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Explanation: "gyrocopter" is the same as "gyroplane" and "autogiro".
The Czech word is "vírník" (spelling according to Akademický slovník cizích slov, 2000), which is most general and most frequently used.
The loanwords in Czech are gyroplán, autogyra, but these are less frequent. I have seen even "gyroptera" and "gyroptéra", but cannot recommend that.