  We classify parallelizable noncommutative manifold structures on finite sets
of small size in the general formalism of framed quantum manifolds and
vielbeins introduced previously. The full moduli space is found for $\le 3$
points, and a restricted moduli space for 4 points. The topological part of the
moduli space is found for $\le 9$ points based on the known atlas of regular
graphs. We also discuss aspects of the quantum theory defined by functional
integration.
