  Thurston's fibered face theory allows us to partition the set of
pseudo-Anosov mapping classes on different compact oriented surfaces into
subclasses with related dynamical behavior. This is done via a correspondence
between the rational points on fibered faces in the first cohomology of a
hyperbolic 3-manifold and the monodromies of fibrations of the 3-manifold over
the circle. In this paper, we generalize examples of Penner, and define
quotient families of mapping classes. We show that these mapping classes
correspond to open linear sections of fibered faces. The construction gives a
simple way to produce families of pseudo-Anosov mapping classes with bounded
normalized dilatation and computable invariants, and gives concrete examples of
mapping classes associated to sequences of points tending to the interior and
to the boundary of fibered faces.
