  Open, connected, saturated sets W without holonomy in codimension one
foliations play key roles as fundamental building blocks. Here, for the case of
foliated 3-manifolds, we produce a finite system of closed, convex,
non-overlapping polyhedral cones in the first cohomology of W with real
coefficients such that the isotopy classes of possible foliations of W without
holonomy, either dense leaved in W or proper, correspond one-to-one to the rays
in the interiors of these cones. This generalizes our classification of depth
one foliations to foliations of finite depth and more general foliations.
