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Using the finite-difference time-domain method, we show that the plasmons of a nanostar result from hybridization of plasmons of the core and tips of the nanoparticle. The nanostar core serves as a nanoscale antenna, dramatically increasing the excitation cross section and the electromagnetic field enhancements of the tip plasmons. Our analysis demonstrates that the plasmon hybridization picture can be combined with numerical approaches to interpret the physical origin of the plasmons of highly complex nanostructures.