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Intersexuality is the state of a living thing of a gonochoristic species whose sex chromosomes, genitalia and/or secondary sex characteristics are determined to be neither exclusively male nor female. An organism with intersex may have biological characteristics of both the male and female sexes. 
Intersexuality is the word that medicine started to use around the fifties applied to human beings who cannot be classified as either male or female.
Intersexuality is also the word adopted by the identitary-political movement, surged at nineties, to criticize medical protocols in sex assignment and to claim the right to be heard in the construction of a new ones.