PtBi2 is a polymorphic system with interesting electronic properties. Here we report optimized crystal growth and structural characterization of pyrite-type and trigonal modification of PtBi2. Selected area electron diffraction, x-ray powder diffraction, and further Rietveld refinement confirms that trigonal PtBi2 crystallizes in the noncentrosymmetric P31m space group, and pyrite-type PtBi2 crystallizes in the Pa3¯ space group. A series of Pt1-xRhxBi2 samples was obtained for x=0,0.03,0.35 in the trigonal PtBi2 structure. These Pt1-xRhxBi2 compounds become superconducting where the critical temperature increases from Tc=600 mK for x=0 up to Tc=2.7 K for x=0.35. Furthermore, we calculate the electronic band structure using the obtained structure parameters. The calculated density of states shows a minimum for the stoichiometric compound at the Fermi level. These findings warrant further research using a broader array of experimental techniques, as well as on the effect of the substitution on the nontrivial band structure.