distances ranging from 2.52-3.01 Å. In the eighth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. Both Ga(4)-Gd(1) bond lengths are 2.99 Å. The Ga(4)-Ga(2) bond length is 3.00 Å. In the ninth Ga site, Ga(4) is bonded in a 11-coordinate geometry to two equivalent Gd(1); two equivalent Co(2); one Ga(1); one Ga(2); and five Ga(4,4,4) atoms. Both Ga(4)-Gd(1) bond lengths are 2.99 Å. The Ga(4)-Ga(2) bond length is 3.00 Å.