Precision mass measurements of neutron-rich rhodium isotopes have been performed at the JYFLTRAP Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line (IGISOL) facility. We report results on ground-and isomeric-state masses in 110,112,114,116,118 Rh and the very first mass measurement of 120 Rh. The isomeric states were separated and measured for the first time using the phase-imaging ion-cyclotron-resonance (PI-ICR) technique. For 112 Rh, we also report new half-lives for both the ground state and the isomer. The results are compared to theoretical predictions using the BSkG1 mass model and discussed in terms of triaxial deformation.