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A three-arm Michelson-Fabry-Pérot detector for gravitational waves is designed.It consists of three Michelson Fabry-Pérot interferometers,one for each pair of arms.The new detector can be used to confirm whether the gravitational waves are in general relativity polarization states and to set the strong constraints on non-GR gravitational wave polarization states.By the new detectors,the angular resolution of sources can be improved significantly.With the new detector,it is easier to search for and confirm a gravitational wave signal in the observation data.