He-beam diffraction data evaluated for clean Rh(311) yield a best-fit corrugation, which shows a pronounced corrugation amplitude along the (100)-microfacets and a practically vanishing amplitude along the (111)-microfacets in agreement with expectation, but in contrast to Ni(311) where the reverse situation was found. Hydrogen adsorption leads to a sequence of c(1 x 1), c(1 x 3), p(1 x 1), c(1 x 3), and p(1 x 1)Rw phases. The fact that the c(1 x 1) phase was observed with He-diffraction, but not in previous LEED studies, again proves the exceptional sensitivity of He scattering for adsorbed hydrogen. Surface charge density calculations were performed to reproduce the shape and amplitude of the best-fit corrugation function of the c(1 x 1)H-phase. In this way we found that the H atoms occupy places between the topmost bridge sites and the adjacent threefold hollow sites on the (111)-microfacets; the H-Rh bond length amounts to 1.92 +/- 0.1 Angstrom.