Local field enhancements produced by metal nanoparticles have been widely investigated in the visible range for common metals like gold and silver, but recent interest in ultraviolet plasmonics has required consideration of alternate metals. Aluminum and gallium are particularly attractive, but the native oxide that forms on them consumes the metal in the smallest nanoparticles and limits the usefulness of larger nanoparticles for applications that require contact with a bare metal surface. The widely used catalyst rhodium is a noble metal that forms no native oxide under normal atmospheric conditions and has recently been shown to exhibit UV plasmonic behavior. Here we analyze the plasmonic properties of the most easily synthesized rhodium nanoparticle shapes and sizes and compare them to other UV plasmonic metals. Of particular interest is the tripod star monomer and dimer, for which we show the dependence of the absorption cross-section and the local electric field intensity on the constituent size and shape of tripod arms, and the gap distance in dimers, in representative dielectric hosts. It is shown that rhodium nanoparticles are particularly compelling for UV plasmonic applications requiring nanoparticles smaller than 20 nm. (Figure Presented).