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RhHg2 crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. Rh is bonded in a body-centered cubic geometry to eight equivalent Hg atoms. All Rh–Hg bond lengths are 2.79 Å. Hg is bonded in a 4-coordinate geometry to four equivalent Rh atoms.
RhHg3 is Uranium Silicide-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Rh is bonded to twelve Hg atoms to form RhHg12 cuboctahedra that share corners with four equivalent RhHg12 cuboctahedra, edges with eight equivalent RhHg12 cuboctahedra, edges with sixteen equivalent HgHg8Rh4 cuboctahedra, faces with four equivalent RhHg12 cuboctahedra, and faces with eight equivalent HgHg8Rh4 cuboctahedra. There are four shorter (2.94 Å) and eight longer (3.10 Å) Rh–Hg bond lengths. There are two inequivalent Hg sites. In the first Hg site, Hg is bonded to four equivalent Rh and eight Hg atoms to form HgHg8Rh4 cuboctahedra that share corners with twelve equivalent HgHg8Rh4 cuboctahedra, edges with eight equivalent RhHg12 cuboctahedra, edges with eight equivalent HgHg8Rh4 cuboctahedra, faces with four equivalent RhHg12 cuboctahedra, and faces with ten equivalent HgHg8Rh4 cuboctahedra. There are four shorter (2.94 Å) and four longer (3.10 Å) Hg–Hg bond lengths. In the second Hg site, Hg is bonded in a distorted square co-planar geometry to four equivalent Rh and eight equivalent Hg atoms.
RhHg3 is beta Cu3Ti-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Rh is bonded to twelve equivalent Hg atoms to form RhHg12 cuboctahedra that share corners with six equivalent RhHg12 cuboctahedra, corners with twelve equivalent HgHg8Rh4 cuboctahedra, edges with eighteen equivalent HgHg8Rh4 cuboctahedra, faces with eight equivalent RhHg12 cuboctahedra, and faces with twelve equivalent HgHg8Rh4 cuboctahedra. There are six shorter (3.01 Å) and six longer (3.05 Å) Rh–Hg bond lengths. Hg is bonded to four equivalent Rh and eight equivalent Hg atoms to form distorted HgHg8Rh4 cuboctahedra that share corners with four equivalent RhHg12 cuboctahedra, corners with fourteen equivalent HgHg8Rh4 cuboctahedra, edges with six equivalent RhHg12 cuboctahedra, edges with twelve equivalent HgHg8Rh4 cuboctahedra, faces with four equivalent RhHg12 cuboctahedra, and faces with sixteen equivalent HgHg8Rh4 cuboctahedra. There are a spread of Hg–Hg bond distances ranging from 2.93–3.10 Å.