  We study the link between a compact hypersurface in $\P^{n+1}$ and the set of
all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of
linear subspaces of codimension one by orthogonal complementarity. This gives
rise to a kind of duality which has already been studied Bruce and
Romerro-Fuster, and relates a hypersurface to the set of its tangent planes.
But in these papers the dual, in this sense, of the set of tangent planes of a
hypersurface was not defined and iteration of the procedure was not possible.
Therefore we extend this type of duality to more general sets and achieve a
procedure which can be iterated and gives in fact an involution.
