  We show a duality which arises from distributions of Cartan type, having
growth (2, 3, 5), from the view point of geometric control theory. In fact we
consider the space of singular (or abnormal) paths on a given five dimensional
space endowed with a Cartan distribution, which form another five dimensional
space with a cone structure. We regard the cone structure as a control system
and show that the space of singular paths of the cone structure is naturally
identified with the original space. Moreover we observe an asymmetry on this
duality in terms of singular paths.
