AgBi3S5 crystallizes in the monoclinic C2/m space group. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to two equivalent S(2) and four equivalent S(1) atoms to form AgS6 octahedra that share corners with two equivalent Bi(2)S6 octahedra, corners with four equivalent Bi(1)S5 square pyramids, edges with two equivalent Ag(1)S6 octahedra, and edges with six equivalent Bi(1)S5 square pyramids. The corner-sharing octahedral tilt angles are 54°. In the second Ag site, Ag(2) is bonded to two equivalent S(4) and four equivalent S(5) atoms to form AgS6 octahedra that share corners with four equivalent Bi(3)S6 octahedra, edges with two equivalent Ag(2)S6 octahedra, edges with four equivalent Bi(2)S6 octahedra, and edges with six equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles are 5°. There are three inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to two equivalent S(2) and three equivalent S(1) atoms to form BiS5 square pyramids that share corners with two equivalent Ag(1)S6 octahedra, corners with two equivalent Bi(2)S6 octahedra, edges with three equivalent Ag(1)S6 octahedra, and edges with four equivalent Bi(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 14-63°. In the second Bi site, Bi(2) is bonded to one S(2), one S(5), two equivalent S(3), and two equivalent S(4) atoms to form BiS6 octahedra that share  a cornercorner with one Ag(1)S6 octahedra, corners with three equivalent Bi(3)S6 octahedra, corners with two equivalent Bi(1)S5 square pyramids, edges with two equivalent Ag(2)S6 octahedra, edges with two equivalent Bi(2)S6 octahedra, and edges with three equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 7-54°. In the third Bi site, Bi(3) is bonded to one S(3), two equivalent S(4), and three equivalent S(5) atoms to form BiS6 octahedra that share corners with two equivalent Ag(2)S6 octahedra, corners with three equivalent Bi(2)S6 octahedra, edges with three equivalent Ag(2)S6 octahedra, edges with three equivalent Bi(2)S6 octahedra, and edges with four equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 5-15°. There are five inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Ag(1) and three equivalent Bi(1) atoms to form a mixture of corner and edge-sharing SAg2Bi3 square pyramids. In the second S site, S(2) is bonded in a distorted rectangular see-saw-like geometry to one Ag(1), one Bi(2), and two equivalent Bi(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Bi(3) and two equivalent Bi(2) atoms. In the fourth S site, S(4) is bonded to one Ag(2), two equivalent Bi(2), and two equivalent Bi(3) atoms to form SAgBi4 square pyramids that share corners with two equivalent S(5)Ag2Bi4 octahedra,  a cornercorner with one S(4)AgBi4 square pyramid, edges with five equivalent S(5)Ag2Bi4 octahedra, and edges with two equivalent S(4)AgBi4 square pyramids. The corner-sharing octahedral tilt angles are 9°. In the fifth S site, S(5) is bonded to two equivalent Ag(2), one Bi(2), and three equivalent Bi(3) atoms to form SAg2Bi4 octahedra that share corners with two equivalent S(5)Ag2Bi4 octahedra, corners with two equivalent S(4)AgBi4 square pyramids, edges with five equivalent S(5)Ag2Bi4 octahedra, and edges with five equivalent S(4)AgBi4 square pyramids. The corner-sharing octahedra are not tilted.
AgBi3S5 crystallizes in the monoclinic C2/m space group. There are two inequivalent Ag sites. In the first Ag site, Ag(1) is bonded to two equivalent S(2) and four equivalent S(1) atoms to form AgS6 octahedra that share corners with two equivalent Bi(2)S6 octahedra, corners with four equivalent Bi(1)S5 square pyramids, edges with two equivalent Ag(1)S6 octahedra, and edges with six equivalent Bi(1)S5 square pyramids. The corner-sharing octahedral tilt angles are 54°. Both Ag(1)-S(2) bond lengths are 2.56 Å. All Ag(1)-S(1) bond lengths are 2.89 Å. In the second Ag site, Ag(2) is bonded to two equivalent S(4) and four equivalent S(5) atoms to form AgS6 octahedra that share corners with four equivalent Bi(3)S6 octahedra, edges with two equivalent Ag(2)S6 octahedra, edges with four equivalent Bi(2)S6 octahedra, and edges with six equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles are 5°. Both Ag(2)-S(4) bond lengths are 2.55 Å. All Ag(2)-S(5) bond lengths are 3.02 Å. There are three inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to two equivalent S(2) and three equivalent S(1) atoms to form BiS5 square pyramids that share corners with two equivalent Ag(1)S6 octahedra, corners with two equivalent Bi(2)S6 octahedra, edges with three equivalent Ag(1)S6 octahedra, and edges with four equivalent Bi(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 14-63°. Both Bi(1)-S(2) bond lengths are 2.82 Å. There is one shorter (2.60 Å) and two longer (2.85 Å) Bi(1)-S(1) bond lengths. In the second Bi site, Bi(2) is bonded to one S(2), one S(5), two equivalent S(3), and two equivalent S(4) atoms to form BiS6 octahedra that share  a cornercorner with one Ag(1)S6 octahedra, corners with three equivalent Bi(3)S6 octahedra, corners with two equivalent Bi(1)S5 square pyramids, edges with two equivalent Ag(2)S6 octahedra, edges with two equivalent Bi(2)S6 octahedra, and edges with three equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 7-54°. The Bi(2)-S(2) bond length is 2.67 Å. The Bi(2)-S(5) bond length is 2.98 Å. Both Bi(2)-S(3) bond lengths are 2.78 Å. Both Bi(2)-S(4) bond lengths are 2.91 Å. In the third Bi site, Bi(3) is bonded to one S(3), two equivalent S(4), and three equivalent S(5) atoms to form BiS6 octahedra that share corners with two equivalent Ag(2)S6 octahedra, corners with three equivalent Bi(2)S6 octahedra, edges with three equivalent Ag(2)S6 octahedra, edges with three equivalent Bi(2)S6 octahedra, and edges with four equivalent Bi(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 5-15°. The Bi(3)-S(3) bond length is 2.73 Å. Both Bi(3)-S(4) bond lengths are 2.91 Å. There are two shorter (2.76 Å) and one longer (2.91 Å) Bi(3)-S(5) bond length. There are five inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Ag(1) and three equivalent Bi(1) atoms to form a mixture of corner and edge-sharing SAg2Bi3 square pyramids. In the second S site, S(2) is bonded in a distorted rectangular see-saw-like geometry to one Ag(1), one Bi(2), and two equivalent Bi(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Bi(3) and two equivalent Bi(2) atoms. In the fourth S site, S(4) is bonded to one Ag(2), two equivalent Bi(2), and two equivalent Bi(3) atoms to form SAgBi4 square pyramids that share corners with two equivalent S(5)Ag2Bi4 octahedra,  a cornercorner with one S(4)AgBi4 square pyramid, edges with five equivalent S(5)Ag2Bi4 octahedra, and edges with two equivalent S(4)AgBi4 square pyramids. The corner-sharing octahedral tilt angles are 9°. In the fifth S site, S(5) is bonded to two equivalent Ag(2), one Bi(2), and three equivalent Bi(3) atoms to form SAg2Bi4 octahedra that share corners with two equivalent S(5)Ag2Bi4 octahedra, corners with two equivalent S(4)AgBi4 square pyramids, edges with five equivalent S(5)Ag2Bi4 octahedra, and edges with five equivalent S(4)AgBi4 square pyramids. The corner-sharing octahedra are not tilted.