  We study families of faces for convex semi-algebraic sets via the normal
cycle which is a semi-algebraic set similar to the conormal variety in
projective duality theory. We propose a convex algebraic notion of a "patch" --
a term recently coined by Ciripoi, Kaihnsa, L\"ohne, and Sturmfels as a tool
for approximating the convex hull of a semi-algebraic set. We discuss geometric
consequences, both for the semi-algebraic and convex geometry of the families
of faces, as well as variations of our definition and their consequences.
