  This paper is motivated by the recent demonstration of three-wave mixing
based phononic frequency comb. While the previous experiments have shown the
existence of three-wave mixing pathway in a system of two-coupled phonon modes,
this work demonstrates a similar pathway in a system of three-coupled phonon
modes. The paper also presents a number of interesting experimental facts
concomitant to the three-mode three-wave mixing based frequency comb observed
in a specific micromechanical device. The experimental validation of three-mode
three-wave mixing along with the previous demonstration of two-mode three-wave
mixing points to the ultimate possibility of multimode frequency combs.
