Relatives of the quotient of the complex projective plane by the complex cojugation V.I.Arnold May 26, 1998 It is proved that the quotient space of the four-dimensional quaternionic projective space by the automorphism group of the quaternionic algebra becomes the 13-dimensional sphere when quotiented by the quaternionic conjugation. This fact and its various generalisations are proved using the results of the theory of hyperbolic partial differential equations, providing also the proof of the theorem (which was, it seems, known to L.S.Pontriagin already in the thirties) claiming that the quotient of the complex projective plane by the complex conjugation is the 4-sphere.