We present DFT calculations of the energetics of the elementary reaction steps in the dehydrogenation of CH4 to C on extended Rh(111) and Rh(211) surfaces. The results are compared to the energetics for the same reactions on a planar (111) surface and the edge atoms that are shared between two (111) facets of a nanorod model. The adsorption energies between comparable surfaces of the extended and nanorod models are very similar. Only C adsorbs significantly stronger on the planar surface of the nanorod model than on the extended (111) surface due to the involvement of more reactive edge atoms. Also, the reaction energies between the two types of surface models are very similar. The small differences in reaction and activation energies are largely due to small geometrical differences. In all cases, CH dissociation has the highest activation barrier. However, dissociative CH4 adsorption is rate controlling under typical steam reforming conditions because of the entropy loss associated with methane adsorption. The barrier for CH4 dissociation significantly decreases with a decrease of the coordination number of the surface metal atoms. Accordingly, the corrugated surfaces are predicted to be more reactive for methane dissociation than the planar ones.