Ordered phases of ABC star terpolymer melts are investigated using a generic reciprocal-space implementation of the self-consistent field theory (SCFT) of polymers. The most important feature of ABC star triblock terpolymers is that their three blocks are joined at one junction point. This distinct topology of ABC star terpolymers constraints the junction points in one-dimensional lines in an ordered phase, resulting novel microphase-separated morphologies such as tiling patterns. Two types of star triblock terpolymers, with symmetric and asymmetric interaction parameters, are studied in detail. A variety of tiling patterns in ABC star terpolymers have been predicted from the SCFT calculation and relevant phase diagrams have been constructed. The predicted phase transition sequences from the SCFT calculations are in qualitative agreement with experimental and Monte Carlo simulation results.