Pfaffian systems from twistor fibrations

Canonical twistor fibrations lead to Pfaffian systems by means of their superhorizontal distribution. The aim of this note is to identify explicitly the Pfaffian systems of five or less variables that arise in this way in terms of the classification given in [A. Awane, M. Goze, Pfaffian Systems, k-Symplectic Systems, Kluwer Academic Publishers, Dordrecht, ISBN 0-7923-6373-6, 2000].