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Optical phonon modes confined in nearly spherical InP quantum dots (QDs) prepared by colloidal synthesis were studied experimentally, by means of far-infrared (FIR) and Raman spectroscopy, and theoretically. Both FIR transmittance and Raman spectra contain some new features, compared to QDs of other polar semiconductor materials produced by the same technique. These peculiarities can be explained by the fact that there is a gap in the optical phonon band of bulk InP. Our calculations show that gap modes with angular momenta l>0 can appear in InP QDs when the high-frequency dielectric constant of the surrounding medium exceeds certain value. The gap modes are shown to determine the shape of the far-infrared and Raman spectra of the dots.